Study of the Influence of Different Methods of Taking into Account the Coulomb Interaction on Determining Asymptotic Normalization Coefficients within the Framework of Exactly Solvable Model

It is shown that the Schrödinger equation for the sum of the potential of a square well and the Coulomb potential of a uniformly charged sphere admits an analytical solution for arbitrary values of the orbital angular momentum. An explicit form of this solution has been found. Using the obtained solution, the influence of the Coulomb interaction for both point and distributed nuclear charges on the values of asymptotic normalization coefficients for various nuclear systems is investigated. It is shown that taking into account the non-point distribution of the nuclear charge has little effect on the calculated values of the asymptotic normalization coefficients, provided that the binding energy of the system is assumed to be fixed.

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

It is known that the calculated values of log<i>ft</i> 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<i>ft </i>beta decay of nuclei containing one nucleon in the outer-most shell. We also emphasize on the dominant role of the asymptotic normalization coefficient that takes into account the many-particle effect and allows us to obtain the spectroscopic factor necessary to describe the reaction ¹³N → ¹³C+β⁺+ν_e. We find the asymptotic normalization coefficients using the experimental data of the elastic scattering phase-shift of 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 single-particle function and the root of the corresponding spectroscopic factor.