Self-consistent Continuum Random Phase Approximation calculations with finite-range interactions

TL;DR

This paper introduces a self-consistent method for solving the continuum Random Phase Approximation with finite-range interactions, enabling accurate excitation spectrum calculations without approximations, and compares results with experimental data and other models.

Contribution

It presents a novel technique for continuum RPA calculations with finite-range interactions that treats the continuum spectrum exactly and self-consistently.

Findings

Accurate electric dipole and quadrupole excitation results for several nuclei.

Good agreement with experimental photoabsorption cross sections.

Demonstrates the importance of continuum and self-consistency in RPA calculations.

Abstract

We present a technique which allows us to solve the Random Phase Approximation equations with finite-range interactions and treats the continuum part of the excitation spectrum without approximations. The interaction used in the Hartree-Fock calculations to generate the single particle basis is also used in the Continuum Random Phase Approximation calculations. We present results for the electric dipole and quadrupole excitations in the $^{16}$O, $^{22}$O, $^{24}$O, $^{40}$Ca, $^{48}$Ca and $^{52}$Ca nuclei. We compare our results with those of the traditional discrete Random Phase Approximation, with the continuum mean-field results and with the results obtained by a phenomenological approach. We study the relevance of the continuum, of the residual interaction and of the self-consistency. We also compare our results with the available total photoabsorption cross section data. We compare our photoabsorption cross section in $^4$He with that obtained by a calculation which uses a microscopic interaction.