Dynamic many-body theory: Pair fluctuations in bulk ⁴He

Dynamical excitations in bulk liquid ⁴He are investigated by using a manifestly microscopic theory of excitations that includes multiple-phonon scattering. The wave function of the dynamic system is represented in terms of one- and two-body excitation amplitudes. Equations of motion for the linear response of boson liquids to a scalar external field are then derived from a stationarity principle. For a consistent treatment of long- and short-wavelength properties of the excitation amplitudes we derive and solve three sets of generic “hypernetted chain” equations determining the basic ingredients of the theory. From those ingredients, we calculate a dynamic structure function for ⁴He at saturation density. It is shown that the complete solution of the hypernetted chain equations leads, partly by the cancellation of errors, to an insignificantly improved theoretical prediction for the dynamic structure function compared with approximations introduced by Jackson, Feenberg, and Campbell. The implications of this result and the need for including higher-order multiparticle fluctuations are discussed.