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The interference phase of the high energy mass neutrinos and the low energythermal neutrons in a gravitational field are studied. For the mass neutrinos,we obtain that the phase calculated along the null is equivalent to the halfphase along the geodesic in the high energy limit, which means that the correctrelative phase of the mass neutrinos is either the null phase or the halfgeodesic phase.  Further we point out the importance of the energy condition in calculatingthe mass neutrino interference phase. Moreover, we apply the covariant phase tothe calculation of the thermal neutron interference phase, and obtain theconsistent result with that exploited in COW experiment.Comment: 14 pages, 1 figur

The General Treatment of the High and Low Energy Particle Interference Phase in a Gravitational Field