Influence of the recoil-order and radiative correction on the beta decay correlation coefficients in mirror decays

Abstract

Measurements of the beta decay correlation coefficients in nuclear decay aim for a precision below $1\%$ and theoretical predictions should follow this trend. In this work, the influence of the two dominant Standard Model correction terms, i.e. the recoil-order and the radiative correction, are studied for the most commonly measured beta correlations, i.e. the $\beta$-asymmetry parameter ($A_{\beta }$) and the $\beta -\nu$ angular correlation ($a_{\beta \nu }$). The recoil-order correction is calculated with the well-known Holstein formalism using the impulse approximation to evaluate experimentally inaccessible form factors. For the $\beta -\nu$ angular correlation previously unpublished, semi-analytical radiative correction values are tabulated. Results are presented for the mirror beta decays up to $A=45$. We examine the effect of both corrections and provide a comparison between different isotopes. This comparison will help planning, analysing, and comparing future experimental efforts.

16 pages, 10 figures

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Cited by in corpus (2)

• $\mathcal{F}t$ values of the mirror $\beta$ transitions and the weak magnetism induced current in allowed nuclear $\beta$ decay
• Opportunities and open questions in modern $\beta$ decay