Background: For radioactive nuclear data, β decay is one of the most important information and is applied to various fields. However, some of the β-decay data are not available due to experimental difficulties. From this respect, theoretically calculated results have been embedded in the β-decay data to compensate the missing information.Purpose: Theoretical β-decay calculations are required to treat various nuclear correlations as precise as possible. In particular, the pairing correlation is one of the most important factors to reproduce the β-decay half-lives correctly. First of all, we study the effect of zero-and finite-range isovector pairings on half-lives. We then study the isoscalar pairing strengths, which are determined through experimental data of half-life, and finally predict the isoscalar pairing strengths and half-lives of neutron-rich nuclei. Methods: To calculate the β-decay half-lives, a proton-neutron quasi-particle random phase approximation on top of a Skryme energy density functional is applied with an assumption of spherical symmetry. The half-lives are calculated by including the allowed and first-forbidden transitions. The isoscalar pairing strength is estimated by a Bayesian neutral network (BNN). We verify the predicted isoscalar pairing strengths by preparing the training data and test data. Results: It was confirmed that the finite-range isovector pairing ensures the β-decay half-lives insensitive to the model space, while the zero-range one was largely dependent on it. The half-lives calculated with the BNN isoscalar pairing strengths reproduced most of experimental data, although those of highly deformed nuclei were underestimated. We also studied that the predictive performance on new experimental data that were not used for the BNN training and found that they were reproduced well. Conclusions: Our study demonstrates that the isoscalar pairing strengths determined by the BNN can reproduce experimental data in the same accuracy as other theoretical works. To achieve a more precise prediction, the nuclear deformation is important.
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