Bivariate distributions in statistical spectroscopy studies: IV. Interacting particle Gamow-Teller strength densities and ?-decay rates offp-shell nuclei for presupernova stars

Abstract

A method to calculate temperature dependentβ-decay rates is developed by writing the expression for the rates explicitly in terms of bivariateGT strength densities (I (GT)) for a given hamiltonianH=h+V and state densities of the parent nucleus besides having the usual phase space factors. The theory developed in the preceding paper (III) for constructing NIP strength densities is applied for generatingI (GT) and thenI (GT) is constructed using the bivariate convolution formI (GT)=Σ S I ⊗ρ V, ; BIV-G . The spreading bivariate Gaussian ρ V ;BIV-G, forfp-shell nuclei, is constructed by assuming that the marginal centroids are zero, the marginal variances are same as the corresponding state density variances and fixing the bivariate correlation coefficient $$\bar \zeta $$ using experimentalβ-decay half lifes. With the deduced values of $$\bar \zeta $$ $$\bar \zeta $$ ∼ 0.67,β-S-decay rates for61,62Fe and62–64Co isotopes are calculated at presupernova matter densitiesρ=107–109 gm/cc, temperaturesT=(3–5)×109 ∘K and electron fractions Ye=0.43–0.5. The convolution form forI O(GT) led to a simple expression for calculatingGT non-energy weighted sum rule strength and it describes (within 10%) the shell model results offp-shell nuclei.