Exact solutions for perturbed confined hydrogen atoms: Polarizabilities and nuclear shielding factors

We extend our recent treatment of a well-known model of a nonrelativistic hydrogen-like atom confined within an impenetrable spherical ``box'' of radius . Analytical closed-form solutions are presented for the first-order perturbation corrections appropriate to the dipole polarization of states. solutions are expressed conveniently in terms of Kummer (confluent hypergeometric) functions, exactly as for the field-free atom, by exploiting several well-known recurrence and differential relations for these functions. The functions and all necessary integrals are evaluated using standard routines, which exploit analytical properties of these functions. The accuracy of our procedures has been checked by a similar calculation of the dipole shielding factors. Our procedures are easily extended to states of nonzero angular momentum, as well as to higher-multipole perturbations. Our exact values may be of interest in assessing the utility of this simple model of atomic confinement.

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