Study of Gamow–Teller transitions in isotopes of titanium within the quasi particle random phase approximation

Abstract

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.

Spin-isospin transitions in chromium isotopes within the quasiparticle random phase approximation

“…It was shown in Ref. (Cakmak et. al., 2014) that the pn-QRPA (C) (incorporating pp and ph forces as well as deformations) was a far better model than pn-QRPA (A) (basic model in which only the interaction in ph channel was considered) and pn-QRPA (B) (including both pp and ph forces but no deformation).…”

“…Further the pn-QRPA (C) was the only model that was satisfying the Ikeda Sum Rule. On the other hand, the SM and PM showed satisfying results in their respective subcategories for calculation of GT transitions (Cakmak et. al., 2014).…”

“…al., 2014). Based on the results of (Cakmak et. al., 2014), we decided to categorize the PM and SM models in two categories as Model (A) and Model (B).…”

“…In this section, we give necessary formalism used in the PM, SM and pn-QRPA models. Detailed formalism may be seen in (Cakmak et. al., 2014) and is not reproduced here for space consideration.…”

First-forbidden transitions and stellarβ-decay rates of Zn and Ge isotopes

“…For U1F transitions authors in [25] employed a much tighter quenching factor of 0.5. In order to compare our results with experimental data and previous calculations, we introduced a quenching factor of 0.6 [26,27,28] in both pn-QRPA(WS) and pn-QRPA(N) models as also used in shell model calculations. In future we would like to explore the effect of using different quenching factor for allowed, FF and U1F transitions in pn-QRPA(WS) and pn-QRPA(N) models.…”