Signal of high-energy phonons created by low-energy phonons in superfluid helium

Abstract

Starting from the solution of the kinetic equation, we have calculated the distribution function for the high-energy phonons, which are created by a short pulse of low-energy phonons moving in superfluid helium. This enables an explicit expression for the energy density flux to be derived. Hence we find the amplitude of the high-energy phonon signal as a function of time on a bolometer. We divide this signal into two halves: the ``head'' and ``tail'' which arrive before and after the peak signal, respectively. We analyze which high-energy phonons form the head and tail of the signal. The half-widths of head and tail are calculated and approximate formulas which describe the shapes of them are obtained. The partial contribution of high-energy phonons, with different momenta, to the total signal at different times is determined. These results are compared with the experimental results given in the preceding paper [R. V. Vovk, C. D. H. Williams, and A. F. G. Wyatt, Phys. Rev. B 69, 144524 (2004)].