The violated supersymmetry property of the pairing interaction between nucleons were restored using the Pyatov method [Pyatov and Salamov, Nucleonica 22, 127 (1977)]. The eigenvalues and eigenfunctions of the restored Hamiltonian with the separable residual Gamow-Teller effective interactions in the particle-hole and particle-particle channels were solved within the framework of proton-neutron quasirandom phase approximation (pnQRPA). The Gamow-Teller resonance energies for 112−124 Sb isotopes and the differential cross-sections for Sn( 3 He, t)Sb reactions at E( 3 He) = 200 MeV occurring by the excitation of the Gamow-Teller resonance state were calculated. The calculated values were compared with other calculations and the corresponding experimental data.
First-forbidden (FF) charge-changing transitions become relatively important for nuclei as their proton number increases. This is because the strength of allowed Gamow-Teller (GT) transitions decreases with increasing Z. The FF transitions play an important role in reducing the half-lives as against those calculated from taking the GT transitions alone into account. In this paper we calculate allowed GT as well as 0 + → 0 − and 0 + → 2 − transitions for neutron-rich Zn and Ge isotopes. Two different pn-QRPA models were used with a schematic separable interaction to calculate GT and FF transitions. Half-lives calculated after inclusion of FF transitions were in excellent agreement with the experimental data. Our calculations were also compared to previous QRPA calculations and were found to be in better agreement with measured data. Stellar β-decay rates were calculated for these nuclei including allowed GT and unique FF transitions for astrophysical applications. 86,88 Ge has a sizeable contribution to the total stellar rate from unique FF transitions.
The 0 + ↔ 0 − first-forbidden β decay transitions have been investigated for some spherical nuclei. The theoretical framework is based on a proton-neutron quasiparticle random phase approximation (pnQRPA). The Woods-Saxon potential basis has been used in our calculations. The transition probabilities have been calculated within the ξ approximation. The relativistic β moment matrix element has been calculated both directly without any assumption and assuming that it is proportional to the non-relativistic one.Keywords. First-forbidden β decay; proton-neutron quasiparticle random phase approximation; shell model.
PACSNos 23.40.Bw; 23.40.-s; 23.40.Hc
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