On Statistical Properties of the Gamow–Teller Strength Distribution in $${}^{\mathbf{60}}$$Ca

Abstract

The $$\beta$$ -decay half-life and the delayed neutron emission of $${}^{60}$$ Ca are studied within a microscopic model, which is based on the Skyrme interaction T45 to construct single-particle and phonon spaces. We observe a redistribution of the Gamow–Teller strength due to the phonon-phonon coupling and the tensor correlations, considered in the model. For $${}^{60}$$ Sc, the spin-parity of the ground state is found to be $$1^{+}$$ . We predict that the half-life of $${}^{60}$$ Ca is 0.3 ms, while the total probabilities of the $$\beta xn$$ emission is 6.1%. To elucidate the obtained results, the random matrix theory has been applied to analyse the statistical properties of the $$1^{+}$$ spectrum populated in the $$\beta$$ -decay. We found a remarkable agreement between the GT strength distribution, obtained within the microscopic approach, and the ones, generated by means of the random coupling between the one- and two-phonon configurations.