TY - JOUR
T1 - Exact solutions for perturbed confined hydrogen atoms
T2 - Polarizabilities and nuclear shielding factors
AU - Burrows, B. L.
AU - Cohen, M.
PY - 2005/9
Y1 - 2005/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=28844470301&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.72.032508
DO - 10.1103/PhysRevA.72.032508
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AN - SCOPUS:28844470301
SN - 1050-2947
VL - 72
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 3
M1 - 032508
ER -