# Application of the equation-of-motion method to the spectrum of superfluid helium. I

## Abstract

The two three-body correlation terms occurring in the equation of motion for the density response function are expressed in terms of three-point vertex functions. By neglecting retardation effects in the latter, this leads to frequency-dependent effective kinetic and potential energies Keff(q→, ω) and Veff(q→, ω). Keff is expressed by the one-particle correlation functions and Veff by the density correlation function. Keff and Veff determine the density response function χ(q→, ω), the poles of which define the phonon-roton spectrum ωq. In addition, an eigenvalue equation is derived which is shown to have two distinct eigenvalues. While the first is again ωq, the second is identified with the diffuse second branch recently found by Cowley and Woods. It is shown that in the limit q→ the two eigenvalues both merge into the free-particle spectrum. The limit q→0 of the two eigenvalues as well as the end-point singularity of the phonon-roton branch are discussed in a second paper. © 1972 The American Physical Society.