Abstract
The contribution of phonon-phonon interactlon to the energy of elementary excitations in liquid He/sub 4/ is evaluated in the approximation of the Brillouin-Wigner second order energy. The three-particle distribution function p(1,2,3) occurring in the interaction matrix elements is approximated by the Kirkwood superposition form and also by the convolution'' form. A generai criterion is developed to test the accuracy of possible approximations for p(1,2,3). The criterion has the form of a functional X in p(1,2,3) which vanishes if p(1,2,3) is generated by the correct ground state solution of the Schrodinger equation. If an approximate form is used the corresponding functional X/sub a/ does not vanish and thus provides a measure of accuracy. The power of this criterion resides in the fact that X/sub a/ is a function of three variabies, the magnitudes of two wave vectors and the cosine of the angle between them. The computed dispersion curves are compared with the experimental curve constructed by Henshaw and Woods from the inelastic single scattering of slow neutrons in liquid helium (auth)
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