Origin of a sensitive dependence of calculated {beta}{beta}-decay amplitudes on the particle-particle residual interaction

Journal Article · Fri Jul 15 04:00:00 EDT 2011 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.84.014322· OSTI ID:21596568

Rodin, Vadim; Faessler, Amand ^[1]

---

1. Institut fuer Theoretische Physik der Universitaet Tuebingen, D-72076 Tuebingen (Germany)

In the present work the sensitivity of calculated {beta}{beta}-decay amplitudes to a realistic residual interaction is analyzed in the framework of the approach of O. A. Rumyantsev and M. H. Urin, Phys. Lett. B 443, 51 (1998). and V. A. Rodin, M. H. Urin, and A. Faessler, Nucl. Phys. A 747, 297 (2005). Both the Gamow-Teller (GT) and Fermi (F) matrix elements M{sup 2}{nu} for two-neutrino {beta}{beta} decay (2{nu}{beta}{beta} decay), along with the monopole transition contributions to the total matrix elements M{sup 0{nu}} of neutrinoless {beta}{beta} decay (0{nu}{beta}{beta} decay), are calculated within the quasiparticle random-phase approximation (QRPA). In the aforementioned approach decompositions of M{sup 2{nu}} and M{sup 0{nu}} can be obtained in terms of the corresponding energy-weighted sum rules S. It is shown that in most of the cases almost the whole dependence of M{sup 2{nu}} and M{sup 0{nu}} on the particle-particle (p-p) renormalization parameter g{sub pp} is accounted for by the g{sub pp} dependence of the corresponding sum rules S. 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. Thus, the sensitivity of M{sup 2{nu}} and M{sup 0{nu}} to the SU(4)-symmetry-breaking part of the p-p residual interaction is dictated by the generic structure of the {beta}{beta}-decay amplitudes. Therefore, a choice of this part in a particular calculation needs a special caution. Finally, a better isospin-consistent way of renormalization of a realistic residual p-p interaction to use in QRPA calculations is suggested.

• OSTI ID: 21596568
• Journal Information: Physical Review. C, Nuclear Physics, Journal Name: Physical Review. C, Nuclear Physics Journal Issue: 1 Vol. 84; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
AMPLITUDES
APPROXIMATIONS
BETA DECAY
BETA-MINUS DECAY
CALCULATION METHODS
CHEMICAL REACTIONS
DECAY
DECAY AMPLITUDES
DECOMPOSITION
DOUBLE BETA DECAY
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
GAMOW-TELLER RULES
INTERACTIONS
ISOSPIN
LEPTONS
LIE GROUPS
MASSLESS PARTICLES
MULTIPLETS
NEUTRINOS
NUCLEAR DECAY
PARTICLE INTERACTIONS
PARTICLE PROPERTIES
RANDOM PHASE APPROXIMATION
RENORMALIZATION
RESIDUAL INTERACTIONS
SENSITIVITY
SU GROUPS
SU-4 GROUPS
SUM RULES
SYMMETRY BREAKING
SYMMETRY GROUPS
TRANSITION AMPLITUDES
TRIPLETS