No-core shell model for A = 47 and A = 49

TL;DR

This paper applies the no-core shell model to odd-mass nuclei near calcium-48, using a modified Hamiltonian with phenomenological terms to produce reasonable spectra, and compares matrix elements with a known effective interaction.

Contribution

It demonstrates the application of the no-core shell model to A=47 and A=49 nuclei, incorporating phenomenological adjustments and analyzing matrix element correlations with GXPF1.

Findings

Produced reasonable spectra for A=47 and A=49 nuclei

Found good correlation between off-diagonal matrix elements and GXPF1

Highlighted differences in single-particle basis states and Hamiltonian roles

Abstract

We apply the no-core shell model to the nuclear structure of odd-mass nuclei straddling $^{48}$Ca. Starting with the NN interaction, that fits two-body scattering and bound state data we evaluate the nuclear properties of $A = 47$ and $A = 49$ nuclei while preserving all the underlying symmetries. Due to model space limitations and the absence of 3-body interactions, we incorporate phenomenological interaction terms determined by fits to $A = 48$ nuclei in a previous effort. Our modified Hamiltonian produces reasonable spectra for these odd mass nuclei. In addition to the differences in single-particle basis states, the absence of a single-particle Hamiltonian in our no-core approach complicates comparisons with valence effective NN interactions. We focus on purely off-diagonal two-body matrix elements since they are not affected by ambiguities in the different roles for one-body potentials and we compare selected sets of $fp$-shell matrix elements of our initial and modified Hamiltonians in the harmonic oscillator basis with those of a recent model $fp$-shell interaction, the GXPF1 interaction of Honma, Otsuka, Brown and Mizusaki. While some significant differences emerge from these comparisons, there is an overall reasonably good correlation between our off-diagonal matrix elements and those of GXPF1.