Two-particle-two-hole excitations in ³He

We describe the development of a systematic theory of excitations in strongly interacting Fermi systems. Technically, we derive the equations of motion for multi-pair excitations from a stationarity principle. This method has, in Fermi systems, so far been developed only to the level of one-particle-one-hole excitations, where it leads to the (correlated) random phase approximation (RPA). We extend the analysis here to pair excitations. Our work is motivated by the fact that time-dependent pair correlations are necessary for explaining the physics of the phonon-roton spectrum in ⁴He. It is therefore plausible that the same processes also have visible effects in the excitation spectrum of ³He. Further motivation is derived from recent measurements of the dynamic structure function in two-dimensional ³He. We first formulate the theory for a second quantized, weakly interacting Hamiltonian and then generalize the theory to a correlated ground state. We show that the inclusion of Jastrow-Feenberg type correlations leads to prescriptions for calculating weak effective interactions from a microscopic, strongly interacting Hamiltonian.