0-→0+ First Forbidden β-Decay Matrix Elements in Spherical Nuclei

Abstract

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.

The Study of Dependence of the Radial Parts of 0-→0+ First Forbidden β-Decay Matrix Elements on the Parameters in Woods-Saxon Potential

“…The matrix elements which are calculated with the formulas (2) and (3) depend on the Woods-Saxon potential parameter [13]. The dependency of the radial section on the potential parameter has been examined as that dependency occurred with radial part.…”

“…g A and g v refer to axial and vector coupling constant respectively. It can be shown that reduced matrix elements of the operators given in the formulas (2), (3) are proportional to the expressions given below [11][12][13].…”

The investigation of 0+ ↔ 0− β decay in some spherical nuclei

“…The relativistic part of the first-forbidden β decay matrix element has been calculated directly without any assumption. The difference of our calculations from the calculations in refs [16,17] is the inclusion of the contribution coming from the spin-orbit potential in the calculation of the relativistic matrix element. The calculations have been performed within the framework of the pnQRPA method with the separable residual effective interactions in the particle-hole (ph) and the particle-particle (pp) channel.…”

“…In refs [16,17], the 0 + ↔ 0 − first-forbidden β decay has been searched for 206−214 Pb → 206−214 Bi transitions. The calculations have been performed according to two different approximations.…”