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Second-forbidden nonunique \(\beta ^-\) decays of \(^{59,60}\)Fe:possible candidates for \(g_{\mathrm{A}}\) sensitive electron spectral-shape measurements

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Abstract

In this work, we present a theoretical study of the electron spectral shapes for the second-forbidden nonunique \(\beta ^-\)-decay transitions \(^{59}\text {Fe}(3/2^-)\rightarrow \,^{59}\text {Co}(7/2^-)\) and \(^{60}\text {Fe}(0^+)\rightarrow \,^{60}\text {Co}(2^+)\) in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete \(0\hbar \omega \) calculation in the full fp model space using the KB3G and GXPF1A effective interactions. When compared with the available data, these interactions predict the low-energy spectra and electromagnetic properties of the involved nuclei quite successfully. This success paves the way for the computations of the \(\beta \)-decay properties, and comparison with the available data. We have computed the electron spectral shapes of the mentioned decay transitions as functions of the value of the weak axial coupling \(g_{\mathrm{A}}\). By comparing these computed shapes with the measured spectral shapes allows then to extract the effective value of \(g_{\mathrm{A}}\) for these decay transitions. This procedure, coined the spectrum-shape method (SSM) in several earlier studies, complements the method of determining the value of \(g_{\mathrm{A}}\) by reproducing the (partial) half-lives of decay transitions. Here we have enhanced the original SSM by constraining the value of the relativistic vector matrix element, \(^V{\mathcal {M}}^{(0)}_{KK-11}\), using the conserved vector-current hypothesis (CVC) as a starting point. We hope that this finding would be a strong incentive to measure the spectral shapes in the future.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is the theoretical work all results we have already reported.]

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Acknowledgements

A. K. would like to thank the Ministry of Human Resource Development (MHRD), Government of India, for the financial support for his Ph.D. thesis work. P.C.S. acknowledges a research grant from SERB (India), CRG/2019/000556. J. S. has been partially supported by the academy of Finland under the academy project no. 318043.

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Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Anil Kumar & Praveen C. Srivastava

  2. Department of Physics, University of Jyvaskyla, P.O. Box 35 (YFL), 40014, Jyvaskyla, Finland

    Jouni Suhonen

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  1. Anil Kumar
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  2. Praveen C. Srivastava
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Correspondence to Praveen C. Srivastava.

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Communicated by Kamila Sieja.

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Kumar, A., Srivastava, P.C. & Suhonen, J. Second-forbidden nonunique \(\beta ^-\) decays of \(^{59,60}\)Fe:possible candidates for \(g_{\mathrm{A}}\) sensitive electron spectral-shape measurements. Eur. Phys. J. A 57, 225 (2021). https://doi.org/10.1140/epja/s10050-021-00540-6

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