Excitation spectrum for interacting bosons

Abstract

The energy excitation spectrum of a system of bosons interacting through a two-body potential composed of a hard core followed by a sum of two gaussians and having a density equal to that of liquid 4He at the lambda transition temperature ( ϱ λ = 2.06 x 10 22 particles/ cm 3) is obtained using the reaction matrix formalism. The spectrum gives not only a qualitative agreement, showing the “phonon” branch and the “roton” dip clearly, but also a quantitative agreement when compared with the experimental energy excitation spectrum for liquid 4He. The maximum and the minimum of the theoretical energy excitation spectrum occur at k = 1.1 A ̊ -1 , E k/ℵ = 13.56 K , and at k = 1.9 A ̊ -1 , E k/ℵ = 8.692 K , respectively. These values compare very favourably with the experimental values which are maximum at k = 1.1 A ̊ -1 , E k/ℵ = 13.7 K , and minimum at k = 1.91 A ̊ -1 , E k/ℵ = 8.65 K . To obtain good experimental agreement, the other parameters are m ∗/m = 1.2 and the hard-core diameter a = 2.1 A ̊ .