On the nature of the decay phonon spectrum in superfluid helium helium

It is shown that the decay character of the phonon spectrum in superfluid helium is a consequence of the analyticity and parity of the boson self-energy as a function of energy and momentum. Previous self-consistent numerical calculations have shown that because of the strong interaction between the particles in Bose-Einstein condensate the normal and anomalous boson self-energies are analytical functions of the momentum and energy and on the mass shell, in the long-wavelength limit, they depend only on the squared momentum. It is shown on this basis that the phonon spectrum of a bose liquid is a decay spectrum in complete agreement with the experimental data on neutron scattering and the interaction of the high- and low-frequency phonons in superfluid helium. (c) 2010 American Institute of Physics. [doi:10.1063/1.3481582]