Dynamic Multipole Polarizabilities of Two- and Four-Electron Atomic Systems

Dynamic multipole polarizabilities of a number of simple atomic closed-shell systems in their ground states have been calculated within the coupled time-dependent Hartree-Fock scheme. The systems here investigated include He, ${\mathrm{Li}}^{+}$, ${\mathrm{Be}}^{2+}$, ${\mathrm{B}}^{3+}$, ${\mathrm{C}}^{4+}$, Be, ${\mathrm{B}}^{+}$, and ${\mathrm{C}}^{2+}$. In order to acquire some feeling about the obtained results, the dipole polarizabilities have been evaluated either by using a scalar- or a vector-potential representation for the oscillating external field: these two choices give rise to the well-known polarizability expressions in terms of "length" and "velocity" oscillator strengths, respectively. Furthermore, a unitary transformation of the Hartree-Fock Hamiltonian is devised, which allows one to use a perturbation operator corresponding to that involved in the "acceleration" oscillator-strength expression. Estimates of transition energies to low-lying excited states have been also obtained from the frequency values at which the various polarizabilities display discontinuities.