Ab initio effective interactions for sd-shell valence nucleons

TL;DR

This paper develops effective interactions for sd-shell valence nucleons using ab initio no-core shell-model calculations with realistic nucleon-nucleon potentials, enabling accurate shell-model predictions for A=18 and 19 nuclei.

Contribution

It introduces a method to derive A-body effective Hamiltonians from no-core calculations for sd-shell nuclei, bridging ab initio and shell-model approaches.

Findings

Good agreement between shell-model and no-core results for A=18 and 19.

Effective interactions accurately reproduce no-core shell-model energies.

Method provides a pathway for realistic shell-model calculations.

Abstract

We perform \textit{ab initio} no-core shell-model calculations for $A=18$ and $19$ nuclei in a $4\hbar\Omega$, or $N_{\rm max}=4$, model space by using the effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the many-body effective Hamiltonians into the $0\hbar\Omega$ model space to construct the $A$-body effective Hamiltonians in the $sd$-shell. We separate the $A$-body effective Hamiltonians with $A=18$ and $A=19$ into inert core, one-, and two-body components. Then, we use these core, one-, and two-body components to perform standard shell-model calculations for the $A=18$ and $A=19$ systems with valence nucleons restricted to the $sd$ shell. Finally, we compare the standard shell-model results in the $0\hbar\Omega$ model space with the exact no-core shell model results in the $4\hbar\Omega$ model space for the $A=18$ and $A=19$ systems and find good agreement.