Discussion on Excitations in Bulk ⁴He

Abstract

Halley began the discussion of the theory of excitations in Bulk ⁴He with some remarks about the nature of the theoretical problem of describing liquid ⁴He. The main point is that the helium-helium potentiate has a hard core, e.g. V(r) ∝ (σ/r)¹². This means that its Fourier transform V(Q) is extremely large (essentially infinite) at all wavelengths. A theory which expands in powers of V(Q) (as in the formulation of the Glyde-Griffin theory presented this morning) is unlikely to be reliable. The hard core problem is what stimulated Feynman and later Feenberg and others including Krotschek, Campbell, Pandharipande and Manousakis to take a different approach. The variational ground state and excited states which they find take full account of the hard core problem, so they can use microscopic atomic potentials. They then can do a convergent pertubation theory in the interactions of the approximate variational quasiparticle states. The achievements of this approach are impressive and numerous: correct ground state energy, correct phonon-roton spectrum, multiparticle terms S(q,ω), and a condensate fraction ≈ 10%. A weakness is that the theory has not been fully extended to finite temperatures.