Simplified Treatment for Strong Short-Range Repulsions inN-Particle Systems. I. General Theory

A new variational approach is developed for studying the properties of systems of particles interacting through singular short-range repulsions that give rise to strong two-particle correlations. The correlated trial function ${\Psi }_{\gamma }=e^S{\Phi }_{\gamma }$ (state $\gamma$) results, with proper choice of $S$, in a simple form for the energy expectation value $〈H〉$—as well as for other matrix elements of interest—which is devoid of all reference to the strong repulsions except through $e^{2S}$ factors and hence is particularly suited to calculation. In many cases an independent-particle type ${\Phi }_{\gamma }$ seems appropriate. The cluster evaluation of this form for $〈H〉$ is discussed, both in the few-particle and many-particle cases. Using the techniques of Iwamoto and Yamada, simplified convergent cluster expansions for the energy expectation value are derived for many-fermion and many-boson systems. A program for application of this method to nuclear problems is being initiated.