Studies in the Method of Correlated Basis Functions

In this paper exploratory studies are begun on various physical systems within the method of Correlated Basis Functions (CBF) developed by Feenberg and Clark. The purpose of these studies is two-fold: first, to test the CBF method on real many-body systems of current interest and second to provide additional theoretical framework through which CBF theory may be better understood. The ('16)O nucleus is studied first: the variational ground-state energy of the system is calculated assuming simple model two-nucleon interactions. Some low-lying odd-parity excitations of ('16)O are then computed using a simplified CBF configuration-mixing approach. The results are compared with an equally simplified Brueckner-Bethe theory calculation done by earlier workers. Second, a generalized Holstein-Primakoff (HP) theory is worked out for the N-body Bose system. A variant of earlier hydrodynamic approaches to the interacting Bose gas is derived which is free of operator-ordering difficulties. The HP theory is further extended to derive a correlated time -dependent Hartree-Fock approximation (TDHF); this is shown to lead to the Bijl-Feynman phonon-roton spectrum. The correlated TDHF approach is next applied to the one-dimensional planar ferromagnet CsNiF(,3). The approach yields a spectrum of elementary excitations in this system in good quantitative agreement with currently available experimental data. Lastly, the HP theory is worked out for interacting N-body Fermi systems. This theory extends earlier derivations of the random phase approximation (RPA): calculation of systematic corrections to the RPA is reduced to ordinary perturbation theory.