A method of implementing Hartree–Fock calculations with zero- and finite-range interactions

Abstract

We develop a new method of implementing the Hartree–Fock calculations. A class of Gaussian bases is assumed, which includes the Kamimura–Gauss basis-set as well as the set equivalent to the harmonic-oscillator basis-set. By using the Fourier transformation to calculate the interaction matrix elements, we can treat various interactions in a unified manner, including finite-range ones. The present method is numerically applied to the spherically-symmetric Hartree–Fock calculations for the oxygen isotopes with the Skyrme and the Gogny interactions, by adopting the harmonic-oscillator, the Kamimura–Gauss and a hybrid basis-sets. The characters of the basis-sets are discussed. Adaptable to slowly decreasing density distribution, the Kamimura–Gauss set is suitable to describe unstable nuclei. A hybrid basis-set of the harmonic-oscillator and the Kamimura–Gauss ones is useful to accelerate the convergence, both for stable and unstable nuclei.