CORRELATED-STATE EVALUATION OF THE 2ND VIRIAL-COEFFICIENT

The difference R(z) between the resolvents of the interacting and free Hamiltonians is inherently associated with (pair) particle correlations and can also be used for the evaluation of the second virial coefficient. This paper explores the operator properties of R(z) and the analytical continuation of its momentum matrix elements. Correlated-state wave functions are identified when making a pole expansion of the analytically continued matrix elements. These square-integrable wave functions have a one-to-one correspondence with resolvent poles, and as such are associated with resonance-bound-, and virtual-state momenta. Their properties and use in evaluating the second virial coefficient are discussed. Except for the bound states, these wave functions are not eigenvectors of the interacting Hamiltonian. The separable Yamaguchi potential is used to illustrate these properties.