  The first order perturbations of the energy levels of a stationary hydrogen
atom in static external gravitational field, with Schwarzschild metric, are
investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P,
3S, 3P, 3D, 4S, 4P, 4D and 4F levels. The results show that the energy-level
shifts of the states with total angular momentum quantum number 1/2 are all
zero, and the ratio of absolute energy shifts with total angular momentum
quantum number 5/2 is 1:4:5. This feature can be used to help us to distinguish
the gravitational effect from other effect.
