Origin of a sensitive dependence of calculated $\beta \beta$-decay amplitudes on the particle-particle residual interaction

Abstract

In the present work the sensitivity of the QRPA calculation results to a realistic residual interaction is analyzed in the framework of the approach of Refs. \cite{Rum98,Rodin05}. Both Gamow-Teller (GT) and Fermi (F) \bb-decay amplitudes $M^{2\nu }$, along with the corresponding energy-weighted sum rules $S$, are calculated. General expressions relating $S$ to a realistic residual particle-particle interaction are derived, which show a pronounced sensitivity of $S$ to the singlet-channel interaction in the case of F transitions, and to the triplet-channel interaction in the case of GT transitions. Decompositions of $M^{2\nu }$, as well as the monopole transition contributions to $M^{0\nu }$, are obtained by the method of Refs. \cite{Rum98,Rodin05}. It is shown that in most of the cases almost the whole dependence of $M^{2\nu }$ and $M^{0\nu }$ on the particle-particle renormalization parameter $g_{pp}$ is accounted for by the $g_{pp}$-dependence of the corresponding sum rules $S$. Thus, the $g_{pp}$-sensitivity of calculated $M^{2\nu }$ and $M^{0\nu }$ is unavoidable since it is dictated by the generic structure of the $\beta \beta$ amplitudes. Finally, a better isospin-consistent way of a renormalization of the realistic residual particle-particle interaction to use in QRPA calculations is suggested.

15 pages, 4 figures, to be published in PRC

References in corpus (13)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Anatomy of nuclear matrix elements for neutrinoless double-beta decay
• The influence of pairing on the nuclear matrix elements of the neutrinoless double beta decays
• 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
• Precise half-life values for two neutrino double beta decay
• Nuclear Structure Aspects of the Neutrinoless Double Beta Decay
• Nuclear deformation and neutrinoless double-$\beta$ decay of ${}^{94,96}$Zr, ${}^{98,100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te and ${}^{150}$Nd nuclei in mass mechanism
• Neutrinoless double beta decay of ${}^{150}$Nd with account for deformation
• Deformation effects and neutrinoless positron $\beta \beta$ decay of ${}^{96}$Ru, ${}^{102}$Pd, ${}^{106}$Cd, ${}^{124}$Xe, ${}^{130}$Ba and ${}^{156}$Dy isotopes within Majorona neutrino mass mechanism
• Novel Nuclear Structure Aspects of the Neutrinoless Double Beta Decay

Cited by in corpus (5)

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• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Many-body correlations of quasiparticle random-phase approximation in nuclear matrix element of neutrinoless double-beta decay
• NMEs for $0\nu \beta \beta (0^{+}\to 2^{+})$ of two-nucleon mechanism for ${}^{76}$Ge
• $2\nu \beta \beta$-decay to first $2^{+}$ state with partial isospin symmetry restoration from spherical QRPA calculations