DISPERSION-RELATIONS FOR STARK ENERGY SHIFTS IN HYDROGEN-ATOM

On the basis of an approximate but nonperturbative expression for the energy shift δE in the ground state of the hydrogen atom in the presence of an electric field of strength E, we deduce that δE has a branch point at E = 0, and an asymptotic behavior δE → -1 2 E ln E as E → ∞. These properties lead to a twice-subtracted dispersion relation for δE as a function of E. The dispersion relations in conjunction with the WKB approximation and the perturbation series allow us to (i) deduce the large-n behavior of the coefficient of En in the perturbation series for δE(E) including 1 n corrections and (ii) obtain the energy shift and the level width of the ground state for a large range of values of E. The agreement with the earlier numerical calculations is very satisfactory. © 1979.