Anisotropic multicluster model in light nuclei

TL;DR

This paper extends multicluster models for light nuclei by incorporating anisotropic harmonic oscillators, allowing for more detailed descriptions of nucleon arrangements and achieving good energy results for several nuclei.

Contribution

It introduces an anisotropic extension to multicluster models, with analytical calculations and variational parameter fixing, enhancing the modeling of light nuclei.

Findings

Accurate energy calculations for 8 Be, 12 C, and 10 Be.

Detailed nucleon disposition analysis via projection methods.

Analytical computation of matrix elements with minimal numerical integration.

Abstract

Multicluster models consider that the nucleons can be moving around different centers in the nuclei. These models have been widely used to describe light nuclei but always considering that the mean field is composed of isotropic harmonic oscillators with different centers. In this work, we propose an extension of these models by using anisotropic harmonic oscillators. The strenghts of these oscillators, the distance among the different centers and the disposition of the nucleons inside every cluster are free parameters which have been fixed using the variational criterion. We have used a hamiltonian with the kinetic energy terms and a phenomenological two-body potential like Volkov V2 potential. All the one-body and two-body matrix elements have been analytically calculated. Only a numerical integration on the Euler angles, it is needed to carry out the projection on the values of the total spin of the state and its third component. We have studied the ground state and the first excited states of 8 Be, 12 C and 10 Be getting good results for the energies. The disposition of the nucleons in the different clusters have been also analyzed by using projection on the different cartesian planes getting much more information than when the radial one-body density is used.