The general treatment of the high and low energy particle interference phase in a gravitational field

The interference phase of the high energy mass neutrinos and the low energy thermal neutrons in a gravitational field are studied. For the mass neutri nos, we obtain that the phase calculated along the null is equivalent to th e half phase along the geodesic in the high energy limit, which means that the correct relative phase of the mass neutrinos is either the null phase o r the half geodesic phase. Further we point out the importance of the energ y condition in calculating the mass neutrino interference phase. Moreover, we apply the covariant phase to the calculation of the thermal neutron inte rference phase, and obtain the consistent result with that exploited in COW experiment.