Non-Relativistic Limit of Neutron Beta-Decay Cross-Section in the Presence of Strong Magnetic Field

Abstract

One of the most important reactions of the URCA that lead to the cooling of a neutron star, is neutron beta-decay ( ). In this research, the energy spectra and wave functions of massive fermions taking into account the Anomalous Magnetic Moment (AMM) in the presence of a strong changed magnetic field are calculated. For this purpose, the Dirac-Pauli equation for charged and neutral fermions is solved by Perturbation and Frobenius series method, respectively. The results of the Frobenius series method are in good agreement with the results of Nikiforov-Uvarov method (NU). In continuous, using the calculated wave functions, the general relation of neutron decay cross-section in the non-relativistic limit has been obtained. This relation has been derived by the four-fermion Lagrangian within the framework of the standard model of weak interactions. These calculations from the perspective of nuclear astrophysics can be important.