Total reflection as derived from statistical scattering and coherent scattering theories
Identifieur interne : 000383 ( Istex/Corpus ); précédent : 000382; suivant : 000384Total reflection as derived from statistical scattering and coherent scattering theories
Auteurs : D. A. L. PaulSource :
- Nature [ 0028-0836 ] ; 1974-11-01.
Abstract
IN the past ten years there has been much investigation of the interesting phenomenon of microscopic bubbles in liquids, particularly liquid helium, which are maintained by the presence of a light particle, such as an electron1 or positron2. In both cases, with liquid helium the bubble is believed to arise from an effective repulsive potential between bulk liquid and the light particle. Coopersmith3 derived an expression for this effective potential by calculating the free energy of a light particle moving in a space having randomly distributed hard spheres.
Url:
DOI: 10.1038/252034a0
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Rev.</title></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>252</volume><pages><last>35</last><first>34</first></pages><issn><json:string>0028-0836</json:string></issn><issue>5478</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Nature</title></host><categories><wos><json:string>science</json:string><json:string>multidisciplinary sciences</json:string></wos><scienceMetrix><json:string>general</json:string><json:string>general science & technology</json:string><json:string>general science & technology</json:string></scienceMetrix></categories><publicationDate>1974</publicationDate><copyrightDate>1974</copyrightDate><doi><json:string>10.1038/252034a0</json:string></doi><id>38BBC1FCDD04CD8C3DCAEBE0B083C4FD7847AF7D</id><score>0.5895642</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/38BBC1FCDD04CD8C3DCAEBE0B083C4FD7847AF7D/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/38BBC1FCDD04CD8C3DCAEBE0B083C4FD7847AF7D/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/38BBC1FCDD04CD8C3DCAEBE0B083C4FD7847AF7D/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Total reflection as derived from statistical scattering and coherent scattering theories</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Nature Publishing Group</publisher><availability><p>©1974 Nature Publishing Group</p></availability><date>1974</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Total reflection as derived from statistical scattering and coherent scattering theories</title><author xml:id="author-1"><persName><forename type="first">D. 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A. L.</fnm><snm>PAUL</snm><inits>D. A. L.</inits></au><aff>University Trier-Kaiserslautern, 675 Kaiserslautern, Postfach 1049, Germany</aff></aug><hst><re year="1974" month="8" day="12"></re></hst><fp><p>IN the past ten years there has been much investigation of the interesting phenomenon of microscopic bubbles in liquids, particularly liquid helium, which are maintained by the presence of a light particle, such as an electron<super>1</super> or positron<super>2</super>. In both cases, with liquid helium the bubble is believed to arise from an effective repulsive potential between bulk liquid and the light particle. Coopersmith<super>3</super> derived an expression for this effective potential by calculating the free energy of a light particle moving in a space having randomly distributed hard spheres.</p></fp></fm><bdy>
The hard spheres move as in a classical ideal gas and statistical equilibrium between light particle and gas is assumed. Only s-wave scattering was considered. The mean free energy of the light particle is found to have a minimum energy which is due to space-limitation of its motion. The interaction free energy was shown rigorously to be
EF=2nnash2/m (1)
due to single scattering, all higher order multiple scattering effects being zero. In equation (1) n is the density of scattering centres, as the scattering length and m the light particle mass. Thus a particle of mass m striking the surface of a liquid having n molecules per unit volume from outside would require a kinetic energy at least k2h2/2m=EF in order not to be totally reflected from the liquid surface. Therefore, the critical wave number for total reflection at normal incidence is given by
k2=4nnas (2)
Eighteen years earlier, Goldberger and Seitz4 investigated coherent scattering from randomly distributed scattering centres, and produced results which have, for example, been applied to neutron refraction at liquid surfaces. According to their theory a particle of mass m will be totally externally reflected when normally incident upon a liquid surface unless
k* > 2A/(7ras)1/2(3)
which agrees with equation (2) if we put ss=4pas2 and take the positive square root, indicating repulsion.
So these two strikingly different approaches yield the same result in the low energy limit, for s-wave scattering.</bdy><bm><bibl><bib id="b1"><reftxt><refau><snm>Northby</snm>, <fnm>J. A.</fnm></refau>, and <refau><snm>Sanders</snm>, <fnm>T. M.</fnm></refau>, <jtl>Phys. Rev. Lett.</jtl>, <vid>18</vid>, <ppf>1184</ppf> (<cd year="1967">1967</cd>).</reftxt></bib><bib id="b2"><reftxt><refau><snm>Briscoe</snm>, <fnm>C. V.</fnm></refau>, <refau><snm>Choi</snm>, <fnm>S.-I.</fnm></refau>, and <refau><snm>Stewart</snm>, <fnm>A. T.</fnm></refau>, <jtl>Phys. Rev. Lett.</jtl>, <vid>20</vid>, <ppf>493</ppf> (<cd year="1968">1968</cd>).</reftxt></bib><bib id="b3"><reftxt><refau><snm>Coopersmith</snm>, <fnm>M.</fnm></refau>, <jtl>Phys. Rev.</jtl> A, <vid>139</vid>, <ppf>1359</ppf> (<cd year="1965">1965</cd>).</reftxt></bib><bib id="b4"><reftxt><refau><snm>Goldberger</snm>, <fnm>M. L.</fnm></refau>, and <refau><snm>Seitz</snm>, <fnm>F.</fnm></refau>, <jtl>Phys. Rev.</jtl>, <vid>71</vid>, <ppf>294</ppf> (<cd year="1947">1947</cd>).</reftxt></bib></bibl></bm></headerx></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Total reflection as derived from statistical scattering and coherent scattering theories</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Total reflection as derived from statistical scattering and coherent scattering theories</title></titleInfo><name type="personal"><namePart type="given">D. A. L.</namePart><namePart type="family">PAUL</namePart><affiliation>University Trier-Kaiserslautern, 675 Kaiserslautern, Postfach 1049, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Letters to Nature"></genre><originInfo><publisher>Nature Publishing Group</publisher><dateIssued encoding="w3cdtf">1974-11-01</dateIssued><dateCaptured encoding="w3cdtf">1974-08-12</dateCaptured><copyrightDate encoding="w3cdtf">1974</copyrightDate></originInfo><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract>IN the past ten years there has been much investigation of the interesting phenomenon of microscopic bubbles in liquids, particularly liquid helium, which are maintained by the presence of a light particle, such as an electron1 or positron2. In both cases, with liquid helium the bubble is believed to arise from an effective repulsive potential between bulk liquid and the light particle. Coopersmith3 derived an expression for this effective potential by calculating the free energy of a light particle moving in a space having randomly distributed hard spheres.</abstract><relatedItem type="host"><titleInfo><title>Nature</title></titleInfo><genre type="journal" displayLabel="journal"></genre><identifier type="ISSN">0028-0836</identifier><part><date>1974</date><detail type="volume"><caption>vol.</caption><number>252</number></detail><detail type="issue"><caption>no.</caption><number>5478</number></detail><extent unit="pages"><start>34</start><end>35</end></extent></part></relatedItem><identifier type="istex">38BBC1FCDD04CD8C3DCAEBE0B083C4FD7847AF7D</identifier><identifier type="DOI">10.1038/252034a0</identifier><identifier type="ArticleID">252034a0</identifier><accessCondition type="use and reproduction" contentType="copyright">©1974 Nature Publishing Group</accessCondition><recordInfo><recordContentSource>NATURE</recordContentSource></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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