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Energy spectrum of the excitations in liquid helium

Feynman, R. P. and Cohen, Michael (1956) Energy spectrum of the excitations in liquid helium. Physical Review, 102 (5). pp. 1189-1204. ISSN 0031-899X. doi:10.1103/PhysRev.102.1189.

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A wave function previously used to represent an excitation (phonon or roton) in liquid helium, inserted into a variational principle for the energy, gave an energy-momentum curve having the qualitative shape suggested by Landau; but the value computed for the minimum energy Δ of a roton was 19.1°K, while thermodynamic data require Δ=9.6°K. A new wave function is proposed here. The new value computed for Δ is 11.5°K. Qualitatively, the wave function suggests that the roton is a kind of quantum-mechanical analog of a microscopic vortex ring, of diameter about equal to the atomic spacing. A forward motion of single atoms through the center of the ring is accompanied by a dipole distribution of returning flow far from the ring. In the computation both the two-atom and three-atom correlation functions appear. The former is known from x-rays, while for the latter the Kirkwood approximation of a product of three two-atom correlation functions is used. A method is developed to estimate and correct for most of the error caused by this approximation, so that the residual uncertainty due to this source is negligible.

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Additional Information:©1956 The American Physical Society. Received 27 February 1956. This paper is based on a Ph.D. submitted to California Institute of Technology in November, 1955. A preliminary report of this work has appeared [R.P. Feynman and Michael Cohen, Prog. Theoret. Phys. Japan 14, 261 (1955.]
Issue or Number:5
Record Number:CaltechAUTHORS:FEYpr56
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3549
Deposited By: Tony Diaz
Deposited On:14 Jun 2006
Last Modified:08 Nov 2021 19:57

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