On the spectrum of elementary excitations in superfluid helium

Abstract

Feynman has recently advanced physical arguments to deduce an approximate form for the wave function of an elementary excitation in helium. Qualitatively, his theory leads to an excitation spectrum similar to that postulated by Landau; however, serious quantitative discrepancies remain in the ‘roton ’ region of the spectrum. It is shown here that improved wave functions may be constructed by using combinations of wave functions for single and double Feynman excitations—this amounts to a self-energy correction to the roton spectrum, arising mainly from roton-phonon interactions. The numerical value of the roton energy agrees remarkably well with Landau’s value. The treatment depends, however, on the use of perturbation theory, where the perturbation is not small. Little confidence should therefore be placed in the actual value found.