Analysis of β+ decay of 13N nucleus using a modified one-particle approach

It is known that the calculated values of log(ft) and the half-life of beta decay are less than the measured values when a single-particle approach is used to calculate these quantities. In this article, we discuss the importance of taking into account the spectroscopic factor in the calculation of the half-life and log(ft) beta decay of nuclei containing one nucleon in the outermost shell. We also emphasize the dominant role of the asymptotic normalization coefficient, which takes into account the many-particle effect and allows us to obtain the spectroscopic factor necessary to describe the reaction 13N → 13C + β+ + νe . We find the asymptotic normalization coefficients using the experimental data of the elastic scattering phase-shift of the proton and neutron on 12C. Using overlap functions instead of single-particle functions, we obtain a better comparison with the experimental data. The overlap function is represented as the product of the single-particle function and the root of the corresponding spectroscopic factor.