Role of individual components of two-nucleon interaction in nuclear matrix elements of $2\nu \beta \beta$ and $0\nu \beta \beta$ of ${}^{\text{48}}$Ca: Beyond the closure approximation

Abstract

In the present work, we examine the role of central (C), spin-orbit (SO) and tensor (T) components of two-nucleon interaction in the nuclear matrix elements (NMEs) of the two-neutrino double beta decay ($2\nu \beta \beta$) and the light neutrino-exchange mechanism of neutrinoless double beta decay ($0\nu \beta \beta$) of ${}^{48}$Ca in closure approximation and nonclosure approach. The NMEs are calculated in the nuclear shell-model framework using two-nucleon effective interaction GXPF1A used for $pf$ shell. The decomposition of the shell model two-nucleon interaction into its individual components is performed using the spin-tensor decomposition (STD). The NMEs for $2\nu \beta \beta$ are calculated in running nonclosure method. The NMEs for $0\nu \beta \beta$ are calculated with four different methods, namely, closure, running closure, running nonclosure, and mixed method. Results show that the magnitude of NMEs for $2\nu \beta \beta$ decreases about 7\% with the C+SO component of the interaction as compared to the C component. The magnitude of NMEs is further decreased about 9\% by adding T component to the C+SO component. The NMEs of $0\nu \beta \beta$ calculated in running nonclosure method are enhanced by about 8-10\%, 8-10\%, and 9-12\%, respectively, as compared to corresponding NMEs calculated in running closure method with C, C+SO components and total (C+SO+T) GXPF1A interaction for different SRC parametrization. For both $2\nu \beta \beta$ and $0\nu \beta \beta$, the NMEs calculated with C+SO component is in opposite phase with the NMEs calculated with C component and the total GXPF1A interaction.

arXiv comment12 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2003.04002

References in corpus (14)

• New effective interaction for $pf$-shell nuclei and its implications for the stability of the $N$=$Z$=28 closed core
• Theory of neutrinoless double beta decay
• The influence of pairing on the nuclear matrix elements of the neutrinoless double beta decays
• Additional Nucleon Current Contributions to Neutrinoless Double Beta Decay
• Erratum: Assessment of uncertainties in QRPA $0\nu \beta \beta$-decay nuclear matrix elements [Nucl. Phys. A 766, 107 (2006)]
• The 0nbb-decay nuclear matrix elements with self-consistent short-range correlations
• Double Beta Decay
• Limits on the neutrino mass from neutrinoless double-$\beta$ decay
• Uncertainties in nuclear transition matrix elements for neutrinoless $\beta \beta$ decay within the PHFB model
• Shell evolution and nuclear forces
• Large-scale shell-model analysis of the neutrinoless $\beta \beta$ decay of ${}^{48}$Ca
• Shell Model Analysis of the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Relativistic description of nuclear matrix elements in neutrinoless double-$\beta$ decay
• Neutrinoless double beta decay of 48Ca in the shell model: Closure versus nonclosure approximation