Effect of external magnetic field on nucleon mass in hot and dense medium : Inverse Magnetic Catalysis in Walecka Model

Vacuum to nuclear matter phase transition has been studied in presence of constant external background magnetic field with the mean field approximation in Walecka model. The anomalous nucleon magnetic moment has been taken into account using the modified "weak" field expansion of the fermion propagator having non-trivial correction terms for charged as well as for neutral particles. The effect of nucleon magnetic moment is found to favour the magnetic catalysis effect at zero temperature and zero baryon density. However, extending the study to finite temperatures, it is observed that the anomalous nuclear magnetic moment plays a crucial role in characterizing the qualitative behaviour of vacuum to nuclear matter phase transition even in case of the weak external magnetic fields . The critical temperature corresponding to the vacuum to nuclear medium phase transition is observed to decrease with the external magnetic field which can be identified as the inverse magnetic catalysis in Walecka model whereas the opposite behaviour is obtained in case of vanishing magnetic moment indicating magnetic catalysis.