A Study of Elementary Excitations of Liquid Helium-4 Using Macro-orbital Microscopic Theory

Energy of elementary excitations and the anomalous nature of small Q phonons in He-II are studied by using our macro-orbital microscopic theory of a system of interacting bosons (cond-mat/0606571). It is observed that : (i) the experimental E(Q) of He-II not only agrees with our theoretical relation $E(Q) = \hbar^2Q^2/4mS(Q)$ but also supports an important conclusion of Price that S(0) should have zero value for quantum fluids, and (ii) Feynman’s energy of excitations $E(Q{)}_{Fyn}={\mathrm{\hslash }}^2{Q}^2\mathrm{/}2mS(Q)$ equals approximately to $2E(Q{)}_{exp}$ even at low Q. Three problems with the Feynman’s inference that $E(Q{)}_{Fyn}$ has good agreement with $E(Q{)}_{exp}$ at low Q are identified. It is argued that the theory can also be used to understand similar spectrum of the BEC state of a dilute gas reported by O’Dell et al.