Bound Roton Pairs in Superfluid Helium

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Abstract
It has recently been proposed that several anomalous features in Raman and neutron scattering experiments on superfluid helium can be explained by the formation of two-roton bound states. In the present paper we analyze in detail the structure in the superfluid helium excitation spectrum associated with bound roton pairs and propose further experiments to examine the nature of the bound states. The two-roton spectrum is calculated including roton-roton interactions over a wide momentum range, and exhibits structure due to bound states which is in remarkable agreement with experiment. Interaction of the two-roton bound state with the single-particle excitations results in a hybridization of these states and a consequent splitting of the single-particle spectrum into two branches; the calculated momentum dependence of these branches is consistent with the neutron data. Inclusion of a finite roton lifetime is shown to be essential to the interpretation of the experimentally observed excitation spectrum in the vicinity of the bound-state energy. Possible physical mechanisms for the roton-roton interaction are considered, and the angular momentum character of the bound states is briefly discussed.