The study of dependence of the radial parts of $0^-\rightarrow 0^+$ first forbidden $\beta$-decay matrix elements on the parameters in Woods-Saxon potential

Abstract

Abstract-In this paper, $0^-\rightarrow 0^+$ first forbidden $\beta$-decay matrix elements have been calculated. For $^{206-214}Pb\rightarrow ^{206-214}Bi$ transitions relativistic $M^{\pm}(P_A,\lambda=0)$ and nonrelativistic $M^{\pm}(j_A,K =1,\lambda=0)$ matrix elements have been calculated. In this calculations, the eigenfunctions and eigenvalues of Schrodinger equation solved by the more realistic Woods-Saxon potential have been used. The dependence of the radial parts in the matrix elements on the parameters ($r_0$: the radii of nucleus, $\eta$: isovector parameter, $r_c$: Coulomb radius and $\chi$ diffusion parameter) of Woods-Saxon potential has been investigated.

Abstract-In this paper, $0^-\rightarrow 0^+$ first forbidden $\beta$-decay matrix elements have been calculated. For $^{206-214}Pb\rightarrow ^{206-214}Bi$ transitions relativistic $M^{\pm}(P_A,\lambda=0)$ and nonrelativistic $M^{\pm}(j_A,K =1,\lambda=0)$ matrix elements have been calculated. In this calculations, the eigenfunctions and eigenvalues of Schrodinger equation solved by the more realistic Woods-Saxon potential have been used. The dependence of the radial parts in the matrix elements on the parameters ($r_0$: the radii of nucleus, $\eta$: isovector parameter, $r_c$: Coulomb radius and $\chi$ diffusion parameter) of Woods-Saxon potential has been investigated.