Reference Spectrum Method for Nuclear Matter

Abstract

A new method is presented for the calculation of the reaction matrix $G$ of the Brueckner-Goldstone theory. The spectrum of the intermediate states is replaced by a "reference spectrum" of the form $A+B{k}^2$ where the constants $A$ and $B$ are chosen so as to approximate, as closely as possible, the actual particle energies for $k$ between 3 and 6 ${\mathrm{F}}^{-1\mathrm{}}$. The reason for this choice is explained. With the reference spectrum, the Brueckner integral equation reduces to a differential equation which is easily solved. The case of a repulsive core can be solved explicitly, and can be summed over angular momentum, taking into account the correct statistical weights. If an attractive potential is added to the repulsive core, a simple "modified Born approximation" can be developed. Noncentral forces, such as tensor forces, are considered.