Temperature and Momentum Dependence of Phonon Energies in Superfluid ⁴He

Abstract

One of the challenging theoretical problems relating to superfluid ⁴He is the detailed form of the phonon portion of the elementary excitation spectrum ε _p . For wave vectors p/ħ in the range 0.2–1.0 Å⁻¹, the inelastic neutron scattering data¹ yield ε _p = c _o p,(1 − γ p ² − δ p ⁴ − ...), where γ = (0 ± 2) × 10³⁶ g⁻² cm⁻² sec² and δ = (2.4 ± 0.2) × 10⁷⁵ g⁻⁴ cm⁻⁴ sec⁴. For these wave vectors the term γ p ² can be neglected and thus 1 − δ p ⁴ are the leading terms for ε _p /c _o p. To date no theoretical work yields 1 − δ p ⁴ as the leading terms for ε _p /c _o p.