Collective oscillations at long wavelengths in liquid4He

The recent successful calculation of the lower collective branch of the excitation spectrum in liquid ⁴ He by Sunakawaet al. contains a phenomenological parameter (k) whose relation to microscopic theory is obscure. To clarify matters, an exact identity is presented for the absorptive part of the density-density correlation function and is employed to show that Pines' zero-sound concept of the phonon in liquid ⁴ He is accurate in the limit of infinitely long wavelengths. Since the zero-sound theory can be made to produce an explicit relation between (k) and the two-particle potential in the liquid, the foundation has been laid for a microscopic expression for the excitation spectrum in the range of very low wave numbers, where the classic Feynman theory of the phonon is known to be accurate. A numerical calculation of (k) using this expression results in a theoretical excitation spectrum which is in excellent agreement with neutron scattering measurements in the regionk0.4 Å ^–1 .