Magnetic Quadrupole Polarizability of Closed-Shell Atoms

The magnetic quadrupole polarizability tensor determines the quadrupole moment induced in an atomic system by a nonuniform external magnetic field. From the analogy to the corresponding electric field case, this quantity is defined and simplified for a spherically symmetric system in an axially symmetric external field. Expressions are presented for the magnetic vector potential corresponding to the first three terms of a Taylor-series expansion for the magnetic field vector, and the Hamiltonian operator is obtained for a many-electron atom in an axially symmetric magnetic field with first-order gradients. Calculations are presented for the magnetic quadrupole polarizability for closed-shell atoms and ions with two to eighteen electrons. These calculations employ the fully coupled Hartree-Fock variation-perturbation procedure. The magnetic quadrupole polarizability shows a rapid decrease with atomic number within each isoelectronic series. Positive values are obtained for all atoms and ions except Li^-, Be, and Na^-.