Comparison and Appraisal of Approximation Formulas for Total Elastic Molecular Scattering Cross Sections
dc.contributor.author | Bernstein, R. B. | en_US |
dc.contributor.author | Kramer, K. H. | en_US |
dc.date.accessioned | 2010-05-06T22:19:26Z | |
dc.date.available | 2010-05-06T22:19:26Z | |
dc.date.issued | 1963-05-15 | en_US |
dc.identifier.citation | Bernstein, R. B.; Kramer, K. H. (1963). "Comparison and Appraisal of Approximation Formulas for Total Elastic Molecular Scattering Cross Sections." The Journal of Chemical Physics 38(10): 2507-2511. <http://hdl.handle.net/2027.42/70541> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/70541 | |
dc.description.abstract | The Massey—Mohr (MM), Schiff (S), and Landau—Lifshitz (LL) approximations for the total elastic cross section (Q) are intercompared. All can be shown to follow from the same assumption, (i.e., the classical small‐angle deflection function, thence the Jeffreys—Born phases via the semiclassical equivalence relationship), sufficing to determine the velocity dependence of Q. Thus, for V=±C(s)/rs, Q(s)=p(s)[C(s)/hv ]2/(s—1) The coefficient p(s) is the same for the S and LL approximations; the ratio pSLL(s)/pMM(s)≥1, (<1.075); it is 1.0709 and 1.0458 for s=6 and 12, respectively.A numerical calculation for a repulsive (s=12) interaction shows that the SLL formula reproduces the partial‐wave calculated Q to within ☒%. A graphical presentation suggests the generality of this result; it also indicates the source of bias in the MM approximation. For a ``realistic'' intermolecular potential, (restricting consideration to collisions in the ``thermal'' energy range), the influence of the repulsion is only to produce undulations in Q(v); the correct value of C(6) may be obtained by velocity averaging the ``apparent'' CSLL(6). | en_US |
dc.format.extent | 3102 bytes | |
dc.format.extent | 300062 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Comparison and Appraisal of Approximation Formulas for Total Elastic Molecular Scattering Cross Sections | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Chemistry Departments, University of Michigan, Ann Arbor, Michigan, and University of Wisconsin, Madison, Wisconsin | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/70541/2/JCPSA6-38-10-2507-1.pdf | |
dc.identifier.doi | 10.1063/1.1733533 | en_US |
dc.identifier.source | The Journal of Chemical Physics | en_US |
dc.identifier.citedreference | H. S. W. Massey and C. B. O. Mohr, Proc. Roy. Soc. (London) A144, 188 (1934). | en_US |
dc.identifier.citedreference | H. S. W. Massey and R. A. Buckingham, Nature 138, 77 (1936). | en_US |
dc.identifier.citedreference | E. W. Rothe and R. B. Bernstein, J. Chem. Phys. 31, 1619 (1959). | en_US |
dc.identifier.citedreference | H. Schumacher, R. B. Bernstein, and E. W. Rothe, J. Chem. Phys. 33, 584 (1960). | en_US |
dc.identifier.citedreference | H. Pauly, Z. Naturforsch. 15a, 277 (1960). | en_US |
dc.identifier.citedreference | R. C. Schoonmaker, J. Phys. Chem. 65, 892 (1961). | en_US |
dc.identifier.citedreference | E. W. Rothe, P. K. Rol, S. M. Trujillo, and R. H. Neynaber, Phys. Rev. 128, 659 (1962). | en_US |
dc.identifier.citedreference | Deviations have been observed for systems in which dipole‐dipole forces play a role4 and for systems involving the lighter atoms.7,9–11. For the latter case the deviations are satisfactorily explained in a semiquantitative way.12,13. | en_US |
dc.identifier.citedreference | H. U. Hostettler and R. B. Bernstein, Phys. Rev. Letters 5, 318 (1960). | en_US |
dc.identifier.citedreference | H. Harrison, J. Chem. Phys. 37, 1164 (1962). | en_US |
dc.identifier.citedreference | P. K. Rol and E. W. Rothe, Phys. Rev. Letters 9, 494 (1962). | en_US |
dc.identifier.citedreference | R. B. Bernstein, J. Chem. Phys. 37, 1880 (1962). | en_US |
dc.identifier.citedreference | R. B. Bernstein, J. Chem. Phys. 38, (1963) 38, 515 (1963). | en_US |
dc.identifier.citedreference | For a review, see H. Pauly, Fortschr. Physik 9, 613 (1961). | en_US |
dc.identifier.citedreference | E. W. Rothe, L. L. Marino, R. H. Neynaber, P. K. Rol, and M. Trujillo, Phys. Rev. 126, 598 (1962). | en_US |
dc.identifier.citedreference | R. B. Bernstein, J. Chem. Phys. 33, 795 (1960); 34, 361 (1961). | en_US |
dc.identifier.citedreference | R. Helbing and H. Pauly, Diplomarbeit (Helbing), University of Bonn, 1961. | en_US |
dc.identifier.citedreference | E. W. Rothe, P. K. Rol, and R. B. Bernstein, Phys. Rev. 129, (1963) (in press). | en_US |
dc.identifier.citedreference | R. B. Bernstein, “Semiclassical Analysis of the Extrema in the Velocity Dependence of Total Elastic Scattering Cross Sections: Relation to the Bound States,” J. Chem. Phys. (to be published). | en_US |
dc.identifier.citedreference | Used, for example, by E. A. Mason (private communication, 1962). | en_US |
dc.identifier.citedreference | L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, Ltd., London, 1959), p. 416. | en_US |
dc.identifier.citedreference | First applied to the molecular scattering problem by C. Schlier; see, for example, K. Berkling, R. Helbing, K. Kramer, H. Pauly, Ch. Schlier, and P. Toschek, Z. Physik. 166, 406 (1962); see also references 14 and 17. | en_US |
dc.identifier.citedreference | L. I. Schiff, Phys. Rev. 103, 443 (1956). | en_US |
dc.identifier.citedreference | E. H. Kennard, Kinetic Theory of Gases (McGraw‐Hill Book Company, Inc., New York, 1938). | en_US |
dc.identifier.citedreference | R. B. Bernstein, J. Chem. Phys. 36, 1403 (1962). Erratum: Eq. (7b) should read ηl=3π322μC(6)ℏ2k4(l+12)5; see reference 13 for list of other errata. | en_US |
dc.identifier.citedreference | J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954). | en_US |
dc.owningcollname | Physics, Department of |
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