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 neutrinos, we obtain that the phase calculated along the null is equivalent to the 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 or the half geodesic phase. Further we point out the importance of the energy condition in calculating the mass neutrino interference phase. Moreover, we apply the covariant phase to the calculation of the thermal neutron interference phase, and obtain the consistent result with that exploited in COW experiment.