The URCA processes in the presence of a strong magnetic field in neutron stars due to emitting neutrinos lead to cooling them, so studying these processes are very important in view of astrophysical applications. The neutron beta decay is one of the most important the URCA processes. In this research, at first we calculated the wave functions and energy spectrum of the fermions in the non-relativistic limit by solving the Dirac-Pauli equation with the aid of the time independent disturbation theory in the presence of a strong changed magnetic field. Then, we obtained the general form of cross-section of Neutron Beta decay by using four-fermion lagrangian. All calculations of this study have been done by considering the anomalous magnetic moment (AMM) of massive fermions.
