Symmetry Restoration Effect on Induced Weak Currents in Double Beta Decay

A.R. SAMANA; V. DOS S. FERREIRA; F. KRMPOTIC; C. BARBERO

Natal

Workshop; XXXIX Reuni ̃ao de Trabalho de F ́ısica Nuclear no Basil; 2016

Much attention was devoted recently to the restoration of isospin symmetry in evaluating ββ-decaymatrix elements within the quasiparticle random-phase approximation (QRPA) [1]. This is done byseparating the particle-particle (pp) parameter gpp of the proton-neutron interaction into isovectorgT=1, and isoscalar gT=0 parts, and by choosing the first one to be essentially equal to the average pp    pppairing constant gpair, while the second one is obtained by fitting the calculated Gamow-Teller (GT) 2νββ moments M2ν    to their experimental values. In this way, the 2νββ Fermi (F) moment M2νGT Fvanishes, the corresponding 0νββ moment M0ν is substantially reduced, and the full matrix element FM0ν = M0ν + M0ν    is reduced by ≈ 10%. F GTThe above studies made us bring up to date our previous QRPA studies done on the same issues [2],i.e., on consequences of restoration of the spin-isospin SU(4) symmetry on F and GT moments inββ-decay. We extend this analysis here to pseudoscalar (P) and weak-magnetism (WM) moments,M0ν and M0ν    , which arise from induced weak currents, and, as shown by Sˇimkovic et al. [1], they PWMare quite significant for the 0νββ-decay. The main features of our formalism are:(i) We solve the RPA equations only once for the intermediate (N − 1, Z + 1) nucleus [3], while theyare usually solved twice for (N, Z) and (N − 2, Z + 2) nuclei.(ii) The residual interaction is described by a δ-force, which depends of only two free parametersvs, and vt. Within the pp channel, these coupling constants are equivalent to gT=1, and gT=1, pp    ppand are fixed by requiring that the F and GT β+-decay strengths become minimal, which reflects the restoration of isospin and spin-isospin SU(4) symmetries, respectively. Within the particle-hole channel they are monitored by the experimental energy splitting between the F and GT resonances, which is a consequence of spin-isospin SU(4) symmetry breaking.(iii) The outstanding difference between our procedure and other QRPA studies is that we do not use the experimental M2ν    moments for fixing the isoscalar pp parameter, which makes our calculation,GTunlike other studies, to be predictable regarding this observable.We conclude that the effect of the restoration of spin-isospin SU(4) symmetry is quite significantfor the induced current moments M0ν and M0ν    , but is not as important as in the case of the F PWMand GT ones.[1] F. Sˇimkovic et al., Phys.Rev. C87 (2013) 045501, and references therein. [2] F. Krmpoti ́c and S. Shelly Sharma, Nucl. Phys. A572 (1994) 329, and references therein. [3] C. Barbero, F. Krmpoti ́c, A. Mariano and D. Tadi ́c, Nucl. Phys. A650 (1999) 485, and references therein.