Theory of Inelastic Scattering of Cold Neutrons from Liquid Helium

Michael Cohen and Richard P. Feynman
Phys. Rev. 107, 13 – Published 1 July 1957
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Abstract

A measurement of the energy losses of monoenergetic neutrons scattered from liquid He II would permit a determination of the energy-versus-momentum relation for the elementary excitations (phonons and rotons) in the liquid. A major part of the scattering at a fixed angle arises from production or annihilation of a single excitation and appears as sharp lines in the energy spectrum. From the position of these lines the energy-versus-momentum relation of the excitations can be inferred. Other processes, such as production or annihilation of multiple excitations, contribute a continuous background, and occur at a negligible rate if the incident neutrons are slow (λ4A) and the helium cold (T<2°K). The total cross-section data can be accounted for by production of single excitations; the theoretical cross section, computed from a wave function previously proposed to represent excitations, agrees with experiment over the entire energy range, within 30%. Line widths in the discrete spectrum are negligible at 1°K because of the long lifetime of phonons and rotons.

  • Received 25 March 1957

DOI:https://doi.org/10.1103/PhysRev.107.13

©1957 American Physical Society

Authors & Affiliations

Michael Cohen* and Richard P. Feynman

  • California Institute of Technology, Pasadena, California

  • *Richard C. Tolman Fellow.

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Issue

Vol. 107, Iss. 1 — July 1957

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