Influence of the Axial-Vector Coupling Constant and the Energy Distribution Function on β-Decay Rates Within the Gross Theory of Beta Decay

Abstract

We evaluate the β-decay rates within the gross theory of beta decay (GTBD) and compare the results for different values of the axial-vector coupling constant, g A = 0.76, g A = 0.88, g A = 1, g A = 1.13, and g A = 1.26, and also different energy distribution functions like Gaussian, exponential, Lorentzian, and modified Lorentzian ones. We use new sets of parameters as well as updated experimental mass defects and also an improved approximation for the Fermi function. We compare our calculated results for a set of 94 nuclei of interest in pre-supernova phase, with experimental data in terrestrial conditions and also with other theoretical models like the QRPA, the shell model (SM), and different versions of the GTBD. We show that best results are obtained with g A = 1 using Gaussian and Lorentzian distributions, being the rates for the 74 and 80% of our sample, respectively, of the same order of magnitude that of experimental data. Finally, we show that the present results within the GTBD are better than those within the QRPA model and also older versions of the GTBD for the isotopes of cobalt and iron families, and comparable with SM for some elements.

Beta Decay Rates Evaluated Within the Gross Theory Using Experimental Data for the Gamow-Teller Resonance Parameter

“…[1]. We have evaluated the β − -decay rates considering the new relevant modifications within the GTBD scheme, namely: for the Q-values we used the updated experimental data present in the Letter of Nuclides [5], the Fermi function has been calculated following the improved approximation from Aufderheide et al [6], we have used the Gaussian energy distribution function and for the axial-vector weak coupling constant we have used |g A | = 1 [1]. We have selected only the value |g A | = 1 for the axial-vector coupling constant because we have shown in Ref.…”

“…They were calculated for the data sample composed of 94 isotopes of the families of iron, cobalt, nickel, manganese, chromium, copper, titanium and scandium, including all isotopes of these families that decay spontaneously via β − -decay through allowed transitions (we imposed the condition log f t < 6) with mass in the range 46 < A < 70, which are of interest in astrophysical studies. The results obtained in this way for σ N were shown in Table 1 from [1]: 8.14 for odd-odd nuclei, 7.48 for odd-even, 7.7 for even-even and 6.6 for even-odd ones.…”

“…Among them, β-decay and electron capture are of particular interest since they are relevant in astrophysical processes in the pre-supernova stage. Among the various nuclear models existing in the literature for βdecay, we choose to use the Gross Theory of Beta Decay (GTBD) in this work because it has advantages when working with a large number of nuclei, thus facilitating [1][2][3] and references therein).…”

“…In this context, we remark that the adjustment parameter σ N related to the standard deviation for the Gamow-Teller resonance and used so far in Ref. [1,2], was obtained by minimization of the χ 2 -function. The values obtained in this way correspond to an average value for each N − Z parity.…”

“…The arguments mentioned above motivate us to analyze in the present work how the substitution of the adjustment parameters σ N by their experimental values modifies the β − -decay rates when they are evaluated in the context of the same version of the GTBD from Ref. [1]. The paper is organized as follows.…”