Realistic shell model for ordinary muon capture of sd-shell nuclei

TL;DR

This paper develops a realistic shell-model study of ordinary muon capture in sd-shell nuclei to test nuclear matrix elements relevant for neutrinoless double-beta decay. It constructs two effective Hamiltonians from realistic forces (CD-Bonn $V_{\rm low\!-}k$ and chiral EFT $2N$+$3N$) and derives consistent effective decay operators, enabling calculation of OMC partial rates and spectroscopy without empirical parameter tuning. The results show that the chiral EFT Hamiltonian better reproduces sd-shell spectroscopy and yields OMC rates in closer agreement with data, establishing a link between spectroscopic fidelity and high-momentum weak-transition observables; discrepancies in some transitions point to missing two-body currents or model-space limitations and motivate future extensions. The work supports the reliability of microscopic NMEs for $0\nu\beta\beta$ decay when the nuclear wave functions are well constrained, and highlights avenues such as two-body currents and expanded model spaces to further reduce uncertainties.

Abstract

We report about a study of the ordinary muon capture in nuclei belonging to the sd shell, an electroweak process that occurs with exchange momenta far larger than ordinary beta decays (approximately 100 MeV). Such a characteristic places this transition in an energy range that is consistent with the neutrinoless double-beta decay, and represents an interesting test for nuclear models to support their predictions of the nuclear matrix elements for such an unobserved process. For the first time, the calculations are carried out within the realistic shell model (RSM), namely employing effective shell-model Hamiltonians and decay operators derived from realistic nuclear forces, without resorting to any empirical adjustment of the coupling constants. This is a chapter of a research program that is aimed to assess the realistic shell model in reproducing the observables related to electroweak processes in nuclei, and then to evaluate the reliability of nuclear matrix elements for the neutrinoless double-beta decay that are calculated within this approach. We calculate the partial capture rates for many nuclear systems in the sd-shell region, as well as their spectroscopic properties, and compare the results with the available experimental counterparts. Such a comparison tests the relevance of a microscopic approach to the renormalization of transition operators to reproduce data and provide solid predictions of unknown observables.

Figures (21)

• Figure 1: Experimental and calculated two-neutron separation energies for even-mass oxygen isotopes from $A = 18$ to 26. Data are taken from Kondev21, see text for details.
• Figure 2: Neutron ESPEs from ChPT (a) and $V_{{\rm low}\hbox{-}k}$ (b) $H_{\rm eff}$s for oxygen isotopes as a function of the neutron number.
• Figure 3: Experimental and calculated excitation energies of the yrast $J^{\pi}=2^+$ states for even-mass oxygen isotopes from $A = 18$ to 24. See text for details.
• Figure 4: Experimental and calculated low-energy spectra of $^{23}$Na and $^{23}$Ne. The calculated spectra are reported both with $V_{{\rm low}\hbox{-}k}$ and ChPT $H_{\rm eff}$s, experimental ones are taken from ensdf.
• Figure 5: Same as in Fig. \ref{['23Na23Ne']}, but for $^{24}$Mg and $^{24}$Na low-energy excitation spectra.