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Splitting the energy levels of a hydrogen-like atom by the electric fieldnonuniform at the atomic scale is studied. This situation is important for themulti-level treatment of the phenomenon of Rydberg blockade [Yu.V. Dumin, J.Phys. B, v.47, p.175502 (2014)]. An explicit formula for the energy levels isderived. A typical value of the energy shift by the electric field gradientturns out to be proportional to the 4th power of the principal quantum number(i.e., the square of atomic size), as would be expected from a qualitativeconsideration. Finally, the fine spatial structure of the Rydberg blockade isanalyzed when the electric-field-gradient term plays the dominant role, and theresults are confronted with the experimental data.

Stark effect in the nonuniform field and its influence on the fine structure of Rydberg blockade