Forbidden nonunique β decays and effective values of weak coupling constantsHaaranen, Mikko; Srivastava, P. C.; Suhonen, Jouni Haaranen, M., Srivastava, P. C., & Suhonen, J. (2016 Forbidden nonunique β decays feature shape functions that are complicated combinations of different nuclear matrix elements and phase-space factors. Furthermore, they depend in a very nontrivial way on the values of the weak coupling constants, g V for the vector part and g A for the axial-vector part. In this work we include also the usually omitted second-order terms in the shape functions to see their effect on the computed decay half-lives and electron spectra (β spectra). As examples we study the fourth-forbidden nonunique ground-state-to-ground-state β − decay branches of 113 Cd and 115 In using the microscopic quasiparticle-phonon model and the nuclear shell model. A striking new feature that is reported in this paper is that the calculated shape of the β spectrum is quite sensitive to the values of g V and g A and hence comparison of the calculated with the measured spectrum shape opens a way to determine the values of these coupling constants. This article is designed to show the power of this comparison, coined spectrum-shape method (SSM), by studying the two exemplary β transitions within two different nuclear-structure frameworks. While the SSM seems to confine the g V values close to the canonical value g V = 1.0, the values of g A extracted from the half-life data and by the SSM emerge contradictory in the present calculations. This calls for improved nuclear-structure calculations and more measured data to systematically employ SSM for determination of the effective value of g A in the future.

Effective values of the axial-vector coupling constant g A have lately attracted much attention due to the prominent role of g A in determining the half-lives of double β decays, in particular their neutrinoless mode. The half-life method, i.e., comparing the calculated half-lives to the corresponding experimental ones, is the most widely used method to access the effective values of g A . The present paper investigates the possibilities offered by a complementary method: the spectrum-shape method (SSM). In the SSM, comparison of the shapes of the calculated and measured β electron spectra of forbidden nonunique β decays yields information on the magnitude of g A . In parallel, we investigate the impact of the next-to-leading-order terms of the β-decay shape function and the radiative corrections on the half-life method and the SSM by analyzing the fourfold forbidden decays of 113 Cd and 115 In by using three nuclear-structure theory frameworks; namely, the nuclear shell model, the microscopic interacting boson-fermion model, and the microscopic quasiparticle-phonon model. The three models yield a consistent result, g A ≈ 0.92, when the SSM is applied to the decay of 113 Cd for which β-spectrum data are available. At the same time the half-life method yields results which are in tension with each other and the SSM result.

Electron spectra in forbidden β decays and the quenching of the weak axial-vector coupling constant gA Kostensalo, Joel; Haaranen, Mikko; Suhonen, Jouni Kostensalo, J., Haaranen, M., & Suhonen, J. (2017). Electron spectra in forbidden β decays and the quenching of the weak axial-vector coupling constant gA. Physical Review C, 95 (4) Evolution of the electron spectra with the effective value of the weak axial-vector coupling constant g A was followed for 26 first-, second-, third-, fourth-and fifth-forbidden β − decays of odd-A nuclei by calculating the involved nuclear matrix elements (NMEs) in the framework of the microscopic quasiparticle-phonon model (MQPM). The next-to-leading-order terms were included in the β-decay shape factor of the electron spectra. The spectrum shapes of third-and fourth-forbidden nonunique decays were found to depend strongly on the value of g A , while first-and second-forbidden decays were mostly unaffected by the tuning of g A . The g A -driven evolution of the normalized β spectra was found to be quite universal, largely insensitive to the small changes in the nuclear mean field and the adopted residual many-body Hamiltonian producing the excitation spectra of the MQPM. This makes the comparison of experimental and theoretical electron spectra, coined "the spectrum-shape method" (SSM), a robust tool for extracting information on the effective values of the weak coupling constants. In this exploratory work two new experimentally interesting decays for the SSM treatment were discovered: the ground-state-to-ground-state decays of 99 Tc and 87 Rb. Comparing the experimental and theoretical spectra of these decays could shed light on the effective values of g A and g V for second-and third-forbidden nonunique decays. The measurable decay transitions of 135 Cs and 137 Cs, in turn, can be used to test the SSM in different many-body formalisms. The present work can also be considered as a (modest) step towards solving the g A problem of the neutrinoless double beta decay.

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In this work we survey the detectability of the β − channel of 50 23 V leading to the first excited 2 + state in 50 24 Cr. The electron-capture (EC) half-life corresponding to the transition of 50 23 V to the first excited 2 + state in 50 22 Ti had been measured earlier. Both of the mentioned transitions are 4th-forbidden non-unique. We have performed calculations of all the involved wave functions by using the nuclear shell model with the GXPF1A interaction in the full f-p shell. The computed half-life of the EC branch is in good agreement with the measured one. The predicted half-life for the β − branch is in the range ≈2 × 10 19 yr whereas the present experimental lower limit is 1.5 × 10 18 yr. We discuss also the experimental lay-out needed to detect the β − -branch decay.

The highly forbidden β − decay of 48 Ca is reexamined by performing shell-model calculations with the GXPF1A effective interaction. We examine the three available decay branches to the lowest 6 + , 5 + , and 4 + states of 48 Sc, and extract a theoretical half-life of T β 1/2 = 5.2 +1.7 −1.3 × 10 20 g −2 A yr for the β − decay, where g A is the value of the axial-vector coupling constant. The current half-life estimate suggests stronger competition between the single-β-decay and double-β-decay branches of 48 Ca than previously expected on theoretical grounds.

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