Effective operators for valence space calculations from the {\itshape ab initio} No-Core Shell Mode

TL;DR

This paper develops a method to derive effective electromagnetic operators for valence space shell model calculations from ab initio no-core shell model results, enabling accurate reproduction of electromagnetic properties in sd-shell nuclei.

Contribution

The authors implement an OLS unitary transformation approach to derive effective electromagnetic operators from NCSM solutions, improving valence space calculations for sd-shell nuclei.

Findings

Exact reproduction of selected NCSM spectra for $^{18}$O, $^{18}$F, and $^{18}$Ne.

Effective $E2$ and $M1$ operators accurately reproduce electromagnetic moments and transitions for $A=17$ and $A=18$.

Remarkable agreement between shell model results using derived operators and full NCSM calculations.

Abstract

In recent years, remarkable progress has been achieved in developing novel non-perturbative techniques for constructing valence space shell model Hamiltonians from realistic internucleon interactions. One of these methods is based on the Okubo--Lee--Suzuki (OLS) unitary transformation applied to no-core shell model (NCSM) solutions. In the present work, we implement the corresponding approach to solve for valence space effective electromagnetic operators. To this end, we use the NCSM results for $A=16-18$, obtained at $N_{\rm max}=4$, to derive a charge-dependent version of the effective interaction for the $sd$ shell, which allows us to exactly reproduce selected NCSM spectra of $^{18}$O, $^{18}$F and $^{18}$Ne within the two valence nucleon space. We then deduce effective single-particle matrix elements of electric quadrupole ($E2$) and magnetic dipole ($M1$) operators by matching them to the electromagnetic transitions and moments for $^{17}$O and $^{17}$F from the NCSM at $N_{\rm max}=4$. Thus, effective $E2$ and $M1$ operators are obtained as sets of single-particle matrix elements for the valence space ($sd$ shell) which allow us to reproduce the NCSM results for $A=17$ exactly. Systematic comparison of a large set of $sd$ shell results on quadrupole and magnetic dipole moments and transitions for $A=18$ using effective $E2$ and $M1$ operators that we derive from the full NCSM calculations demonstrates a remarkable agreement.