Tensor force role in β decays analyzed within the Gogny-interaction shell model

Background: The half-life of the famous C14β decay is anomalously long, with different mechanisms: the tensor force, cross-shell mixing, and three-body forces, proposed to explain the cancellations that lead to a small transition matrix element. Purpose: We revisit and analyze the role of the tensor force for the β decay of C14 as well as of neighboring isotopes. Methods: We add a tensor force to the Gogny interaction, and derive an effective Hamiltonian for shell-model calculations. The calculations were carried out in a p-sd model space to investigate cross-shell effects. Furthermore, we decompose the wave functions according to the total orbital angular momentum L in order to analyze the effects of the tensor force and cross-shell mixing. Results: The inclusion of the tensor force significantly improves the shell-model calculations of the β-decay properties of carbon isotopes. In particular, the anomalously slow β decay of C14 can be explained by the isospin T=0 part of the tensor force, which changes the components of N14 with the orbital angular momentum L=0,1, and results in a dramatic suppression of the Gamow-Teller transition strength. At the same time, the description of other nearby β decays are improved. Conclusions: Decomposition of wave function into L components illuminates how the tensor force modifies nuclear wave functions, in particular suppression of β-decay matrix elements. Cross-shell mixing also has a visible impact on the β-decay strength. Inclusion of the tensor force does not seem to significantly change, however, binding energies of the nuclei within the phenomenological interaction.