Perturbation theory for the hydrogen atom in a spherical cavity with off-centre nucleus

The problem of a hydrogen atom in an impenetrable spherical cavity of small radius R is considered on the basis of the first-order perturbational trea tment of the electron-nucleus interaction taking explicit account of the bo undary condition. An approximate analytic expression is derived for the ele ctronic energy as a function of the shift of the nucleus off the centre. Th e estimations obtained are in good qualitative and semiquantitative agreeme nt with the results of the finite-difference calculations. Some general fea tures of the energy dependences are discussed qualitatively.