Calculation of binding energy of the 16O nucleus

Abstract

A method to calculate binding energies of nuclei by K-matrix theory is presented and applied to 16O. A first-order approximation to the K-matrix is obtained by neglecting the Pauli principle and potential energies in intermediate states. Thus to first order we consider the Puff-Mohling reaction matrix. In light of recent work on the effect of the three-body interaction it seems a reasonable approximation to neglect potential energies in intermediate states. Thus the only correction term is due to the Pauli principle. The method is however easily extended to a more general energy spectrum. It can be applied to finite nuclei as well as to infinite nuclear matter. Formally our method to calculate the K-matrix is similar to the “reference spectrum” method of Bethe, Brandow and Petschek applied by them to infinite nuclear matter. We apply our method to 16O using harmonic oscillator single-particle wave functions and a nucleon-nucleon interaction represented by a spin independent exponential potential giving infinite scattering length and 2.5 fm effective range (Moszkowski-Scott potential) acting only in relative s-states. A binding energy of 2.77 MeV/nucleon is obtained. The Puff-Mohling K-matrix, i.e. our first-order K-matrix, gives 1.7 MeV/nucleon more binding. Comparison with the in principle more approximate separation method calculation gives perfect agreement.