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 R. Analytical closed-form solutions are presented for the first-order perturbation corrections appropriate to the dipole polarization of all s states. Exact solutions are expressed conveniently in terms of Kummer (confluent hypergeometric) M functions, exactly as for the field-free atom, by exploiting several well-known recurrence and differential relations for these functions. The M functions and all necessary integrals are evaluated using standard MAPLE 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.