10 - Two-particle spectrum in Bose-condensed fluids

Summary

At many points in this book, we have mentioned the high-frequency scattering intensity which appears in the S(Q, ω) data. This high-frequency component (see Fig. 1.6) is usually identified with the spectrum of two excitations (with total momentum Q) and is thus referred to as the multiphonon or multiparticle component. In addition to inelastic neutron scattering, this two-excitation spectrum can be more directly probed by inelastic Raman light scattering, but only at Q = 0. In this chapter, we briefly review the microscopic theory of such pair excitations and how they show up in both neutron and Raman scattering cross-sections.

Raman light scattering in superfluid ⁴He has been extensively studied both theoretically and experimentally, especially with regard to the possible formation of bound states involving roton–roton, roton–maxon and maxon–maxon pairs (Ruvalds and Zawadowski, 1970; Iwamoto, 1970). High-resolution Raman experiments over a wide range of pressure and temperature are reviewed by Greytak (1978) and more recently by Ohbayashi (1989, 1991). An excellent theoretical introduction at a phenomenological level is given by Stephen (1976). Our emphasis will be on the role of the Bose broken symmetry.

In earlier chapters, we have carefully distinguished the single-particle Green's function G₁(Q, ω) (which may be a 2 × 2 matrix) and the density-response function χ_nn(Q, ω). The latter gives the dynamic structure factor measured by neutron scattering. In the present chapter, we introduce several additional correlation functions which are needed to describe the pair-excitation spectrum and Raman scattering.