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.

The Gamow-Teller (GT) transition is inarguably one of the most important nuclear weak transitions of the spin-isosopin στ type. It has many applications in nuclear and astrophysics. These include, but are not limited to, r-process β-decays, stellar electron captures, neutrino cooling rates, neutrino absorption and inelastic scattering on nuclei. The quasiparticle random phase approximation (QRPA) is an efficient way to generate GT strength distribution. In order to better understand both theoretical systematics and uncertainties, we compare the GT strength distributions, centroid and width calculations for 40−60 Ti isotopes, using the pn-QRPA, Pyatov method (PM) and the Schematic model (SM). The pn-QRPA and SM are further sub-divided into three categories in order to highlight the role of particle-particle (pp) force and deformation of the nucleus in the GT strength calculations. In PM, we study only the influence of the pp force in the calculation. We also compare with experimental results and other calculations where available. We found that the inclusion of pp force and deformation significantly improves the performance of SM and pn-QRPA models. Incorporation of pp force leads to pinning down the centroid value in the PM. The calculated GT strength functions using the pn-QRPA (C) and SM (C) models are in reasonable agreement with measured data.

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The log(ft) values of allowed β± decay between odd-A nuclei for 125 < A < 180 mass region are investigated. Single particle energies and wave functions are calculated by making use of a deformed Woods-Saxon potential. The calculations are performed in the framework of proton-neutron quasi particle random phase approximation (QRPA) including the schematic residual spin-isospin interaction among the nucleons in the particle hole channel. The calculations indicated that the results obtained through using the χGT=5.2/A0.7 are more in agreement with experimental observations.

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

The Pyatov Method has been used to study the low-lying Gamow-Teller transitions in the mass region of 98 A 130. The eigenvalues and eigenfunctions of the total Hamiltonian have been solved within the framework of proton-neutron quasiparticle random-phase approximation. The low-lying β decay log(f t) values have been calculated for the nuclei under consideration.

Abstract-In this study, the first forbidden beta decay matrix elements have been directly calculated within Saxon-Woods potential. Procedures for calculating the relevant matrix elements and combining them to form the decay rate are described. Calculations have been performed by two different methods. The values of our single particle matrix elements have been compared with the calculated values in the two different tables.

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