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Quantum Statistics and Slow Neutron Scattering by Gases
dc.contributor.authorPlummer, J. P.en_US
dc.contributor.authorSummerfield, G. C.en_US
dc.contributor.authorZweifel, Paul Fredericken_US
dc.date.accessioned2010-05-06T22:51:44Z
dc.date.available2010-05-06T22:51:44Z
dc.date.issued1967-12-15en_US
dc.identifier.citationPlummer, J. P.; Summerfield, G. C.; Zweifel, P. F. (1967). "Quantum Statistics and Slow Neutron Scattering by Gases." The Journal of Chemical Physics 47(12): 4923-4929. <http://hdl.handle.net/2027.42/70882>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70882
dc.description.abstractA surprisingly simple expression in ``closed form'' for the cross section d2σ/dΩdϵ for the scattering of thermal neutrons (including polarized neutrons) from an ideal quantum gas is derived. This result extends the work of Van Hove on the quantum gas. An expansion is obtained for dσ/dϵ. The case of elastic scattering is treated separately. From these expressions is obtained a criterion for ignoring the statistics of the scatterer in favor of classical (Boltzmann) statistics. This criterion should have some validity for weakly interacting systems. It is shown that the effects of statistics on the neutron cross section for a helium‐4 gas range from 5% or less for the noninteracting gas up to as much as 40% for the interacting system.en_US
dc.format.extent3102 bytes
dc.format.extent495124 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleQuantum Statistics and Slow Neutron Scattering by Gasesen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Nuclear Engineering, The University of Michigan, Ann Arbor, Michiganen_US
dc.contributor.affiliationotherDepartment of Physics, Queens College, City University of New York, Flushing, New Yorken_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70882/2/JCPSA6-47-12-4923-1.pdf
dc.identifier.doi10.1063/1.1701741en_US
dc.identifier.sourceThe Journal of Chemical Physicsen_US
dc.identifier.citedreferenceM. Nelkin, Phys. Rev. 127, 979 (1962); W. E. Parry and R. E. Turner, Ann. Phys. (N.Y.) 17, 301 (1962); J. A. Young and J. U. Koppel, Phys. Rev. 135, A603 (1964).en_US
dc.identifier.citedreferenceS. K. Sinha and G. Venkataraman, Phys. Rev. 149, 1 (1966); P. Michael, 138, A692 (1965).en_US
dc.identifier.citedreferenceP. M. Morse, Thermal Physics (W. A. Benjamin, Inc., New York, 1964).en_US
dc.identifier.citedreferenceG. Placzek, Proc. Symp. Math. Statistics Probability 2nd Berkeley, Calif., 69 (1951).en_US
dc.identifier.citedreferenceL. Van Hove, Phys. Rev. 95, 249 (1954).en_US
dc.identifier.citedreferenceSee, for example, R. J. Glauber, in Lectures in Theoretical Physics (Interscience Publishers, Inc., New York, 1962), Vol. 4.en_US
dc.identifier.citedreferenceSee D. Falkoff, “The N‐Body Problem,” in The Many Body Problem, Christian Fronsdal, Ed. (W. A. Benjamin, Inc., New York, 1962).en_US
dc.identifier.citedreference(a) See J. P. Plummer, thesis, The University of Michigan, 1964; (b) J. P. Plummer, Idaho Nuclear Corp. Rept. (unpublished).en_US
dc.identifier.citedreferenceThis sign convention is observed throughout this paper.en_US
dc.identifier.citedreferenceSee, for example, S. Yip, R. K. Osborn, and C. Kikuchi, “Neutron Acoustodynamics,” University of Michigan Rept. No. IP‐524, Chap. 8 (1961).en_US
dc.identifier.citedreferenceThere is an apparent oversight in Ref. 5. In the definition of a quantity called n±(r,t),n±(r,t), and later n(r, t) for the condensed‐phase BE gas, a factor of (2S0+1)(2S0+1) is missing. Also Van Hove absorbs a factor of (2πℏ/m)(2πℏ∕m) into his definition of the scattering length a.en_US
dc.identifier.citedreferenceEquations (8) and (9) must be divided by N, the number of scatterers, to give the cross section per atom.en_US
dc.identifier.citedreferenceE. P. Wigner and J. E. Wilkins, Jr., U.S. Atomic Energy Commission Rept. No. AECD‐2275 (1944).en_US
dc.identifier.citedreferenceArgon, Helium, and the Rare Gases G. A. Cook, Ed. (Interscience Publishers, Inc., New York, 1961), Vol. 1.en_US
dc.owningcollnamePhysics, Department of


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