Purdue Nuclear and Many-Body Theory Group (PNMBTG) Preprint PNMBTG-8-13 (August 2013) 1 Hartree-Fock Theory with Correlation Effects Applied to Nuclear Reaction Rates for Charged Bose Nuclei Confined in a Harmonic Trap

Abstract: Based on Hartree-Fock theory with correlations, approximate solutions of the many-body Schrödinger equation are examined for their use for calculations of nuclear reaction rates for charged Bose nuclei confined in a harmonic trap. It is shown that the nuclear reaction rate calculated with the Hartree-Fock mean field solution makes a significant contribution even in the presence of two-body correlations. The nuclear reaction rates for charged Bose nuclei confined in a harmonic trap has been calculated based on the optical theorem formulation of low-energy nuclear reactions [1] using approximate solutions of the many-body Schrödinger equation [2-15]. The effect of two-body correlations are examined in the context of the Hartree-Fock theory with correlation effects [3]. For N charged Bose nuclei (Z=1) confined in a harmonic trap, the many-body Schrödinger equation is given by H E (1