In the present study, the effect of the pairing interaction and the isovector correlation between nucleons on the properties of the isobar analog resonances (IAR) in 112−124 Sb isotopes and the isospin admixture in 100−124 Sn isotopes is investigated within the framework of the quasiparticle random phase approximation (QRPA). The form of the interaction strength parameter is related to the shell model potential by restoring the isotopic invariance of the nuclear part of the total Hamiltonian. In this respect, the isospin admixtures in the 100−124 Sn isotopes are calculated, and the dependence of the differential cross section and the volume integral J F for the Sn( 3 He,t)Sb reactions at E( 3 He)= 200 MeV occurring by the excitation of IAR on mass number A is examined. Our results show that the calculated value for the isospin mixing in the 100 Sn isotope is in good agreement with Colo et al.'s estimates (4 − 5%), and the obtained values for the volume integral change within the error range of the value reported by Fujiwara et al. (53±5 MeV fm 3 ). Moreover, it is concluded that although the differential cross section of the isobar analog resonance for the ( 3 He,t) reactions is not sensitive to pairing correlations between nucleons, a considerable effect on the isospin admixtures in N ≈ Z isotopes can be seen with the presence of these correlations.
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.
We have tried to give a self-consistent explanation of isospin mixing and Fermi beta decays for 54 ≤ Z ≤ 68 deformed nuclei. The effect of isospin impurity in nuclear ground states on Fermi beta transitions has been investigated considering the restoration of symmetry violations stemming from the mean field approximation. The isobar analogue excitations in neighbor odd-odd nuclei have been obtained by following the proton-neutron quasiparticle random phase approximation (pnQRPA) procedure. The dependence of isospin admixture probability on the deformation parameter has been determined for various isotopes of Z = 54-68 nuclei. Then the variations of isobar analogue state energies and the β decay log(ft) values with deformation parameter have been calculated for the same nuclei. Thus, the influences of the isospin symmetry violations on Fermi transitions can be clearly understood.
We try to give a comparison of the calculated Gamow–Teller [Formula: see text]-decay half-lives for [Formula: see text], [Formula: see text] and [Formula: see text] nuclei with the experimental ones obtained from ([Formula: see text],p), ([Formula: see text],n) and (n,[Formula: see text]) reactions, respectively. The calculations are performed within the framework of quasi-particle phonon nuclear model. The nucleon–nucleon interaction potential is included according to Pyatov’s restoration method. The calculated decay half-lives are also compared with available experimental data in the literature.
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