Total and positronium formation cross sections for positron scattering from H2O and HCOOH
Identifieur interne : 001710 ( Istex/Corpus ); précédent : 001709; suivant : 001711Total and positronium formation cross sections for positron scattering from H2O and HCOOH
Auteurs : Casten Makochekanwa ; Ana Bankovic ; Wade Tattersall ; Adric Jones ; Peter Caradonna ; Daniel S. Slaughter ; Kate Nixon ; Michael J. Brunger ; Zoran Petrovic ; James P. Sullivan ; Stephen J. BuckmanSource :
- New Journal of Physics [ 1367-2630 ] ; 2009.
Abstract
Total and positronium formation cross sections have been measured for positron scattering from H2O and HCOOH using a positron beam with an energy resolution of 60meV (full-width at half-maximum (FWHM)). The energy range covered is 0.560eV, including an investigation of the behavior of the onset of the positronium formation channel using measurements with a 50meV energy step, the result of which shows no evidence of any channel coupling effects or scattering resonances for either molecule.
Url:
DOI: 10.1088/1367-2630/11/10/103036
Links to Exploration step
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<ccc>1367-2630/09/103036+22$30.00</ccc>
<printed></printed>
</article-data>
</article-metadata>
<header><title-group><title>Total and positronium formation cross sections for positron scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH</title>
<short-title>Positron Scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH</short-title>
<ej-title>Total and positronium formation cross sections for positron scattering from H2O and HCOOH</ej-title>
</title-group>
<author-group><author address="nj328064ad1" alt-address="nj328064aad5" email="nj328064ea1"><first-names>Casten</first-names>
<second-name>Makochekanwa</second-name>
</author>
<author address="nj328064ad2"><first-names>Ana</first-names>
<second-name>Bankovic</second-name>
</author>
<author address="nj328064ad1" second-address="nj328064ad3"><first-names>Wade</first-names>
<second-name>Tattersall</second-name>
</author>
<author address="nj328064ad1"><first-names>Adric</first-names>
<second-name>Jones</second-name>
</author>
<author address="nj328064ad1"><first-names>Peter</first-names>
<second-name>Caradonna</second-name>
</author>
<author address="nj328064ad1"><first-names>Daniel S</first-names>
<second-name>Slaughter</second-name>
</author>
<author address="nj328064ad4"><first-names>Kate</first-names>
<second-name>Nixon</second-name>
</author>
<author address="nj328064ad4"><first-names>Michael J</first-names>
<second-name>Brunger</second-name>
</author>
<author address="nj328064ad2"><first-names>Zoran</first-names>
<second-name>Petrovic</second-name>
</author>
<author address="nj328064ad1"><first-names>James P</first-names>
<second-name>Sullivan</second-name>
</author>
<author address="nj328064ad1"><first-names>Stephen J</first-names>
<second-name>Buckman</second-name>
</author>
<short-author-list>C Makochekanwa <italic>et al</italic>
</short-author-list>
</author-group>
<address-group><address id="nj328064ad1" showid="yes">ARC Centre for Antimatter-Matter Studies, Research School of Physics and Engineering, <orgname>Australian National University</orgname>
, Canberra, ACT 0200, <country>Australia</country>
</address>
<address id="nj328064ad2" showid="yes">Institute of Physics Belgrade, <orgname>University of Belgrade</orgname>
, Pregrevica 118, POB 68, 11080 Zemun, <country>Serbia</country>
</address>
<address id="nj328064ad3" showid="yes">ARC Centre for Antimatter-Matter Studies, <orgname>James Cook University</orgname>
, Townsville 4810, <country>Australia</country>
</address>
<address id="nj328064ad4" showid="yes">ARC Centre for Antimatter-Matter Studies, School of Chemistry, Physics and Earth Sciences, <orgname>Flinders University</orgname>
, GPO Box 2100, Adelaide, SA 5001, <country>Australia</country>
</address>
<address id="nj328064aad5" alt="yes" showid="yes">Author to whom any correspondence should be addressed.</address>
<e-address id="nj328064ea1"><email mailto="cxm107@physics.anu.edu.au">cxm107@physics.anu.edu.au</email>
(C Makochekanwa)</e-address>
</address-group>
<history received="12 August 2009" online="21 October 2009"></history>
<abstract-group><abstract><heading>Abstract</heading>
<p indent="no">Total and positronium formation cross sections have been measured for positron scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH using a positron beam with an energy resolution of 60 meV (full-width at half-maximum (FWHM)). The energy range covered is 0.5–60 eV, including an investigation of the behavior of the onset of the positronium formation channel using measurements with a 50 meV energy step, the result of which shows no evidence of any channel coupling effects or scattering resonances for either molecule.</p>
</abstract>
</abstract-group>
</header>
<body refstyle="numeric"><sec-level1 id="nj328064s1" label="1"><heading>Introduction</heading>
<p indent="no">The importance of ionizing radiation in biological molecules has become an area of intense interest of late. The most significant observation is that most of the energy deposited in cells by ionizing radiation is channeled into the production of free secondary electrons with energies below typically 20 eV. In addition, it has also been demonstrated that the subsequent reactions of such electrons, even at energies well below ionization thresholds, induce substantial yields of single- and double-strand breaks in DNA, through the process of dissociative electron attachment [<cite linkend="nj328064bib1">1</cite>
]. Positrons have also been recently highlighted [<cite linkend="nj328064bib2">2</cite>
] as a possible agent in the treatment of tumors—positherapy— and while there may be some similarities in the interaction mechanisms for positrons and electrons with molecules in the body, there are also many differences.</p>
<p>Water (<inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
) is present in the atmospheres of most planets of the solar system, as well as the Sun itself. It is also the third most abundant molecule in the Universe (after <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
</math-text>
</inline-eqn>
and CO) [<cite linkend="nj328064bib3">3</cite>
] and is regarded as the most important greenhouse gas in the terrestrial atmosphere [<cite linkend="nj328064bib4">4</cite>
], in the standard thermal balance of the atmosphere. It makes up the main constituent of all living organisms and provides the medium for most chemical and biochemical processes that take place therein [<cite linkend="nj328064bib5">5</cite>
]. Formic acid (HCOOH) is the simplest organic acid, and is thought to play a major role in the formation of some larger biomolecules such as glycine and acetic acid. In addition, the derivative formate group (–COOH) is a key component of more complex biomolecules including some of the amino acids and DNA bases [<cite linkend="nj328064bib6">6</cite>
].</p>
<p>The most notable use of positrons in the human context, however, is in positron emission tomography (PET) scans. This essentially non-invasive, medical diagnostic tool has become widely utilized in most major hospitals as an early detection mechanism for tumors, and a general diagnostic of metabolic activity. PET scans involve the release of a high-energy positron into the body, and the detection of the resultant gamma rays which arise upon annihilation with an electron. The processes that occur between the emission of the high-energy particle and the production of gamma rays, involve positron–molecule scattering, but as yet there is essentially no fundamental, quantitative knowledge of these interactions. For example, an understanding of the atomic and molecular processes that take place when a positron interacts with water or the DNA base molecules would be invaluable [<cite linkend="nj328064bib7">7</cite>
, <cite linkend="nj328064bib8">8</cite>
]. A knowledge of both integral and angular differential cross-sections underpins the understanding of the microscopic distribution of energy deposition which is needed for accurate dosimetry (see for example [<cite linkend="nj328064bib9">9</cite>
]). Furthermore, studies of positronium (Ps) formation, a critical reaction channel for PET, are likely to be critical in the development of such a dosimetry.</p>
<p>Following the important establishment of the effect of ionizing radiation to biological molecules reported by Boudaiffa <italic>et al</italic>
[<cite linkend="nj328064bib1">1</cite>
] in 2000, much experimental and theoretical activity has become focused on electron scattering from biomolecules, including <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH. The work on <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
has been well summarized in the review article by Itikawa and Mason [<cite linkend="nj328064bib5">5</cite>
], while the recent work on HCOOH is addressed by Zecca <italic>et al</italic>
[<cite linkend="nj328064bib6">6</cite>
] and references therein. While a considerable data library is now available for positron scattering from many atoms and molecules using moderate energy resolutions of a few hundred meV [<cite linkend="nj328064bib10">10</cite>
], data on positron scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH remain scarce and fragmentary, and mainly for grand total cross sections (GTCS).</p>
<p>Previous literature reports for experimental positron scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
are from the Yamaguchi group [<cite linkend="nj328064bib11">11</cite>
]–[<cite linkend="nj328064bib13">13</cite>
], who used a magnetically guided beam in a time-of-flight apparatus to measure GTCS over the energy range 1–400 eV, and the Trento group [<cite linkend="nj328064bib14">14</cite>
] who used an electrostatic and magnetic field experimental apparatus to measure GTCS over the energy range 0.1–20 eV. The group at University College London used a magnetically guided beam to measure GTCS (7–417 eV) [<cite linkend="nj328064bib15">15</cite>
] and Ps formation (10–100 eV) cross sections [<cite linkend="nj328064bib16">16</cite>
], and an electrostatic apparatus to study the energy distributions of positrons scattered at <inline-eqn><math-text>0°</math-text>
</inline-eqn>
from these molecules in coincidence with the remnant ions (<inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
<sup>+</sup>
</math-text>
</inline-eqn>
, <inline-eqn><math-text><upright>OH</upright>
<sup>+</sup>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><upright>H</upright>
<sup>+</sup>
</math-text>
</inline-eqn>
) at 100 and 153 eV incident energies [<cite linkend="nj328064bib17">17</cite>
]. As for the experimental literature on HCOOH, once again the only data are from the Yamaguchi [<cite linkend="nj328064bib13">13</cite>
] and Trento [<cite linkend="nj328064bib6">6</cite>
] groups, who both investigated GTCS over the energy ranges 0.7–600 and 0.3–50.2 eV, respectively. Theoretically, we are only aware of a few reports on positron–<inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
scattering, involving computations of positron annihilation rates, Ps formation, and elastic differential and integral cross sections. See for example Hervieux <italic>et al</italic>
[<cite linkend="nj328064bib18">18</cite>
] and Baluja <italic>et al</italic>
[<cite linkend="nj328064bib19">19</cite>
], and references therein. For positron–HCOOH, we are not aware of any other theoretical work besides the use of the Schwinger multichannel method to calculate elastic integral cross sections—jointly published with the experimental GTCS in [<cite linkend="nj328064bib6">6</cite>
].</p>
<p>In this paper, we report measurements of 0.5–60 eV GTCS and Ps formation cross sections (<inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
) for positron scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH. These measurements were carried out at the Australian Positron Beamline Facility [<cite linkend="nj328064bib20">20</cite>
], using an energy resolution of <inline-eqn><math-text>∼60 <upright>meV</upright>
</math-text>
</inline-eqn>
. Because of this superior energy resolution, we have also carried out high precision measurements to investigate threshold effects in the Ps formation and ionization channels, as well as a search for positron scattering resonances.</p>
</sec-level1>
<sec-level1 id="nj328064s2" label="2"><heading>Experimental procedure</heading>
<p indent="no">The experimental apparatus used for these measurements is based on the Surko trap system, developed at UCSD [<cite linkend="nj328064bib21">21</cite>
, <cite linkend="nj328064bib22">22</cite>
], and has been comprehensively described elsewhere [<cite linkend="nj328064bib20">20</cite>
]. Only a brief overview of the operation will be presented here. Positrons are obtained from a radioactive source of <inline-eqn><math-text><sup>22</sup>
<upright>Na</upright>
</math-text>
</inline-eqn>
, which had an activity of <inline-eqn><math-text>∼25 <upright>mCi</upright>
</math-text>
</inline-eqn>
for the measurements in this paper. A neon moderator is used to form a low energy positron beam with a measured energy width of <inline-eqn><math-text>∼1.5 <upright>eV</upright>
</math-text>
</inline-eqn>
. The moderated beam of positrons is confined radially using solenoidal magnetic fields and sent into a three-stage buffer-gas trap. The trap electrodes form a stepped electrostatic potential well, and positrons lose energy inside the trap through inelastic collisions with a mixture of <inline-eqn><math-text><upright>N</upright>
<sub>2</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><upright>CF</upright>
<sub>4</sub>
</math-text>
</inline-eqn>
buffer gases. They are thus confined in the trap where they continue to collide with the gas until they thermalize to the gas (room) temperature. This trapped cloud of positrons becomes the reservoir for a pulsed positron beam. Trap operation is typically cycled at approximately 100–200 Hz with up to 1000 positrons per pulse. Careful control over the beam formation means that the energy width of the beam is comparable to the temperature of the trapped positron cloud. In these experiments, the typical energy resolution was 60 meV.</p>
<p>The positron beam is directed to a gas cell of length 200 mm and made of gold-plated copper, which contains the target <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
or HCOOH gas. The gas cell entrance and exit apertures are 5 mm in diameter. The potential of the gas cell defines the energy of the positrons within the cell and the target gas is localized to the 200 mm path length. Target density inside the cell is maintained such that the total positron scattering is less than or equal to 10% of the unscattered beam, in order to avoid multiple scattering effects. The beam transmitted through the gas cell passes through a retarding potential analyzer (sensitive only to the parallel energy component of the beam or <inline-eqn><math-text><italic>E</italic>
<sub>∥</sub>
</math-text>
</inline-eqn>
) and then on to a double-stack, micro-channel plate detector. The collected current is measured and the data stored by the experimental control computer. In a collision with a target gas molecule, the positron can be scattered through some angle <inline-eqn><math-text>&thetas;</math-text>
</inline-eqn>
, losing <inline-eqn><math-text><italic>E</italic>
<sub>∥</sub>
</math-text>
</inline-eqn>
, and it can also lose some of its total energy if inelastic processes are energetically allowed [<cite linkend="nj328064bib23">23</cite>
]. Ps formation is also possible above the Ps formation threshold, <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
, corresponding to 5.821 eV for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and 4.53 eV for HCOOH. For the measurements presented in this paper, the incident current (<inline-eqn><math-text><italic>I</italic>
<sub>0</sub>
</math-text>
</inline-eqn>
), the total transmitted current (<inline-eqn><math-text><italic>I</italic>
<sub><upright>T</upright>
</sub>
</math-text>
</inline-eqn>
) and the transmitted current that had lost any portion of parallel energy (<inline-eqn><math-text><italic>I</italic>
<sub><upright>m</upright>
</sub>
</math-text>
</inline-eqn>
) were measured. These cross sections (<inline-eqn><math-text>σ</math-text>
</inline-eqn>
) are derived using the Beer–Lambert attenuation law, namely:
<display-eqn id="nj328064eqn1" textype="equation" notation="LaTeX" eqnnum="1"></display-eqn>
where <inline-eqn><math-text><italic>n</italic>
</math-text>
</inline-eqn>
is the gas number density, <inline-eqn><math-text>ℓ</math-text>
</inline-eqn>
is the path length through the target gas and <inline-eqn><math-text><italic>R</italic>
</math-text>
</inline-eqn>
is the appropriate ratio, as defined below. The ratio <inline-eqn><math-text><italic>I</italic>
<sub><upright>T</upright>
</sub>
/<italic>I</italic>
<sub>0</sub>
</math-text>
</inline-eqn>
gives the <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
, <inline-eqn><math-text><italic>I</italic>
<sub><upright>m</upright>
</sub>
/<italic>I</italic>
<sub>0</sub>
</math-text>
</inline-eqn>
gives the GTCS and <inline-eqn><math-text><italic>I</italic>
<sub><upright>m</upright>
</sub>
/<italic>I</italic>
<sub><upright>T</upright>
</sub>
</math-text>
</inline-eqn>
gives the GTCS without Ps formation, i.e. hereafter abbreviated as <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
. <italic>l</italic>
was taken as the geometrical length of the scattering cell. It was experimentally established to be so, as long as the total scattering probability inside the cell is kept less than 10%, by measurement of the benchmark total cross sections for He [<cite linkend="nj328064bib20">20</cite>
, <cite linkend="nj328064bib24">24</cite>
].</p>
<p>High-purity <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH were used throughout each study. In addition, since the samples come in liquid form, each liquid was degassed with a freeze, pump and thaw procedure. However, at room temperature, HCOOH presents some challenges to the experimentalist as the sample will consists of both its dimer and monomer forms, with the degree of dimerization depending on the pressure and temperature of the HCOOH sample used [<cite linkend="nj328064bib25">25</cite>
]. Following the equations derived by Waring [<cite linkend="nj328064bib26">26</cite>
], from the experimental results of Coolidge [<cite linkend="nj328064bib25">25</cite>
], the percentage dimer target composition as a function of sample pressure, for our cell temperature of <inline-eqn><math-text>30.4 °<upright>C</upright>
</math-text>
</inline-eqn>
, was calculated to be about 0.05% for the highest pressure used in the current measurements (0.2 mTorr). Therefore dimer effects in the present cross sections measurements will be negligible.</p>
<p>It is essential in these types of studies that the energy scale is calibrated accurately. In our experimental technique, the zero for the energy scale is established in the absence of the target gas and was determined here with a retarding potential analysis of the beam, i.e. with the energy scale defined relative to the cut-off position of the beam. The accuracy in this measurement gives an error of <inline-eqn><math-text>∼10 <upright>meV</upright>
</math-text>
</inline-eqn>
in our energy scale. It is also crucial to accurately measure the scattering cell target pressure. The pressure gauge used is a high accuracy Model 690 MKS Baratron capacitance manometer with a full range of 1 Torr and a measurement accuracy of <inline-eqn><math-text>±0.05%</math-text>
</inline-eqn>
. The gauge is regulated to operate at <inline-eqn><math-text>45 °<upright>C</upright>
</math-text>
</inline-eqn>
, while the scattering cell is at a temperature of <inline-eqn><math-text>∼30.4 °<upright>C</upright>
</math-text>
</inline-eqn>
. Since the scattering cell temperature was different from the gauge temperature, a thermal transpiration correction has been applied to the pressure readings. This correction has been calculated according to the model of Takaishi and Sensui [<cite linkend="nj328064bib27">27</cite>
], and is <inline-eqn><math-text>∼2.3%</math-text>
</inline-eqn>
for both <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH over the entire energy range of measurements. The molecular diameter used in this correction was 4.60 Å [<cite linkend="nj328064bib28">28</cite>
] and 3.8 Å [<cite linkend="nj328064bib29">29</cite>
] for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH, respectively. As already highlighted above, our knowledge of positron scattering from both <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH is rather scant. What we know from the literature is that both molecules are highly polar and have large dipole polarizabilities, i.e. 1.85 D and <inline-eqn><math-text>∼10 <upright>a.u.</upright>
</math-text>
</inline-eqn>
for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and 1.41 D and 22.5 a.u. for HCOOH [<cite linkend="nj328064bib30">30</cite>
]. As such, the elastic differential scattering cross sections (DCS) for both molecules are expected to be dominated by the long-range dipole interaction effects, resulting in highly forward peaked cross sections at lower positron impact energies, i.e. typically below 10 eV. Because of the inevitable angular resolution limitation in our experimental technique, this poses the problem that the cross sections we present here will likely be an underestimation of the actual values for energies below a few eV, depending on the nature of the elastic DCS for each molecule. Our technique relies on measuring the transmitted positron current (<inline-eqn><math-text><italic>I</italic>
<sub><upright>m</upright>
</sub>
</math-text>
</inline-eqn>
) at the beam cut-off point on the retarding potential analyzer voltage axis (see [<cite linkend="nj328064bib23">23</cite>
] for full details on this technique). In practice, however, it is not possible to make a measurement of the quantity <inline-eqn><math-text><italic>I</italic>
<sub><upright>m</upright>
</sub>
</math-text>
</inline-eqn>
at exactly the cut-off voltage, as this coincides with the cut-off point of the unscattered positron beam. To avoid effects associated with the cut-off, the positron current must be measured at a retarding potential voltage sufficiently offset from the cut-off. This was done for measurements of both gases at <inline-eqn><math-text>δ<italic>E</italic>
=150 <upright>meV</upright>
</math-text>
</inline-eqn>
(i.e. more than three standard deviations) away from the cut-off, or at <inline-eqn><math-text><italic>E</italic>
−δ<italic>E</italic>
</math-text>
</inline-eqn>
, where <inline-eqn><math-text><italic>E</italic>
</math-text>
</inline-eqn>
is the beam energy. This restriction means that the measured total cross section excludes some contribution from DCS corresponding to this inaccessible <inline-eqn><math-text>δ<italic>E</italic>
</math-text>
</inline-eqn>
range. Using the equations discussed in [<cite linkend="nj328064bib23">23</cite>
], the missing angular range, <inline-eqn><math-text>0°–&thetas;<sub><upright>max</upright>
</sub>
</math-text>
</inline-eqn>
, for a beam energy <inline-eqn><math-text><italic>E</italic>
</math-text>
</inline-eqn>
, was calculated as
<display-eqn id="nj328064eqn2" textype="equation" notation="LaTeX" eqnnum="2"></display-eqn>
and the results are shown in table <tabref linkend="nj328064tab1">1</tabref>
. Note also that in our experimental technique, positrons scattered in the backward direction, i.e. at angles (<inline-eqn><math-text>90°<&thetas;<180°</math-text>
</inline-eqn>
), exit the gas cell, are reflected from the potential wall due to the last electrode of the buffer-gas trap, and can pass through the gas cell once more.</p>
<table id="nj328064tab1" frame="topbot" position="float" width="fit" place="top"><caption type="table" id="nj328064tc1" label="Table 1"><p>Approximate missing angular ranges, <inline-eqn><math-text>0°–&thetas;<sub><upright>max</upright>
</sub>
°</math-text>
</inline-eqn>
, for selected positron scattering energies.</p>
</caption>
<tgroup cols="2"><colspec colnum="1" colname="col1" align="left"></colspec>
<colspec colnum="2" colname="col2" align="center"></colspec>
<thead><row><entry>Energy (eV)</entry>
<entry><inline-eqn><math-text>&thetas;<sub><upright>max</upright>
</sub>
°</math-text>
</inline-eqn>
</entry>
</row>
</thead>
<tbody><row><entry>0.5</entry>
<entry>33</entry>
</row>
<row><entry>1.0</entry>
<entry>23</entry>
</row>
<row><entry>2.5</entry>
<entry>16</entry>
</row>
<row><entry>5.0</entry>
<entry>10</entry>
</row>
<row><entry>15.0</entry>
<entry>6</entry>
</row>
<row><entry>30.0</entry>
<entry>4</entry>
</row>
<row><entry>60.0</entry>
<entry>3</entry>
</row>
</tbody>
</tgroup>
</table>
<p>Therefore, the missing part of the distribution will extend from <inline-eqn><math-text>0°</math-text>
</inline-eqn>
to <inline-eqn><math-text>&thetas;<sub><upright>max</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text>(180−&thetas;<sub><upright>max</upright>
</sub>
)°</math-text>
</inline-eqn>
to <inline-eqn><math-text>180°</math-text>
</inline-eqn>
. However, as both equation (<eqnref linkend="nj328064eqn2">2</eqnref>
) and table <tabref linkend="nj328064tab1">1</tabref>
show, our angular resolution becomes better with increasing impact energy. The amount by which both the present GTCS and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results are underestimated due to these missing angles will not be accurately known until there are reliable experimental elastic DCS for each of these two molecules. Schwinger multichannel calculations for positron scattering from HCOOH [<cite linkend="nj328064bib31">31</cite>
] and R-matrix calculations for positron scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
[<cite linkend="nj328064bib32">32</cite>
] have been made available to us. According to these results for HCOOH, as expected for these highly polar molecules, the positron DCS are as highly forward-peaked as their electron counterparts [<cite linkend="nj328064bib33">33</cite>
] for energies up to 10 eV, suggesting that we are underestimating the GTCS by about 45% at 4 eV, for example. A similar picture was obtained for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
, where the elastic DCS suggested that we are underestimating the GTCS by about 67% at 0.5 eV and 53% at 5 eV. That is, the systematic error involved in our GTCS results at these lower energies is expected to be significant. However, as the impact energy increases above about 10 eV, this systematic error due to the missing angles is expected to become negligible according to equation (<eqnref linkend="nj328064eqn2">2</eqnref>
), albeit depending on the behavior of the DCS. It is important to note, however, that these forward scattering problems only affect the elastic scattering component of the cross sections. As such, only the GTCS and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
are affected but not the <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
. Full results of this forward scattering effect analysis will be discussed in section <secref linkend="nj328064s4">4</secref>
.</p>
<p>The error estimates for the data presented in tables <tabref linkend="nj328064tab2">2</tabref>
–<tabref linkend="nj328064tab7">7</tabref>
and figures <figref linkend="nj328064fig1">1</figref>
–<figref linkend="nj328064fig8">8</figref>
for the present measurements are the total uncertainties, which are almost entirely due to statistical fluctuations in the measured positron current signals. These errors amount to <inline-eqn><math-text><1.6%</math-text>
</inline-eqn>
for GTCS and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
, and <inline-eqn><math-text><8%</math-text>
</inline-eqn>
for <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data of HCOOH, and amount to <inline-eqn><math-text><6%</math-text>
</inline-eqn>
for all of these three data sets in <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
. The magnetic fields in the trap, scattering region and at the retarding potential analyzer are all 530 Gauss and, consequently, corrections due to the helical path length through the cell are small (<inline-eqn><math-text>∼1%</math-text>
</inline-eqn>
at 1 eV scattering energy and reducing as the energy increases), and have not been applied to the data. The other sources of error in the determination of the cross-section magnitude lie in the determination of the number density and path length, and are estimated to be <inline-eqn><math-text><1%</math-text>
</inline-eqn>
in this case.</p>
<table id="nj328064tab2" frame="topbot" position="float" width="fit" place="top"><caption type="table" id="nj328064tc2" label="Table 2"><p><inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
positron impact GTCS (<inline-eqn><math-text>10<sup>−16</sup>
<upright>cm</upright>
<sup>2</sup>
</math-text>
</inline-eqn>
). Numbers in parentheses are the values after the forward scattering effect correction. Errors are as explained in the text.</p>
</caption>
<tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec>
<colspec colnum="2" colname="col2" align="center"></colspec>
<colspec colnum="3" colname="col3" align="center"></colspec>
<colspec colnum="4" colname="col4" align="center"></colspec>
<thead><row><entry>Energy (eV)</entry>
<entry>GTCS</entry>
<entry>Energy (eV)</entry>
<entry>GTCS</entry>
</row>
</thead>
<tbody><row><entry>0.5</entry>
<entry><inline-eqn><math-text>63.756(194.45)±1.148(3.50)</math-text>
</inline-eqn>
</entry>
<entry>25</entry>
<entry><inline-eqn><math-text>8.985(11.38)±0.119(0.15)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>0.75</entry>
<entry><inline-eqn><math-text>50.348(151.73)±1.019(3.07)</math-text>
</inline-eqn>
</entry>
<entry>26</entry>
<entry><inline-eqn><math-text>8.598(10.81)±0.120(0.15)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>1</entry>
<entry><inline-eqn><math-text>39.751(128.87)±1.050(3.40)</math-text>
</inline-eqn>
</entry>
<entry>27</entry>
<entry><inline-eqn><math-text>8.694(10.86)±0.125(0.16)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>1.25</entry>
<entry><inline-eqn><math-text>35.157(115.00)±1.080(3.53)</math-text>
</inline-eqn>
</entry>
<entry>28</entry>
<entry><inline-eqn><math-text>8.569(10.64)±0.136(0.17)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>1.5</entry>
<entry><inline-eqn><math-text>29.762(95.30)±1.076(3.45)</math-text>
</inline-eqn>
</entry>
<entry>29</entry>
<entry><inline-eqn><math-text>8.432(10.41)±0.125(0.15)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>1.75</entry>
<entry><inline-eqn><math-text>28.941(89.61)±1.057(3.27)</math-text>
</inline-eqn>
</entry>
<entry>30</entry>
<entry><inline-eqn><math-text>8.361(10.26)±0.060(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>2</entry>
<entry><inline-eqn><math-text>22.882(68.20)±0.473(1.41)</math-text>
</inline-eqn>
</entry>
<entry>31</entry>
<entry><inline-eqn><math-text>8.307(10.14)±0.058(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>2.25</entry>
<entry><inline-eqn><math-text>23.941(68.63)±1.043(2.99)</math-text>
</inline-eqn>
</entry>
<entry>32</entry>
<entry><inline-eqn><math-text>8.394(10.20)±0.061(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>2.5</entry>
<entry><inline-eqn><math-text>19.648(54.22)±0.469(1.30)</math-text>
</inline-eqn>
</entry>
<entry>33</entry>
<entry><inline-eqn><math-text>8.279(10.01)±0.059(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>3</entry>
<entry><inline-eqn><math-text>16.658(42.82)±0.516(1.33)</math-text>
</inline-eqn>
</entry>
<entry>34</entry>
<entry><inline-eqn><math-text>8.160(9.82)±0.072(0.09)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>3.5</entry>
<entry><inline-eqn><math-text>14.744(35.57)±0.511(1.23)</math-text>
</inline-eqn>
</entry>
<entry>35</entry>
<entry><inline-eqn><math-text>8.121(9.73)±0.071(0.09)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4</entry>
<entry><inline-eqn><math-text>14.539(33.17)±0.493(1.13)</math-text>
</inline-eqn>
</entry>
<entry>36</entry>
<entry><inline-eqn><math-text>8.136(9.71)±0.068(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.5</entry>
<entry><inline-eqn><math-text>12.886(27.99)±0.499(1.08)</math-text>
</inline-eqn>
</entry>
<entry>37</entry>
<entry><inline-eqn><math-text>8.091(9.62)±0.067(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5</entry>
<entry><inline-eqn><math-text>11.141(23.16)±0.130(0.27)</math-text>
</inline-eqn>
</entry>
<entry>38</entry>
<entry><inline-eqn><math-text>8.086(9.58)±0.068(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.5</entry>
<entry><inline-eqn><math-text>11.466(22.93)±0.503(1.01)</math-text>
</inline-eqn>
</entry>
<entry>39</entry>
<entry><inline-eqn><math-text>7.921(9.35)±0.068(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6</entry>
<entry><inline-eqn><math-text>10.951(21.14)±0.130(0.25)</math-text>
</inline-eqn>
</entry>
<entry>40</entry>
<entry><inline-eqn><math-text>7.916(9.32)±0.068(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.5</entry>
<entry><inline-eqn><math-text>10.850(20.30)±0.470(0.88)</math-text>
</inline-eqn>
</entry>
<entry>41</entry>
<entry><inline-eqn><math-text>7.897(9.27)±0.067(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7</entry>
<entry><inline-eqn><math-text>10.462(19.03)±0.125(0.23)</math-text>
</inline-eqn>
</entry>
<entry>42</entry>
<entry><inline-eqn><math-text>7.892(9.23)±0.067(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.5</entry>
<entry><inline-eqn><math-text>10.325(18.30)±0.478(0.85)</math-text>
</inline-eqn>
</entry>
<entry>43</entry>
<entry><inline-eqn><math-text>7.910(9.23)±0.066(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>8</entry>
<entry><inline-eqn><math-text>10.066(17.42)±0.136(0.24)</math-text>
</inline-eqn>
</entry>
<entry>44</entry>
<entry><inline-eqn><math-text>7.879(9.16)±0.068(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>9</entry>
<entry><inline-eqn><math-text>9.879(16.40)±0.130(0.22)</math-text>
</inline-eqn>
</entry>
<entry>45</entry>
<entry><inline-eqn><math-text>7.766(9.01)±0.066(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>10</entry>
<entry><inline-eqn><math-text>9.813(15.72)±0.127(0.20)</math-text>
</inline-eqn>
</entry>
<entry>46</entry>
<entry><inline-eqn><math-text>7.706(8.92)±0.067(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>11</entry>
<entry><inline-eqn><math-text>9.446(14.68)±0.135(0.21)</math-text>
</inline-eqn>
</entry>
<entry>47</entry>
<entry><inline-eqn><math-text>7.776(8.98)±0.065(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>12</entry>
<entry><inline-eqn><math-text>9.509(14.38)±0.133(0.20)</math-text>
</inline-eqn>
</entry>
<entry>48</entry>
<entry><inline-eqn><math-text>7.574(8.72)±0.064(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>13</entry>
<entry><inline-eqn><math-text>9.203(13.60)±0.129(0.19)</math-text>
</inline-eqn>
</entry>
<entry>49</entry>
<entry><inline-eqn><math-text>7.672(8.82)±0.065(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>14</entry>
<entry><inline-eqn><math-text>9.305(13.47)±0.133(0.19)</math-text>
</inline-eqn>
</entry>
<entry>50</entry>
<entry><inline-eqn><math-text>7.507(8.61)±0.066(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>15</entry>
<entry><inline-eqn><math-text>9.191(13.06)±0.132(0.19)</math-text>
</inline-eqn>
</entry>
<entry>51</entry>
<entry><inline-eqn><math-text>7.574(8.67)±0.067(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>16</entry>
<entry><inline-eqn><math-text>9.103(12.72)±0.139(0.19)</math-text>
</inline-eqn>
</entry>
<entry>52</entry>
<entry><inline-eqn><math-text>7.533(8.60)±0.069(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>17</entry>
<entry><inline-eqn><math-text>9.172(12.62)±0.135(0.19)</math-text>
</inline-eqn>
</entry>
<entry>53</entry>
<entry><inline-eqn><math-text>7.499(8.55)±0.068(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>18</entry>
<entry><inline-eqn><math-text>8.991(12.20)±0.130(0.18)</math-text>
</inline-eqn>
</entry>
<entry>54</entry>
<entry><inline-eqn><math-text>7.490(8.52)±0.065(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>19</entry>
<entry><inline-eqn><math-text>9.009(12.08)±0.130(0.17)</math-text>
</inline-eqn>
</entry>
<entry>55</entry>
<entry><inline-eqn><math-text>7.490(8.50)±0.067(0.08)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>20</entry>
<entry><inline-eqn><math-text>8.967(11.88)±0.133(0.18)</math-text>
</inline-eqn>
</entry>
<entry>56</entry>
<entry><inline-eqn><math-text>7.373(8.36)±0.063(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>21</entry>
<entry><inline-eqn><math-text>8.849(11.61)±0.134(0.18)</math-text>
</inline-eqn>
</entry>
<entry>57</entry>
<entry><inline-eqn><math-text>7.382(8.35)±0.062(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>22</entry>
<entry><inline-eqn><math-text>8.666(11.26)±0.123(0.16)</math-text>
</inline-eqn>
</entry>
<entry>58</entry>
<entry><inline-eqn><math-text>7.339(8.29)±0.060(0.07)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>23</entry>
<entry><inline-eqn><math-text>8.825(11.36)±0.129(0.17)</math-text>
</inline-eqn>
</entry>
<entry>59</entry>
<entry><inline-eqn><math-text>7.380(8.32)±0.056(0.06)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>24</entry>
<entry><inline-eqn><math-text>8.659(11.05)±0.120(0.15)</math-text>
</inline-eqn>
</entry>
<entry>60</entry>
<entry><inline-eqn><math-text>7.292(8.21)±0.061(0.07)</math-text>
</inline-eqn>
</entry>
</row>
</tbody>
</tgroup>
</table>
<table id="nj328064tab3" frame="topbot" position="float" width="fit" place="top"><caption type="table" id="nj328064tc3" label="Table 3"><p><inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
positron impact <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
(<inline-eqn><math-text>10<sup>−16</sup>
<upright>cm</upright>
<sup>2</sup>
</math-text>
</inline-eqn>
). Numbers in parentheses are the values after the forward scattering effect correction. Errors are as explained in the text.</p>
</caption>
<tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec>
<colspec colnum="2" colname="col2" align="center"></colspec>
<colspec colnum="3" colname="col3" align="center"></colspec>
<colspec colnum="4" colname="col4" align="center"></colspec>
<thead><row><entry>Energy (eV)</entry>
<entry><inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</entry>
<entry>Energy (eV)</entry>
<entry><inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</entry>
</row>
</thead>
<tbody><row><entry>5</entry>
<entry><inline-eqn><math-text>11.194(23.27)±0.088(0.18)</math-text>
</inline-eqn>
</entry>
<entry>33</entry>
<entry><inline-eqn><math-text>6.172(7.46)±0.040(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6</entry>
<entry><inline-eqn><math-text>10.244(19.78)±0.087(0.17)</math-text>
</inline-eqn>
</entry>
<entry>34</entry>
<entry><inline-eqn><math-text>6.129(7.38)±0.045(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7</entry>
<entry><inline-eqn><math-text>9.044(16.45)±0.082(0.15)</math-text>
</inline-eqn>
</entry>
<entry>35</entry>
<entry><inline-eqn><math-text>6.153(7.37)±0.046(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>8</entry>
<entry><inline-eqn><math-text>8.390(14.52)±0.085(0.15)</math-text>
</inline-eqn>
</entry>
<entry>36</entry>
<entry><inline-eqn><math-text>6.178(7.38)±0.045(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>9</entry>
<entry><inline-eqn><math-text>7.721(12.82)±0.085(0.14)</math-text>
</inline-eqn>
</entry>
<entry>37</entry>
<entry><inline-eqn><math-text>6.158(7.32)±0.045(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>10</entry>
<entry><inline-eqn><math-text>7.408(11.87)±0.087(0.14)</math-text>
</inline-eqn>
</entry>
<entry>38</entry>
<entry><inline-eqn><math-text>6.238(7.39)±0.044(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>11</entry>
<entry><inline-eqn><math-text>7.032(10.92)±0.089(0.14)</math-text>
</inline-eqn>
</entry>
<entry>39</entry>
<entry><inline-eqn><math-text>6.154(7.27)±0.044(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>12</entry>
<entry><inline-eqn><math-text>6.864(10.38)±0.088(0.13)</math-text>
</inline-eqn>
</entry>
<entry>40</entry>
<entry><inline-eqn><math-text>6.215(7.31)±0.044(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>13</entry>
<entry><inline-eqn><math-text>6.527(9.64)±0.084(0.12)</math-text>
</inline-eqn>
</entry>
<entry>41</entry>
<entry><inline-eqn><math-text>6.197(7.27)±0.046(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>14</entry>
<entry><inline-eqn><math-text>6.556(9.49)±0.089(0.13)</math-text>
</inline-eqn>
</entry>
<entry>42</entry>
<entry><inline-eqn><math-text>6.193(7.24)±0.045(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>15</entry>
<entry><inline-eqn><math-text>6.293(8.94)±0.086(0.12)</math-text>
</inline-eqn>
</entry>
<entry>43</entry>
<entry><inline-eqn><math-text>6.274(7.32)±0.043(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>16</entry>
<entry><inline-eqn><math-text>6.308(8.81)±0.086(0.12)</math-text>
</inline-eqn>
</entry>
<entry>44</entry>
<entry><inline-eqn><math-text>6.233(7.25)±0.045(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>17</entry>
<entry><inline-eqn><math-text>6.380(8.78)±0.086(0.12)</math-text>
</inline-eqn>
</entry>
<entry>45</entry>
<entry><inline-eqn><math-text>6.235(7.23)±0.043(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>18</entry>
<entry><inline-eqn><math-text>6.272(8.51)±0.085(0.12)</math-text>
</inline-eqn>
</entry>
<entry>46</entry>
<entry><inline-eqn><math-text>6.225(7.20)±0.045(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>19</entry>
<entry><inline-eqn><math-text>6.233(8.36)±0.084(0.11)</math-text>
</inline-eqn>
</entry>
<entry>47</entry>
<entry><inline-eqn><math-text>6.258(7.22)±0.045(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>20</entry>
<entry><inline-eqn><math-text>6.269(8.31)±0.090(0.12)</math-text>
</inline-eqn>
</entry>
<entry>48</entry>
<entry><inline-eqn><math-text>6.184(7.12)±0.044(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>21</entry>
<entry><inline-eqn><math-text>6.183(8.11)±0.083(0.11)</math-text>
</inline-eqn>
</entry>
<entry>49</entry>
<entry><inline-eqn><math-text>6.263(7.20)±0.044(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>22</entry>
<entry><inline-eqn><math-text>6.023(7.82)±0.083(0.11)</math-text>
</inline-eqn>
</entry>
<entry>50</entry>
<entry><inline-eqn><math-text>6.209(7.12)±0.045(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>23</entry>
<entry><inline-eqn><math-text>6.201(7.98)±0.085(0.11)</math-text>
</inline-eqn>
</entry>
<entry>51</entry>
<entry><inline-eqn><math-text>6.316(7.23)±0.044(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>24</entry>
<entry><inline-eqn><math-text>6.072(7.75)±0.084(0.11)</math-text>
</inline-eqn>
</entry>
<entry>52</entry>
<entry><inline-eqn><math-text>6.245(7.13)±0.046(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>25</entry>
<entry><inline-eqn><math-text>6.346(8.04)±0.082(0.10)</math-text>
</inline-eqn>
</entry>
<entry>53</entry>
<entry><inline-eqn><math-text>6.262(7.14)±0.046(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>26</entry>
<entry><inline-eqn><math-text>6.119(7.70)±0.083(0.10)</math-text>
</inline-eqn>
</entry>
<entry>54</entry>
<entry><inline-eqn><math-text>6.262(7.12)±0.042(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>27</entry>
<entry><inline-eqn><math-text>6.304(7.87)±0.083(0.10)</math-text>
</inline-eqn>
</entry>
<entry>55</entry>
<entry><inline-eqn><math-text>6.272(7.12)±0.046(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>28</entry>
<entry><inline-eqn><math-text>6.091(7.56)±0.088(0.11)</math-text>
</inline-eqn>
</entry>
<entry>56</entry>
<entry><inline-eqn><math-text>6.240(7.07)±0.044(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>29</entry>
<entry><inline-eqn><math-text>6.202(7.65)±0.087(0.11)</math-text>
</inline-eqn>
</entry>
<entry>57</entry>
<entry><inline-eqn><math-text>6.201(7.02)±0.044(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>30</entry>
<entry><inline-eqn><math-text>6.094(7.48)±0.040(0.05)</math-text>
</inline-eqn>
</entry>
<entry>58</entry>
<entry><inline-eqn><math-text>6.225(7.03)±0.042(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>31</entry>
<entry><inline-eqn><math-text>6.088(7.43)±0.038(0.05)</math-text>
</inline-eqn>
</entry>
<entry>59</entry>
<entry><inline-eqn><math-text>6.264(7.06)±0.042(0.05)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>32</entry>
<entry><inline-eqn><math-text>6.202(7.53)±0.040(0.05)</math-text>
</inline-eqn>
</entry>
<entry>60</entry>
<entry><inline-eqn><math-text>6.215(7.00)±0.046(0.05)</math-text>
</inline-eqn>
</entry>
</row>
</tbody>
</tgroup>
</table>
<table id="nj328064tab4" frame="topbot" position="float" width="fit" place="top"><caption type="table" id="nj328064tc4" label="Table 4"><p><inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
positron impact <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
(<inline-eqn><math-text>10<sup>−16</sup>
<upright>cm</upright>
<sup>2</sup>
</math-text>
</inline-eqn>
). Errors are as explained in the text.</p>
</caption>
<tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec>
<colspec colnum="2" colname="col2" align="center"></colspec>
<colspec colnum="3" colname="col3" align="center"></colspec>
<colspec colnum="4" colname="col4" align="center"></colspec>
<thead><row><entry>Energy (eV)</entry>
<entry><inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</entry>
<entry>Energy (eV)</entry>
<entry><inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</entry>
</row>
</thead>
<tbody><row><entry>5</entry>
<entry><inline-eqn><math-text>−0.001±0.101</math-text>
</inline-eqn>
</entry>
<entry>33</entry>
<entry><inline-eqn><math-text>2.108±0.044</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6</entry>
<entry><inline-eqn><math-text>0.750±0.103</math-text>
</inline-eqn>
</entry>
<entry>34</entry>
<entry><inline-eqn><math-text>2.040±0.055</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7</entry>
<entry><inline-eqn><math-text>1.448±0.104</math-text>
</inline-eqn>
</entry>
<entry>35</entry>
<entry><inline-eqn><math-text>1.974±0.055</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>8</entry>
<entry><inline-eqn><math-text>1.683±0.103</math-text>
</inline-eqn>
</entry>
<entry>36</entry>
<entry><inline-eqn><math-text>1.965±0.053</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>9</entry>
<entry><inline-eqn><math-text>2.174±0.104</math-text>
</inline-eqn>
</entry>
<entry>37</entry>
<entry><inline-eqn><math-text>1.942±0.053</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>10</entry>
<entry><inline-eqn><math-text>2.418±0.106</math-text>
</inline-eqn>
</entry>
<entry>38</entry>
<entry><inline-eqn><math-text>1.853±0.052</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>11</entry>
<entry><inline-eqn><math-text>2.425±0.101</math-text>
</inline-eqn>
</entry>
<entry>39</entry>
<entry><inline-eqn><math-text>1.772±0.053</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>12</entry>
<entry><inline-eqn><math-text>2.665±0.103</math-text>
</inline-eqn>
</entry>
<entry>40</entry>
<entry><inline-eqn><math-text>1.708±0.053</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>13</entry>
<entry><inline-eqn><math-text>2.686±0.104</math-text>
</inline-eqn>
</entry>
<entry>41</entry>
<entry><inline-eqn><math-text>1.704±0.053</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>14</entry>
<entry><inline-eqn><math-text>2.756±0.102</math-text>
</inline-eqn>
</entry>
<entry>42</entry>
<entry><inline-eqn><math-text>1.707±0.053</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>15</entry>
<entry><inline-eqn><math-text>2.918±0.104</math-text>
</inline-eqn>
</entry>
<entry>43</entry>
<entry><inline-eqn><math-text>1.644±0.051</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>16</entry>
<entry><inline-eqn><math-text>2.813±0.104</math-text>
</inline-eqn>
</entry>
<entry>44</entry>
<entry><inline-eqn><math-text>1.657±0.051</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>17</entry>
<entry><inline-eqn><math-text>2.820±0.109</math-text>
</inline-eqn>
</entry>
<entry>45</entry>
<entry><inline-eqn><math-text>1.538±0.050</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>18</entry>
<entry><inline-eqn><math-text>2.736±0.102</math-text>
</inline-eqn>
</entry>
<entry>46</entry>
<entry><inline-eqn><math-text>1.492±0.052</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>19</entry>
<entry><inline-eqn><math-text>2.804±0.107</math-text>
</inline-eqn>
</entry>
<entry>47</entry>
<entry><inline-eqn><math-text>1.527±0.049</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>20</entry>
<entry><inline-eqn><math-text>2.726±0.105</math-text>
</inline-eqn>
</entry>
<entry>48</entry>
<entry><inline-eqn><math-text>1.397±0.050</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>21</entry>
<entry><inline-eqn><math-text>2.696±0.105</math-text>
</inline-eqn>
</entry>
<entry>49</entry>
<entry><inline-eqn><math-text>1.417±0.050</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>22</entry>
<entry><inline-eqn><math-text>2.664±0.102</math-text>
</inline-eqn>
</entry>
<entry>50</entry>
<entry><inline-eqn><math-text>1.305±0.050</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>23</entry>
<entry><inline-eqn><math-text>2.650±0.103</math-text>
</inline-eqn>
</entry>
<entry>51</entry>
<entry><inline-eqn><math-text>1.267±0.052</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>24</entry>
<entry><inline-eqn><math-text>2.593±0.092</math-text>
</inline-eqn>
</entry>
<entry>52</entry>
<entry><inline-eqn><math-text>1.300±0.051</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>25</entry>
<entry><inline-eqn><math-text>2.672±0.098</math-text>
</inline-eqn>
</entry>
<entry>53</entry>
<entry><inline-eqn><math-text>1.248±0.050</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>26</entry>
<entry><inline-eqn><math-text>2.495±0.096</math-text>
</inline-eqn>
</entry>
<entry>54</entry>
<entry><inline-eqn><math-text>1.238±0.049</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>27</entry>
<entry><inline-eqn><math-text>2.424±0.099</math-text>
</inline-eqn>
</entry>
<entry>55</entry>
<entry><inline-eqn><math-text>1.228±0.048</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>28</entry>
<entry><inline-eqn><math-text>2.519±0.100</math-text>
</inline-eqn>
</entry>
<entry>56</entry>
<entry><inline-eqn><math-text>1.141±0.048</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>29</entry>
<entry><inline-eqn><math-text>2.253±0.099</math-text>
</inline-eqn>
</entry>
<entry>57</entry>
<entry><inline-eqn><math-text>1.192±0.046</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>30</entry>
<entry><inline-eqn><math-text>2.278±0.048</math-text>
</inline-eqn>
</entry>
<entry>58</entry>
<entry><inline-eqn><math-text>1.124±0.045</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>31</entry>
<entry><inline-eqn><math-text>2.229±0.047</math-text>
</inline-eqn>
</entry>
<entry>59</entry>
<entry><inline-eqn><math-text>1.124±0.044</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>32</entry>
<entry><inline-eqn><math-text>2.206±0.047</math-text>
</inline-eqn>
</entry>
<entry>60</entry>
<entry><inline-eqn><math-text>1.088±0.041</math-text>
</inline-eqn>
</entry>
</row>
</tbody>
</tgroup>
</table>
<table id="nj328064tab5" frame="topbot" position="float" width="fit" place="top"><caption type="table" id="nj328064tc5" label="Table 5"><p>HCOOH positron impact GTCS (<inline-eqn><math-text>10<sup>−16</sup>
<upright>cm</upright>
<sup>2</sup>
</math-text>
</inline-eqn>
). Numbers in parentheses are the values after the forward scattering effect correction. Errors are as explained in the text.</p>
</caption>
<tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec>
<colspec colnum="2" colname="col2" align="center"></colspec>
<colspec colnum="3" colname="col3" align="center"></colspec>
<colspec colnum="4" colname="col4" align="center"></colspec>
<thead><row><entry>Energy (eV)</entry>
<entry>GTCS</entry>
<entry>Energy (eV)</entry>
<entry>GTCS</entry>
</row>
</thead>
<tbody><row><entry>4</entry>
<entry><inline-eqn><math-text>17.754(31.54)±0.175(0.31)</math-text>
</inline-eqn>
</entry>
<entry>25</entry>
<entry><inline-eqn><math-text>15.378(15.51)±0.145(0.15)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.2</entry>
<entry><inline-eqn><math-text>17.766(30.95)±0.193(0.32)</math-text>
</inline-eqn>
</entry>
<entry>26</entry>
<entry><inline-eqn><math-text>15.480(15.57)±0.234(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.4</entry>
<entry><inline-eqn><math-text>17.617(30.08)±0.197(0.31)</math-text>
</inline-eqn>
</entry>
<entry>27</entry>
<entry><inline-eqn><math-text>15.151(15.26)±0.225(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.6</entry>
<entry><inline-eqn><math-text>17.331(29.02)±0.195(0.29)</math-text>
</inline-eqn>
</entry>
<entry>28</entry>
<entry><inline-eqn><math-text>15.405(15.50)±0.245(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.8</entry>
<entry><inline-eqn><math-text>17.451(28.62)±0.188(0.26)</math-text>
</inline-eqn>
</entry>
<entry>29</entry>
<entry><inline-eqn><math-text>15.240(15.39)±0.240(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5</entry>
<entry><inline-eqn><math-text>17.522(28.13)±0.189(0.25)</math-text>
</inline-eqn>
</entry>
<entry>30</entry>
<entry><inline-eqn><math-text>15.463(15.59)±0.232(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.2</entry>
<entry><inline-eqn><math-text>17.499(27.57)±0.205(0.25)</math-text>
</inline-eqn>
</entry>
<entry>31</entry>
<entry><inline-eqn><math-text>15.100(15.25)±0.234(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.4</entry>
<entry><inline-eqn><math-text>17.523(27.05)±0.194(0.25)</math-text>
</inline-eqn>
</entry>
<entry>32</entry>
<entry><inline-eqn><math-text>15.292(15.43)±0.229(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.6</entry>
<entry><inline-eqn><math-text>17.851(27.01)±0.197(0.24)</math-text>
</inline-eqn>
</entry>
<entry>33</entry>
<entry><inline-eqn><math-text>15.438(15.58)±0.229(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.8</entry>
<entry><inline-eqn><math-text>17.506(25.94)±0.188(0.23)</math-text>
</inline-eqn>
</entry>
<entry>34</entry>
<entry><inline-eqn><math-text>15.316(15.45)±0.225(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6</entry>
<entry><inline-eqn><math-text>17.634(25.58)±0.195(0.23)</math-text>
</inline-eqn>
</entry>
<entry>35</entry>
<entry><inline-eqn><math-text>14.715(14.84)±0.223(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.2</entry>
<entry><inline-eqn><math-text>17.609(25.12)±0.187(0.23)</math-text>
</inline-eqn>
</entry>
<entry>36</entry>
<entry><inline-eqn><math-text>15.167(15.32)±0.219(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.4</entry>
<entry><inline-eqn><math-text>17.639(24.75)±0.195(0.23)</math-text>
</inline-eqn>
</entry>
<entry>37</entry>
<entry><inline-eqn><math-text>15.178(15.33)±0.224(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.6</entry>
<entry><inline-eqn><math-text>17.453(24.08)±0.185(0.22)</math-text>
</inline-eqn>
</entry>
<entry>38</entry>
<entry><inline-eqn><math-text>14.890(15.04)±0.224(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.8</entry>
<entry><inline-eqn><math-text>17.551(23.80)±0.187(0.22)</math-text>
</inline-eqn>
</entry>
<entry>39</entry>
<entry><inline-eqn><math-text>14.655(14.81)±0.229(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7</entry>
<entry><inline-eqn><math-text>17.238(22.94)±0.143(0.17)</math-text>
</inline-eqn>
</entry>
<entry>40</entry>
<entry><inline-eqn><math-text>14.827(14.97)±0.228(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.2</entry>
<entry><inline-eqn><math-text>17.333(22.90)±0.171(0.20)</math-text>
</inline-eqn>
</entry>
<entry>41</entry>
<entry><inline-eqn><math-text>14.933(15.14)±0.222(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.4</entry>
<entry><inline-eqn><math-text>17.670(23.16)±0.162(0.20)</math-text>
</inline-eqn>
</entry>
<entry>42</entry>
<entry><inline-eqn><math-text>14.549(14.70)±0.231(0.24)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.6</entry>
<entry><inline-eqn><math-text>17.391(22.61)±0.158(0.19)</math-text>
</inline-eqn>
</entry>
<entry>43</entry>
<entry><inline-eqn><math-text>14.589(14.75)±0.215(0.22)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.8</entry>
<entry><inline-eqn><math-text>17.223(22.20)±0.148(0.18)</math-text>
</inline-eqn>
</entry>
<entry>44</entry>
<entry><inline-eqn><math-text>14.489(14.68)±0.225(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>8</entry>
<entry><inline-eqn><math-text>17.252(22.01)±0.125(0.15)</math-text>
</inline-eqn>
</entry>
<entry>45</entry>
<entry><inline-eqn><math-text>14.234(14.37)±0.214(0.22)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>9</entry>
<entry><inline-eqn><math-text>16.575(20.23)±0.231(0.28)</math-text>
</inline-eqn>
</entry>
<entry>46</entry>
<entry><inline-eqn><math-text>14.394(14.59)±0.226(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>10</entry>
<entry><inline-eqn><math-text>16.347(19.03)±0.260(0.28)</math-text>
</inline-eqn>
</entry>
<entry>47</entry>
<entry><inline-eqn><math-text>14.246(14.43)±0.202(0.21)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>11</entry>
<entry><inline-eqn><math-text>16.601(18.84)±0.252(0.26)</math-text>
</inline-eqn>
</entry>
<entry>48</entry>
<entry><inline-eqn><math-text>13.867(14.00)±0.217(0.22)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>12</entry>
<entry><inline-eqn><math-text>16.216(17.92)±0.178(0.19)</math-text>
</inline-eqn>
</entry>
<entry>49</entry>
<entry><inline-eqn><math-text>14.058(14.22)±0.211(0.21)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>13</entry>
<entry><inline-eqn><math-text>16.480(17.64)±0.176(0.19)</math-text>
</inline-eqn>
</entry>
<entry>50</entry>
<entry><inline-eqn><math-text>13.784(13.96)±0.217(0.23)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>14</entry>
<entry><inline-eqn><math-text>16.327(17.00)±0.161(0.17)</math-text>
</inline-eqn>
</entry>
<entry>51</entry>
<entry><inline-eqn><math-text>14.014±0.207</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>15</entry>
<entry><inline-eqn><math-text>16.366(16.52)±0.160(0.16)</math-text>
</inline-eqn>
</entry>
<entry>52</entry>
<entry><inline-eqn><math-text>13.886±0.216</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>16</entry>
<entry><inline-eqn><math-text>15.551(15.74)±0.253(0.27)</math-text>
</inline-eqn>
</entry>
<entry>53</entry>
<entry><inline-eqn><math-text>13.607±0.211</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>17</entry>
<entry><inline-eqn><math-text>15.762(15.92)±0.258(0.25)</math-text>
</inline-eqn>
</entry>
<entry>54</entry>
<entry><inline-eqn><math-text>13.613±0.211</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>18</entry>
<entry><inline-eqn><math-text>15.550(15.67)±0.229(0.24)</math-text>
</inline-eqn>
</entry>
<entry>55</entry>
<entry><inline-eqn><math-text>13.449±0.215</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>19</entry>
<entry><inline-eqn><math-text>15.349(15.45)±0.262(0.27)</math-text>
</inline-eqn>
</entry>
<entry>56</entry>
<entry><inline-eqn><math-text>13.579±0.211</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>20</entry>
<entry><inline-eqn><math-text>15.488(15.60)±0.240(0.25)</math-text>
</inline-eqn>
</entry>
<entry>57</entry>
<entry><inline-eqn><math-text>13.608±0.199</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>21</entry>
<entry><inline-eqn><math-text>15.480(15.59)±0.203(0.22)</math-text>
</inline-eqn>
</entry>
<entry>58</entry>
<entry><inline-eqn><math-text>13.282±0.199</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>22</entry>
<entry><inline-eqn><math-text>15.343(15.46)±0.218(0.23)</math-text>
</inline-eqn>
</entry>
<entry>59</entry>
<entry><inline-eqn><math-text>13.504±0.193</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>23</entry>
<entry><inline-eqn><math-text>15.354(15.45)±0.234(0.23)</math-text>
</inline-eqn>
</entry>
<entry>60</entry>
<entry><inline-eqn><math-text>13.375±0.172</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>24</entry>
<entry><inline-eqn><math-text>15.379(15.44)±0.152(0.16)</math-text>
</inline-eqn>
</entry>
<entry></entry>
<entry></entry>
</row>
</tbody>
</tgroup>
</table>
<table id="nj328064tab6" frame="topbot" position="float" width="fit" place="top"><caption type="table" id="nj328064tc6" label="Table 6"><p>HCOOH positron impact <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
(<inline-eqn><math-text>10<sup>−16</sup>
<upright>cm</upright>
<sup>2</sup>
</math-text>
</inline-eqn>
). Numbers in parentheses are the values after the forward scattering effect correction. Errors are as explained in the text.</p>
</caption>
<tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec>
<colspec colnum="2" colname="col2" align="center"></colspec>
<colspec colnum="3" colname="col3" align="center"></colspec>
<colspec colnum="4" colname="col4" align="center"></colspec>
<thead><row><entry>Energy (eV)</entry>
<entry><inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</entry>
<entry>Energy (eV)</entry>
<entry><inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</entry>
</row>
</thead>
<tbody><row><entry>4</entry>
<entry><inline-eqn><math-text>18.009(31.99)±0.112(0.20)</math-text>
</inline-eqn>
</entry>
<entry>25</entry>
<entry><inline-eqn><math-text>10.868(10.97)±0.100(0.10)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.2</entry>
<entry><inline-eqn><math-text>17.786(31.13)±0.105(0.18)</math-text>
</inline-eqn>
</entry>
<entry>26</entry>
<entry><inline-eqn><math-text>11.006(11.11)±0.130(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.4</entry>
<entry><inline-eqn><math-text>17.620(30.38)±0.114(0.20)</math-text>
</inline-eqn>
</entry>
<entry>27</entry>
<entry><inline-eqn><math-text>10.934(11.04)±0.137(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.6</entry>
<entry><inline-eqn><math-text>17.025(28.90)±0.109(0.18)</math-text>
</inline-eqn>
</entry>
<entry>28</entry>
<entry><inline-eqn><math-text>11.084(11.20)±0.132(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.8</entry>
<entry><inline-eqn><math-text>16.706(27.93)±0.110(0.18)</math-text>
</inline-eqn>
</entry>
<entry>29</entry>
<entry><inline-eqn><math-text>10.980(11.09)±0.137(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5</entry>
<entry><inline-eqn><math-text>16.426(27.03)±0.115(0.19)</math-text>
</inline-eqn>
</entry>
<entry>30</entry>
<entry><inline-eqn><math-text>11.262(11.38)±0.133(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.2</entry>
<entry><inline-eqn><math-text>16.018(25.99)±0.117(0.19)</math-text>
</inline-eqn>
</entry>
<entry>31</entry>
<entry><inline-eqn><math-text>11.065(11.18)±0.141(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.4</entry>
<entry><inline-eqn><math-text>15.667(25.06)±0.106(0.17)</math-text>
</inline-eqn>
</entry>
<entry>32</entry>
<entry><inline-eqn><math-text>11.114(11.24)±0.134(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.6</entry>
<entry><inline-eqn><math-text>15.633(24.65)±0.112(0.18)</math-text>
</inline-eqn>
</entry>
<entry>33</entry>
<entry><inline-eqn><math-text>11.333(11.46)±0.138(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.8</entry>
<entry><inline-eqn><math-text>15.054(23.39)±0.109(0.17)</math-text>
</inline-eqn>
</entry>
<entry>34</entry>
<entry><inline-eqn><math-text>11.341(11.47)±0.126(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6</entry>
<entry><inline-eqn><math-text>14.960(22.90)±0.114(0.18)</math-text>
</inline-eqn>
</entry>
<entry>35</entry>
<entry><inline-eqn><math-text>11.068(11.19)±0.130(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.2</entry>
<entry><inline-eqn><math-text>14.637(22.08)±0.121(0.18)</math-text>
</inline-eqn>
</entry>
<entry>36</entry>
<entry><inline-eqn><math-text>11.442(11.58)±0.136(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.4</entry>
<entry><inline-eqn><math-text>14.426(21.45)±0.119(0.18)</math-text>
</inline-eqn>
</entry>
<entry>37</entry>
<entry><inline-eqn><math-text>11.357(11.49)±0.129(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.6</entry>
<entry><inline-eqn><math-text>14.101(20.65)±0.115(0.17)</math-text>
</inline-eqn>
</entry>
<entry>38</entry>
<entry><inline-eqn><math-text>11.468(11.61)±0.123(0.12)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.8</entry>
<entry><inline-eqn><math-text>14.030(20.24)±0.115(0.17)</math-text>
</inline-eqn>
</entry>
<entry>39</entry>
<entry><inline-eqn><math-text>11.251(11.39)±0.139(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7</entry>
<entry><inline-eqn><math-text>13.595(19.31)±0.085(0.12)</math-text>
</inline-eqn>
</entry>
<entry>40</entry>
<entry><inline-eqn><math-text>11.466(11.61)±0.129(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.2</entry>
<entry><inline-eqn><math-text>13.590(19.16)±0.118(0.17)</math-text>
</inline-eqn>
</entry>
<entry>41</entry>
<entry><inline-eqn><math-text>11.573(11.72)±0.131(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.4</entry>
<entry><inline-eqn><math-text>13.666(19.12)±0.111(0.16)</math-text>
</inline-eqn>
</entry>
<entry>42</entry>
<entry><inline-eqn><math-text>11.466(11.61)±0.142(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.6</entry>
<entry><inline-eqn><math-text>13.355(18.54)±0.113(0.16)</math-text>
</inline-eqn>
</entry>
<entry>43</entry>
<entry><inline-eqn><math-text>11.395(11.54)±0.126(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.8</entry>
<entry><inline-eqn><math-text>13.219(18.21)±0.110(0.15)</math-text>
</inline-eqn>
</entry>
<entry>44</entry>
<entry><inline-eqn><math-text>11.541(11.69)±0.135(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>8</entry>
<entry><inline-eqn><math-text>13.068(17.86)±0.086(0.12)</math-text>
</inline-eqn>
</entry>
<entry>45</entry>
<entry><inline-eqn><math-text>11.368(11.51)±0.128(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>9</entry>
<entry><inline-eqn><math-text>12.198(15.83)±0.136(0.18)</math-text>
</inline-eqn>
</entry>
<entry>46</entry>
<entry><inline-eqn><math-text>11.548(11.70)±0.138(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>10</entry>
<entry><inline-eqn><math-text>11.765(14.45)±0.158(0.19)</math-text>
</inline-eqn>
</entry>
<entry>47</entry>
<entry><inline-eqn><math-text>11.549(11.70)±0.121(0.12)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>11</entry>
<entry><inline-eqn><math-text>11.695(13.88)±0.158(0.19)</math-text>
</inline-eqn>
</entry>
<entry>48</entry>
<entry><inline-eqn><math-text>11.149(11.29)±0.133(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>12</entry>
<entry><inline-eqn><math-text>11.454(13.12)±0.100(0.11)</math-text>
</inline-eqn>
</entry>
<entry>49</entry>
<entry><inline-eqn><math-text>11.446(11.60)±0.131(0.13)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>13</entry>
<entry><inline-eqn><math-text>11.282(12.45)±0.117(0.13)</math-text>
</inline-eqn>
</entry>
<entry>50</entry>
<entry><inline-eqn><math-text>11.301(11.45)±0.135(0.14)</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>14</entry>
<entry><inline-eqn><math-text>11.128(11.82)±0.106(0.11)</math-text>
</inline-eqn>
</entry>
<entry>51</entry>
<entry><inline-eqn><math-text>11.650±0.126</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>15</entry>
<entry><inline-eqn><math-text>11.234(11.47)±0.109(0.11)</math-text>
</inline-eqn>
</entry>
<entry>52</entry>
<entry><inline-eqn><math-text>11.570±0.133</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>16</entry>
<entry><inline-eqn><math-text>10.749(10.95)±0.150(0.15)</math-text>
</inline-eqn>
</entry>
<entry>53</entry>
<entry><inline-eqn><math-text>11.369±0.126</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>17</entry>
<entry><inline-eqn><math-text>10.919(11.10)±0.147(0.15)</math-text>
</inline-eqn>
</entry>
<entry>54</entry>
<entry><inline-eqn><math-text>11.464±0.134</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>18</entry>
<entry><inline-eqn><math-text>10.892(11.04)±0.148(0.15)</math-text>
</inline-eqn>
</entry>
<entry>55</entry>
<entry><inline-eqn><math-text>11.391±0.130</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>19</entry>
<entry><inline-eqn><math-text>10.519(10.63)±0.166(0.17)</math-text>
</inline-eqn>
</entry>
<entry>56</entry>
<entry><inline-eqn><math-text>11.601±0.130</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>20</entry>
<entry><inline-eqn><math-text>10.817(10.91)±0.153(0.15)</math-text>
</inline-eqn>
</entry>
<entry>57</entry>
<entry><inline-eqn><math-text>11.596±0.129</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>21</entry>
<entry><inline-eqn><math-text>10.805(10.90)±0.128(0.13)</math-text>
</inline-eqn>
</entry>
<entry>58</entry>
<entry><inline-eqn><math-text>11.427±0.140</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>22</entry>
<entry><inline-eqn><math-text>10.769(10.86)±0.138(0.14)</math-text>
</inline-eqn>
</entry>
<entry>59</entry>
<entry><inline-eqn><math-text>11.445±0.133</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>23</entry>
<entry><inline-eqn><math-text>10.771(10.87)±0.147(0.15)</math-text>
</inline-eqn>
</entry>
<entry>60</entry>
<entry><inline-eqn><math-text>11.505±0.132</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>24</entry>
<entry><inline-eqn><math-text>10.726(10.83)±0.097(0.10)</math-text>
</inline-eqn>
</entry>
<entry></entry>
<entry></entry>
</row>
</tbody>
</tgroup>
</table>
<table id="nj328064tab7" frame="topbot" position="float" width="fit" place="top"><caption type="table" id="nj328064tc7" label="Table 7"><p>HCOOH positron impact <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
(<inline-eqn><math-text>10<sup>−16</sup>
<upright>cm</upright>
<sup>2</sup>
</math-text>
</inline-eqn>
). Errors are as explained in the text.</p>
</caption>
<tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec>
<colspec colnum="2" colname="col2" align="center"></colspec>
<colspec colnum="3" colname="col3" align="center"></colspec>
<colspec colnum="4" colname="col4" align="center"></colspec>
<thead><row><entry>Energy (eV)</entry>
<entry><inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</entry>
<entry>Energy (eV)</entry>
<entry><inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</entry>
</row>
</thead>
<tbody><row><entry>4</entry>
<entry><inline-eqn><math-text>−0.240±0.166</math-text>
</inline-eqn>
</entry>
<entry>25</entry>
<entry><inline-eqn><math-text>4.533±0.106</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.2</entry>
<entry><inline-eqn><math-text>−0.008±0.160</math-text>
</inline-eqn>
</entry>
<entry>26</entry>
<entry><inline-eqn><math-text>4.456±0.198</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.4</entry>
<entry><inline-eqn><math-text>0.012±0.166</math-text>
</inline-eqn>
</entry>
<entry>27</entry>
<entry><inline-eqn><math-text>4.216±0.195</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.6</entry>
<entry><inline-eqn><math-text>0.315±0.162</math-text>
</inline-eqn>
</entry>
<entry>28</entry>
<entry><inline-eqn><math-text>4.301±0.199</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>4.8</entry>
<entry><inline-eqn><math-text>0.755±0.158</math-text>
</inline-eqn>
</entry>
<entry>29</entry>
<entry><inline-eqn><math-text>4.292±0.197</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5</entry>
<entry><inline-eqn><math-text>1.103±0.157</math-text>
</inline-eqn>
</entry>
<entry>30</entry>
<entry><inline-eqn><math-text>4.213±0.193</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.2</entry>
<entry><inline-eqn><math-text>1.499±0.166</math-text>
</inline-eqn>
</entry>
<entry>31</entry>
<entry><inline-eqn><math-text>4.064±0.190</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.4</entry>
<entry><inline-eqn><math-text>1.865±0.166</math-text>
</inline-eqn>
</entry>
<entry>32</entry>
<entry><inline-eqn><math-text>4.192±0.192</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.6</entry>
<entry><inline-eqn><math-text>2.230±0.163</math-text>
</inline-eqn>
</entry>
<entry>33</entry>
<entry><inline-eqn><math-text>4.124±0.187</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>5.8</entry>
<entry><inline-eqn><math-text>2.462±0.154</math-text>
</inline-eqn>
</entry>
<entry>34</entry>
<entry><inline-eqn><math-text>3.982±0.193</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6</entry>
<entry><inline-eqn><math-text>2.681±0.153</math-text>
</inline-eqn>
</entry>
<entry>35</entry>
<entry><inline-eqn><math-text>3.647±0.191</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.2</entry>
<entry><inline-eqn><math-text>2.977±0.149</math-text>
</inline-eqn>
</entry>
<entry>36</entry>
<entry><inline-eqn><math-text>3.748±0.184</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.4</entry>
<entry><inline-eqn><math-text>3.220±0.153</math-text>
</inline-eqn>
</entry>
<entry>37</entry>
<entry><inline-eqn><math-text>3.840±0.197</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.6</entry>
<entry><inline-eqn><math-text>3.356±0.150</math-text>
</inline-eqn>
</entry>
<entry>38</entry>
<entry><inline-eqn><math-text>3.435±0.189</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>6.8</entry>
<entry><inline-eqn><math-text>3.531±0.149</math-text>
</inline-eqn>
</entry>
<entry>39</entry>
<entry><inline-eqn><math-text>3.419±0.192</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7</entry>
<entry><inline-eqn><math-text>3.633±0.121</math-text>
</inline-eqn>
</entry>
<entry>40</entry>
<entry><inline-eqn><math-text>3.362±0.186</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.2</entry>
<entry><inline-eqn><math-text>3.748±0.124</math-text>
</inline-eqn>
</entry>
<entry>41</entry>
<entry><inline-eqn><math-text>3.421±0.193</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.4</entry>
<entry><inline-eqn><math-text>4.009±0.130</math-text>
</inline-eqn>
</entry>
<entry>42</entry>
<entry><inline-eqn><math-text>3.089±0.187</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.6</entry>
<entry><inline-eqn><math-text>4.040±0.118</math-text>
</inline-eqn>
</entry>
<entry>43</entry>
<entry><inline-eqn><math-text>3.204±0.183</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>7.8</entry>
<entry><inline-eqn><math-text>4.002±0.108</math-text>
</inline-eqn>
</entry>
<entry>44</entry>
<entry><inline-eqn><math-text>2.992±0.186</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>8</entry>
<entry><inline-eqn><math-text>4.150±0.094</math-text>
</inline-eqn>
</entry>
<entry>45</entry>
<entry><inline-eqn><math-text>2.860±0.175</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>9</entry>
<entry><inline-eqn><math-text>4.369±0.201</math-text>
</inline-eqn>
</entry>
<entry>46</entry>
<entry><inline-eqn><math-text>2.898±0.187</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>10</entry>
<entry><inline-eqn><math-text>4.577±0.196</math-text>
</inline-eqn>
</entry>
<entry>47</entry>
<entry><inline-eqn><math-text>2.729±0.169</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>11</entry>
<entry><inline-eqn><math-text>4.911±0.177</math-text>
</inline-eqn>
</entry>
<entry>48</entry>
<entry><inline-eqn><math-text>2.709±0.173</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>12</entry>
<entry><inline-eqn><math-text>4.771±0.146</math-text>
</inline-eqn>
</entry>
<entry>49</entry>
<entry><inline-eqn><math-text>2.628±0.167</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>13</entry>
<entry><inline-eqn><math-text>5.138±0.143</math-text>
</inline-eqn>
</entry>
<entry>50</entry>
<entry><inline-eqn><math-text>2.507±0.189</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>14</entry>
<entry><inline-eqn><math-text>5.149±0.127</math-text>
</inline-eqn>
</entry>
<entry>51</entry>
<entry><inline-eqn><math-text>2.383±0.176</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>15</entry>
<entry><inline-eqn><math-text>5.047±0.109</math-text>
</inline-eqn>
</entry>
<entry>52</entry>
<entry><inline-eqn><math-text>2.321±0.173</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>16</entry>
<entry><inline-eqn><math-text>4.790±0.224</math-text>
</inline-eqn>
</entry>
<entry>53</entry>
<entry><inline-eqn><math-text>2.231±0.168</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>17</entry>
<entry><inline-eqn><math-text>4.824±0.196</math-text>
</inline-eqn>
</entry>
<entry>54</entry>
<entry><inline-eqn><math-text>2.166±0.168</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>18</entry>
<entry><inline-eqn><math-text>4.636±0.192</math-text>
</inline-eqn>
</entry>
<entry>55</entry>
<entry><inline-eqn><math-text>2.032±0.170</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>19</entry>
<entry><inline-eqn><math-text>4.811±0.212</math-text>
</inline-eqn>
</entry>
<entry>56</entry>
<entry><inline-eqn><math-text>2.015±0.162</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>20</entry>
<entry><inline-eqn><math-text>4.694±0.193</math-text>
</inline-eqn>
</entry>
<entry>57</entry>
<entry><inline-eqn><math-text>2.030±0.158</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>21</entry>
<entry><inline-eqn><math-text>4.692±0.175</math-text>
</inline-eqn>
</entry>
<entry>58</entry>
<entry><inline-eqn><math-text>1.887±0.150</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>22</entry>
<entry><inline-eqn><math-text>4.596±0.186</math-text>
</inline-eqn>
</entry>
<entry>59</entry>
<entry><inline-eqn><math-text>2.109±0.145</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>23</entry>
<entry><inline-eqn><math-text>4.579±0.178</math-text>
</inline-eqn>
</entry>
<entry>60</entry>
<entry><inline-eqn><math-text>1.889±0.119</math-text>
</inline-eqn>
</entry>
</row>
<row><entry>24</entry>
<entry><inline-eqn><math-text>4.611±0.121</math-text>
</inline-eqn>
</entry>
<entry></entry>
<entry></entry>
</row>
</tbody>
</tgroup>
</table>
<figure id="nj328064fig1" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="26.3pc" printcolour="no" filename="images/nj328064fig1.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="yes" filename="images/nj328064fig1.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc1" label="Figure 1"><p indent="no">Present positron impact <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
GTCS and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
compared with the literature for GTCS and elastic integral cross section (ECS) results.</p>
</caption>
</figure>
<figure id="nj328064fig2" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="22.0pc" printcolour="no" filename="images/nj328064fig2.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj328064fig2.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc2" label="Figure 2"><p indent="no">Present positron impact <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
<inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results compared with literature experimental and theoretical results.</p>
</caption>
</figure>
<figure id="nj328064fig3" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="25.6pc" printcolour="no" filename="images/nj328064fig3.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj328064fig3.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc3" label="Figure 3"><p indent="no">Present positron impact <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results in the vicinity of the Ps threshold (<inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
=5.821 <upright>eV</upright>
</math-text>
</inline-eqn>
).</p>
</caption>
</figure>
<figure id="nj328064fig4" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="25.9pc" printcolour="no" filename="images/nj328064fig4.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj328064fig4.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc4" label="Figure 4"><p indent="no">Same as figure <figref linkend="nj328064fig3">3</figref>
but in the vicinity of the ionization threshold (<inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
=12.621 <upright>eV</upright>
</math-text>
</inline-eqn>
).</p>
</caption>
</figure>
<figure id="nj328064fig5" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="25.6pc" printcolour="no" filename="images/nj328064fig5.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj328064fig5.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc5" label="Figure 5"><p indent="no">Present positron impact <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
GTCS results compared with those of Zecca <italic>et al</italic>
below <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
.</p>
</caption>
</figure>
<figure id="nj328064fig6" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="24.6pc" printcolour="no" filename="images/nj328064fig6.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="yes" filename="images/nj328064fig6.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc6" label="Figure 6"><p indent="no">Present positron impact HCOOH GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
compared with literature for GTCS and elastic integral (ECS) results (a) over the whole energy range of measurement and (b) below 30 eV.</p>
</caption>
</figure>
<figure id="nj328064fig7" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="24.0pc" printcolour="no" filename="images/nj328064fig7.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj328064fig7.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc7" label="Figure 7"><p indent="no">Present positron impact HCOOH GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results in the vicinity of the Ps threshold (<inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
=4.53 <upright>eV</upright>
</math-text>
</inline-eqn>
).</p>
</caption>
</figure>
<figure id="nj328064fig8" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="25.3pc" printcolour="no" filename="images/nj328064fig8.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj328064fig8.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc8" label="Figure 8"><p indent="no">Present positron impact <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
GTCS before and after correction for the forward scattering effects. Also shown is the GTCS result of Kimura <italic>et al</italic>
[<cite linkend="nj328064bib13">13</cite>
].</p>
</caption>
</figure>
</sec-level1>
<sec-level1 id="nj328064s3" label="3"><heading>Results and discussion</heading>
<p indent="no">The numerical results for the cross sections for positron scattering are shown in tables <tabref linkend="nj328064tab2">2</tabref>
–<tabref linkend="nj328064tab4">4</tabref>
for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and tables <tabref linkend="nj328064tab5">5</tabref>
–<tabref linkend="nj328064tab7">7</tabref>
for HCOOH, respectively. The order of the discussion that follows is that the GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results are presented for each molecule separately, in comparison with data from the literature. This is followed by discussions of the behavior of the cross sections at and near the thresholds for ionization and Ps formation. A comparative study of the <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
for these two molecules is then carried out, before finishing off with a discussion of the results after the forward scattering effect correction has been made.</p>
<sec-level2 id="nj328064s3.1" label="3.1"><heading>H<inline-eqn><math-text><sub>2</sub>
</math-text>
</inline-eqn>
O cross sections</heading>
<sec-level3 id="nj328064s3.1.1" label="3.1.1"><heading>GTCS and <inline-eqn><math-text><italic>GTCS</italic>
−<italic>Q</italic>
<sub><italic>Ps</italic>
</sub>
</math-text>
</inline-eqn>
</heading>
<p indent="no">Figure <figref linkend="nj328064fig1">1</figref>
shows a plot of the present GTCS and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results for positron scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
, with earlier experimental results due to Kimura <italic>et al</italic>
[<cite linkend="nj328064bib13">13</cite>
], Zecca <italic>et al</italic>
[<cite linkend="nj328064bib14">14</cite>
], Beale <italic>et al</italic>
[<cite linkend="nj328064bib15">15</cite>
], and the theoretical elastic integral cross sections (ECS) of Gianturco <italic>et al</italic>
[<cite linkend="nj328064bib34">34</cite>
] and Baluja <italic>et al</italic>
[<cite linkend="nj328064bib19">19</cite>
, <cite linkend="nj328064bib35">35</cite>
].</p>
<p>It is worth noting here that the results of Kimura <italic>et al</italic>
presented in figure <figref linkend="nj328064fig1">1</figref>
are the results of Sueoka <italic>et al</italic>
[<cite linkend="nj328064bib11">11</cite>
, <cite linkend="nj328064bib12">12</cite>
], after a forward scattering correction using electron impact elastic differential cross sections (DCS). This approach was adopted at that time simply because positron elastic DCS were unavailable. As such, the Kimura <italic>et al</italic>
data represent that group's preferred results for this target. Therefore, in the discussions that follow we only make comparison with their data. The present GTCS data monotonically decrease from 0.5 eV (<inline-eqn><math-text>∼63.76 Å<sup>2</sup>
</math-text>
</inline-eqn>
) until our highest energy of 60 eV (<inline-eqn><math-text>∼7.29 Å<sup>2</sup>
</math-text>
</inline-eqn>
). Similarly, the <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data show a smooth energy dependence trend. It is characterized by the decreasing trend from 5.0 eV until it almost flattens off above 15 eV. That the present GTCS results, and those of Zecca <italic>et al</italic>
, rise significantly in magnitude as the positron energy is decreased toward 0 eV points to the importance of long-range polarization effects and<inline-eqn><math-text>/</math-text>
</inline-eqn>
or water's permanent dipole moment at these lower energies. The current GTCS values are in good agreement with those of Zecca <italic>et al</italic>
[<cite linkend="nj328064bib14">14</cite>
] up to <inline-eqn><math-text>∼8 <upright>eV</upright>
</math-text>
</inline-eqn>
. Above this energy the current results are larger in magnitude than the Zecca <italic>et al</italic>
result, with the difference increasing with increasing impact energy, to a maximum of <inline-eqn><math-text>∼12%</math-text>
</inline-eqn>
at their maximum energy point. It is likely that this difference simply reflects small differences in their respective energy-dependent angular resolutions. With our experimental technique the angular resolution becomes better with increasing energy, as can be seen in equation (<eqnref linkend="nj328064eqn2">2</eqnref>
). The present measured GTCS data differ from those of Beale <italic>et al</italic>
[<cite linkend="nj328064bib15">15</cite>
] by about a factor of two over all the energy range of overlap, probably also because of angular resolution. Below 5 eV, the present results are lower than both the close-coupling ECS results calculated by Gianturco <italic>et al</italic>
[<cite linkend="nj328064bib34">34</cite>
], using a parameter-free quantum dynamical model for the electron–positron correlations, and those by Baluja <italic>et al</italic>
[<cite linkend="nj328064bib19">19</cite>
], who performed their calculations within the fixed-nuclei approximation, corrected with the standard Born-closure formula. The present results also differ qualitatively and quantitatively from the theoretical ECS calculations of Baluja and Jain [<cite linkend="nj328064bib35">35</cite>
] who used a spherical-complex-optical-potential method. In addition, although it is not included in the plot for reasons of clarity, there is another calculation by De-Heng <italic>et al</italic>
[<cite linkend="nj328064bib36">36</cite>
], which agrees very well with the Beale <italic>et al</italic>
[<cite linkend="nj328064bib15">15</cite>
] data, but also differs from the present results. These authors employed a complex-optical-potential approach and applied the additivity rule to sum the cross sections calculated for the constituent atoms. It is intriguing to note that above 10 eV the present <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data agree in both magnitude and energy dependence with the GTCS data of Beale <italic>et al</italic>
[<cite linkend="nj328064bib15">15</cite>
]. This could be fortuitous, given that these two results are not corrected for the forward scattering effect. The result of Kimura <italic>et al</italic>
is greater than the present GTCS results over all the energy
range of overlap. However, it is not appropriate to discuss the comparison between these two results here because, as highlighted above, the Kimura <italic>et al</italic>
data have been corrected for forward scattering effects whereas the present data are not. We therefore defer discussion of the comparison with their data to section <secref linkend="nj328064s4">4</secref>
, where their data will be compared with our data after correction for the forward scattering effect.</p>
</sec-level3>
<sec-level3 id="nj328064s3.1.2" label="3.1.2"><heading>Positronium formation cross sections: <inline-eqn><math-text><italic>Q</italic>
<sub><italic>Ps</italic>
</sub>
</math-text>
</inline-eqn>
</heading>
<p indent="no">Figure <figref linkend="nj328064fig2">2</figref>
shows the present <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data in comparison with the preliminary experimental results of Murtagh <italic>et al</italic>
[<cite linkend="nj328064bib16">16</cite>
] and the theoretical results of Hervieux <italic>et al</italic>
[<cite linkend="nj328064bib18">18</cite>
]. The latter authors employed the so-called independent electron model in which the wavefunction of the water molecule was described by a linear combination of atomic orbitals centered on the oxygen atom. In their <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
determination, Hervieux <italic>et al</italic>
[<cite linkend="nj328064bib18">18</cite>
] evaluate contributions from different initial molecular orbitals. They present <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data for ground state Ps formation (Ps(1s)), and Ps formation in the 2s excited states (Ps(2s)). Their data shown in figure <figref linkend="nj328064fig2">2</figref>
represent their total <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
, i.e. for <inline-eqn><math-text><upright>Ps</upright>
(1<upright>s</upright>
)+<upright>Ps</upright>
(2<upright>s</upright>
)</math-text>
</inline-eqn>
. Our measured <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data, and those of Murtagh <italic>et al</italic>
[<cite linkend="nj328064bib16">16</cite>
], represent the sum of all possible Ps formation pathways.</p>
<p>There is a fair agreement between the present results and those of the UCL group, Murtagh <italic>et al</italic>
, for the energy dependence of <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
below 45 eV, albeit with some subtle qualitative and quantitative differences. The threshold for Ps formation in <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
, <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
, is at 5.821 eV. The results by the UCL group show a nonzero <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
value at their lowest energy of 4 eV. In contrast, the current results show a cross section of <inline-eqn><math-text>∼0 Å<sup>2</sup>
</math-text>
</inline-eqn>
at 5 eV, i.e. the lowest energy point presented in this figure. Both results show the broad peak in the cross-section spanning the energy range of <inline-eqn><math-text>∼10–30 <upright>eV</upright>
</math-text>
</inline-eqn>
, albeit with varying magnitude differences, amounting to <inline-eqn><math-text>∼30%</math-text>
</inline-eqn>
at 14 eV, and increasing to <inline-eqn><math-text>∼70%</math-text>
</inline-eqn>
at 43 eV. The difference between the current results and the theoretical values of Hervieux <italic>et al</italic>
is obvious below 50 eV. Above this energy, however, there is better agreement as the theoretical result crosses over the current <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
curve to become larger in magnitude. An intriguing observation is that these theoretical <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data show an <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
of <inline-eqn><math-text>∼12.7 <upright>eV</upright>
</math-text>
</inline-eqn>
. That the theoretical <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
is almost equal to the ionization potential of the highest occupied molecular orbital in <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
(<inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
=12.621 <upright>eV</upright>
</math-text>
</inline-eqn>
) perhaps highlights one of the common problems that theory has in handling Ps formation below <inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
</math-text>
</inline-eqn>
. In this region the Ps formation channel competes with the elastic and any open inelastic channel, making it difficult for theoretical treatments as this requires a two-centre expansion for accurate calculations. However, even above the <inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
</math-text>
</inline-eqn>
, the theoretical values are considerably smaller than the current <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
values below 50 eV.</p>
</sec-level3>
<sec-level3 id="nj328064s3.1.3" label="3.1.3"><heading>Ps formation and ionization threshold regions</heading>
<p indent="no">In figures <figref linkend="nj328064fig3">3</figref>
and <figref linkend="nj328064fig4">4</figref>
, we present GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results in the vicinity of <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
</math-text>
</inline-eqn>
for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
. In particular, the energy region from <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
through to the first electronic excitation energy, called the Ore-gap, is of interest to us following predictions and<inline-eqn><math-text>/</math-text>
</inline-eqn>
or observations of channel coupling effects in similar regions in He [<cite linkend="nj328064bib37">37</cite>
] and Ar and Xe [<cite linkend="nj328064bib38">38</cite>
].</p>
<p>In principle, there is a chance of these effects occurring at the opening of every inelastic channel, and thus our choice of the current measurements around <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
</math-text>
</inline-eqn>
, which are expected to be the most significant in terms of the size of the cross-section contribution to the GTCS. Conclusions on the existence of these effects have been drawn from the observed <inline-eqn><math-text>∼25%</math-text>
</inline-eqn>
decrease in <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data in the Ore-gap to produce the reported cusp in He [<cite linkend="nj328064bib37">37</cite>
], and the sharp (<inline-eqn><math-text>∼50%</math-text>
</inline-eqn>
) rise in <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
in the Ore-gap observed in Ar and Xe [<cite linkend="nj328064bib38">38</cite>
], where it was attributed to virtual Ps formation. Figure <figref linkend="nj328064fig3">3</figref>
shows that the Ps formation channel opens up and increases smoothly in cross-section magnitude with no obvious features. In addition, the <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
values gradually become smaller than the GTCS values. There is no sudden change of slope in this cross-section curve that would be indicative of any channel coupling effects similar to those reported for He [<cite linkend="nj328064bib37">37</cite>
] and Ar and Xe [<cite linkend="nj328064bib38">38</cite>
]. The results in figure <figref linkend="nj328064fig4">4</figref>
again show no such signatures of channel coupling around <inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
</math-text>
</inline-eqn>
, with all three cross-section curves being almost flat across the whole energy region investigated, i.e. from 0.5 eV below to 0.5 eV above <inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
</math-text>
</inline-eqn>
. In addition, based on these GTCS and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data, there is no peak feature in the cross sections that could be interpreted as evidence for any resonances.</p>
</sec-level3>
<sec-level3 id="nj328064s3.1.4" label="3.1.4"><heading>The energy region 3–4 eV</heading>
<p indent="no">In figure <figref linkend="nj328064fig5">5</figref>
, we present the current GTCS results, measured with a finer energy increment of 50 meV, over the energy region from 3 to 4 eV, in comparison with similar results by Zecca <italic>et al</italic>
[<cite linkend="nj328064bib14">14</cite>
].</p>
<p>The reason for this investigation is that Zecca <italic>et al</italic>
reported a feature centered at <inline-eqn><math-text>∼3.5 <upright>eV</upright>
</math-text>
</inline-eqn>
, observed as a 10% increase in their GTCS, which they reported to be above their statistical uncertainty, reproducible, and not due to any experimental artifact. This would be an important observation of a resonance feature in positron scattering from <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
. We also carried out several experimental runs at different times and got reproducible results, whose error-weighted average is shown in figure <figref linkend="nj328064fig5">5</figref>
. The present GTCS results do not show the structure observed by these authors at 3.5 eV. However, they do show some structures that are above statistics, centered at <inline-eqn><math-text>∼3.65 <upright>eV</upright>
</math-text>
</inline-eqn>
and 3.85 eV. Though not shown in the plot, we tried shifting the Zecca <italic>et al</italic>
data upwards in energy by 150 meV (which is within their stated uncertainty on their energy calibration) and compared it with the current results. That analysis shows the feature they report falling on and resembling the one we observe at <inline-eqn><math-text>∼3.65 <upright>eV</upright>
</math-text>
</inline-eqn>
. In addition, their data shows a change of slope that is similar to what we observe at <inline-eqn><math-text>∼3.85 <upright>eV</upright>
</math-text>
</inline-eqn>
. More experiments are needed, perhaps in discrete scattering channels, to study these features in better detail in order to understand their exact nature and origin. For example, in this energy region where only the elastic scattering channel is open, elastic scattering via resonances is in general masked by the direct elastic component. However, resonances can be clearly revealed in vibrational excitation functions.</p>
</sec-level3>
</sec-level2>
<sec-level2 id="nj328064s3.2" label="3.2"><heading>HCOOH cross sections</heading>
<sec-level3 id="nj328064s3.2.1" label="3.2.1"><heading>GTCS, <inline-eqn><math-text><italic>GTCS</italic>
−<italic>Q</italic>
<sub><italic>Ps</italic>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><italic>Ps</italic>
</sub>
</math-text>
</inline-eqn>
</heading>
<p indent="no">Figures <figref linkend="nj328064fig6">6</figref>
(a) and (b) show the present results for positron scattering from HCOOH, with earlier experimental GTCS results due to Kimura <italic>et al</italic>
[<cite linkend="nj328064bib13">13</cite>
] and Zecca <italic>et al</italic>
[<cite linkend="nj328064bib6">6</cite>
]. Also included in this plot are the Schwinger multichannel theoretical ECS presented in [<cite linkend="nj328064bib6">6</cite>
]. The current GTCS and these two previous experimental results have not been corrected for forward scattering effects. The present GTCS result agrees well, within experimental error, with that of Kimura <italic>et al</italic>
at all energies of overlap above 8.5 eV, with agreement below this energy being marginal. This contrasts with the agreement seen with the results of Zecca <italic>et al</italic>
which is good between about 4 eV and 25 eV, particularly when the total, rather than just statistical, errors on the Trento data are considered. Similar to the case of <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
the current GTCS results are greater in magnitude than those of Zecca <italic>et al</italic>
above 25 eV, with the difference increasing with increasing impact energy, to a maximum of <inline-eqn><math-text>∼10%</math-text>
</inline-eqn>
at their common maximum energy point. We interpret this difference to be due to the same sort of angular resolution issue highlighted above. In principle, this is the same type of situation for the Kimura <italic>et al</italic>
results, so that the broad agreement observed here is much harder to understand.</p>
<p>Figure <figref linkend="nj328064fig6">6</figref>
(b) shows the results over the energy region below 30 eV. It is also worth noting that, despite differences in magnitude between the current GTCS results and those of Kimura <italic>et al</italic>
below 7.5 eV, their data only exhibit the dipole- and<inline-eqn><math-text>/</math-text>
</inline-eqn>
or polarizability-induced enhancement of the GTCS at energies below 4 eV. Contrary to the current GTCS results, in both the Zecca <italic>et al</italic>
and Kimura <italic>et al</italic>
data, a minimum, or change of slope, is observable at <inline-eqn><math-text>∼4.3 <upright>eV</upright>
</math-text>
</inline-eqn>
, which they attribute to the opening of the Ps formation channel. In our experimental technique, the GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data are measured simultaneously, but independently. The lack of an observable change of slope at <inline-eqn><math-text>∼4.5 <upright>eV</upright>
</math-text>
</inline-eqn>
in our GTCS is also consistent with the rapidly decreasing <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
in combination with the rapidly rising <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
. The current GTCS results also differ in both magnitude and energy dependence with the Schwinger multichannel theoretical ECS.</p>
<p>The <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data show no peculiar structure across the whole energy range of measurements. It rises rapidly from threshold, at <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
(=4.53 <upright>eV</upright>
)</math-text>
</inline-eqn>
and reaches a maximum at about <inline-eqn><math-text><italic>E</italic>
<sub><upright>ion</upright>
</sub>
(=11.33 <upright>eV</upright>
)</math-text>
</inline-eqn>
. Above 15 eV, it decreases almost linearly all the way to 60 eV. Similarly, the <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data is also smooth, decreasing rapidly with increasing energy above <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
, and then increasing slowly in magnitude above 15 eV. We note that there are no other measurements of calculations that we can compare the present HCOOH <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data against at this time.</p>
</sec-level3>
<sec-level3 id="nj328064s3.2.2" label="3.2.2"><heading>Ps formation threshold region</heading>
<p indent="no">Figure <figref linkend="nj328064fig7">7</figref>
shows the present GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results in the vicinity of <inline-eqn><math-text><italic>E</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
for HCOOH. We have carried out an investigation similar to that presented for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
earlier, searching for any signatures of positron resonances or temporary bound states as this inelastic channel opens up. Over the 4–5.5 eV energy range, the <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results show that the Ps formation channel opens up very slowly. There is no sudden change of slope in the <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
cross-section curve that would be indicative of any channel coupling or resonance effects.</p>
</sec-level3>
</sec-level2>
</sec-level1>
<sec-level1 id="nj328064s4" label="4"><heading>Forward scattering effect correction: GTCS and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
</heading>
<p indent="no"> Figures <figref linkend="nj328064fig8">8</figref>
and <figref linkend="nj328064fig9">9</figref>
show the results of a forward scattering correction to the GTCS. Note that we have chosen not to plot the <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
data for reasons of clarity of the graphs, and also since these <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
cross sections will be changed by the same absolute values as their corresponding GTCS counterparts. As highlighted in section <secref linkend="nj328064s2">2</secref>
, the forward scattering effects are due to positrons elastically scattered into the experimentally inaccessible angular range <inline-eqn><math-text>0°−&thetas;<sub><upright>max</upright>
</sub>
</math-text>
</inline-eqn>
, i.e. see equation (<eqnref linkend="nj328064eqn2">2</eqnref>
). Therefore this only affects the elastic scattering cross section, by causing it to be underestimated, and thus the correction needs only be done for the measured GTCS and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
.</p>
<figure id="nj328064fig9" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="25.6pc" printcolour="no" filename="images/nj328064fig9.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" printcolour="no" filename="images/nj328064fig9.jpg"></graphic-file>
</graphic>
<caption type="figure" id="nj328064fc9" label="Figure 9"><p indent="no">Same caption as figure <figref linkend="nj328064fig8">8</figref>
, but now for HCOOH.</p>
</caption>
</figure>
<p>The results for both <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
and HCOOH show that the correction leads to an increase in the GTCS values, with the percentage increase decreasing with increasing impact energy. For <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
this increase is still 12.5% at 60 eV, i.e. non-negligible. In comparison, the increases in HCOOH are 0.9% at 15 eV, and less than 1% above this energy. That is, the forward scattering correction for HCOOH becomes negligible above 15 eV, but remains significant over all the current energy range for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
. As shown in table <tabref linkend="nj328064tab1">1</tabref>
, since the experimental configuration and thus range of missing angles were the same for these two targets, these differences in the correction rates directly reflect on the differences in the magnitude and angular dependence of the elastic DCS for these two targets [<cite linkend="nj328064bib31">31</cite>
, <cite linkend="nj328064bib32">32</cite>
].</p>
<p>In figure <figref linkend="nj328064fig8">8</figref>
, we have also included the results of Kimura <italic>et al</italic>
[<cite linkend="nj328064bib13">13</cite>
], i.e. these authors' result after correction for the forward scattering effects in their apparatus. The general qualitative and quantitative agreement between their result and the current corrected GTCS results is very good, but perhaps not surprising. This is because these authors used electron impact <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
elastic DCS to correct their measured positron GTCS, which we find is quite similar in shape and magnitude to the calculated positron impact elastic DCS that we have employed in the present corrected positron GTCS data.</p>
</sec-level1>
<sec-level1 id="nj328064s5" label="5"><heading>Conclusions</heading>
<p indent="no">In this paper, we present high energy resolution measurements of GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
results for positron scattering from HCOOH and <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
molecules over the energy range 4–60 eV and 0.5–60 eV, respectively. The GTCS results for <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
were characterized by a sharply rising trend below about 6 eV, which was attributed to the dipole moment and<inline-eqn><math-text>/</math-text>
</inline-eqn>
or dipole polarizability for this strongly polar molecule. However, in the limit of the current lowest measurement energy of 4 eV for HCOOH, this effect could not be observed for that molecule. We note that such a strongly increasing GTCS for impact energies below 4 eV was observed by both Kimura <italic>et al</italic>
[<cite linkend="nj328064bib13">13</cite>
] and Zecca <italic>et al</italic>
[<cite linkend="nj328064bib6">6</cite>
] in HCOOH. Measurements have also been carried out to investigate the behavior of GTCS, <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
and <inline-eqn><math-text><italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
in the vicinity of the Ps formation and ionization thresholds. No evidence of channel coupling or resonance features has been observed for either target. The Ps formation cross section has been found to be approximately two times greater in magnitude for HCOOH than <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
.</p>
<p>Plans are underway to extend these measurements to cover elastic differential cross sections. In addition to the deeper fundamental insight that these can provide, they will also assist in the correct evaluation of the corrections due to forward scattering, that need to be applied to the current GTCS, and <inline-eqn><math-text><upright>GTCS</upright>
−<italic>Q</italic>
<sub><upright>Ps</upright>
</sub>
</math-text>
</inline-eqn>
, at lower energies. Vibrational excitation cross-section measurements are also planned and these may also prove more conclusive with regard to the existence, or otherwise, of quasi-bound states or resonances.</p>
<p>Another aspect of the work that is under way is the application of the newly measured cross sections in models of positron transport in water vapor and eventually in liquid water. Special properties of such transport phenomena have been found due to large non-conservative Ps formation cross sections in argon and hydrogen [<cite linkend="nj328064bib39">39</cite>
]–[<cite linkend="nj328064bib41">41</cite>
]. We may predict, based on the shape of the cross sections only, that the negative differential conductivity (reduction of the drift velocity with the increasing density normalized electric field <inline-eqn><math-text><italic>E</italic>
/<italic>N</italic>
</math-text>
</inline-eqn>
) will not be as strong as for argon due to greater relative magnitudes of the grand total and Ps formation cross sections which are less pronounced in <inline-eqn><math-text><upright>H</upright>
<sub>2</sub>
<upright>O</upright>
</math-text>
</inline-eqn>
. Whether the effect will exist at all will depend on the relative importance of the inelastic channels such as vibrational excitation, electronic excitations and dissociation to the Ps formation channel. Application of the cross sections found here for the actual liquid medium would require modification of the cross sections mostly at low energies to take into account multiple scattering at high target densities. Thus, one would need an analysis such as that carried out by White and Robson [<cite linkend="nj328064bib42">42</cite>
] but for polar molecules. Still the high density effects are likely to affect the effective cross sections only at energies lower than the threshold for Ps formation.</p>
</sec-level1>
<acknowledgment><heading>Acknowledgments</heading>
<p indent="no">We acknowledge the funding of the Australian Research Council's Centre of Excellence Program. We are also indebted to Graeme Cornish, Stephen Battisson, Ross Tranter and Ron Cruikshank for their excellent technical skills and on-going support. CM and JPS are grateful to the Australian Research Council for financial support under the APD and ARF programs, respectively. AB and ZP would like to acknowledge funding under the MNTRS 141025 Project. KLN thanks the DIISR for her ISL funding. We thank Dr Marcio H F Bettega and Professor Jonathan Tennyson for carrying out positron elastic DCS calculations, and supplying us with the tabulated data prior to publication, and for useful discussions concerning the results. We are also grateful to Professor Osamu Sueoka for providing us with numerical values of their data presented in this paper.</p>
</acknowledgment>
</body>
<back><references><heading>References</heading>
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<first-names>B</first-names>
</au>
<au><second-name>Cloutier</second-name>
<first-names>P</first-names>
</au>
<au><second-name>Hunting</second-name>
<first-names>D</first-names>
</au>
<au><second-name>Huels</second-name>
<first-names>M A</first-names>
</au>
<au><second-name>Sanche</second-name>
<first-names>L</first-names>
</au>
</authors>
<year>2000</year>
<jnl-title>Science</jnl-title>
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<mods version="3.6"><titleInfo lang="eng"><title>Total and positronium formation cross sections for positron scattering from H2O and HCOOH</title>
</titleInfo>
<titleInfo type="abbreviated"><title>Positron Scattering from H2O and HCOOH</title>
</titleInfo>
<titleInfo type="alternative" lang="eng"><title>Total and positronium formation cross sections for positron scattering from H2O and HCOOH</title>
</titleInfo>
<name type="personal"><namePart type="given">Casten</namePart>
<namePart type="family">Makochekanwa</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia</affiliation>
<affiliation>Author to whom any correspondence should be addressed.</affiliation>
<affiliation>E-mail: cxm107@physics.anu.edu.au</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Ana</namePart>
<namePart type="family">Bankovic</namePart>
<affiliation>Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, POB 68, 11080 Zemun, Serbia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Wade</namePart>
<namePart type="family">Tattersall</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia</affiliation>
<affiliation>ARC Centre for Antimatter-Matter Studies, James Cook University, Townsville 4810, Australia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Adric</namePart>
<namePart type="family">Jones</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Peter</namePart>
<namePart type="family">Caradonna</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Daniel S</namePart>
<namePart type="family">Slaughter</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Kate</namePart>
<namePart type="family">Nixon</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, School of Chemistry, Physics and Earth Sciences, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Michael J</namePart>
<namePart type="family">Brunger</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, School of Chemistry, Physics and Earth Sciences, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Zoran</namePart>
<namePart type="family">Petrovic</namePart>
<affiliation>Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, POB 68, 11080 Zemun, Serbia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">James P</namePart>
<namePart type="family">Sullivan</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Stephen J</namePart>
<namePart type="family">Buckman</namePart>
<affiliation>ARC Centre for Antimatter-Matter Studies, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia</affiliation>
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<abstract>Total and positronium formation cross sections have been measured for positron scattering from H2O and HCOOH using a positron beam with an energy resolution of 60meV (full-width at half-maximum (FWHM)). The energy range covered is 0.560eV, including an investigation of the behavior of the onset of the positronium formation channel using measurements with a 50meV energy step, the result of which shows no evidence of any channel coupling effects or scattering resonances for either molecule.</abstract>
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<titleInfo type="abbreviated"><title>New J. Phys.</title>
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<identifier type="ISSN">1367-2630</identifier>
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<part><date>2009</date>
<detail type="volume"><caption>vol.</caption>
<number>11</number>
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<detail type="issue"><caption>no.</caption>
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