A simple polynomial approach to the exact perturbative evaluation of low-frequency dynamic polarizabilities for a ground-state hydrogen atom

An exact perturbative method is presented for evaluating frequency-dependent multipole polarizabilities for a ground-state hydrogen atom in the range of low frequencies. The first-order correction to the unperturbed wavefunction (wf) is expanded in a power series of the frequency with radial coefficients determined by simple polynomial techniques. Almost all real frequencies having physical importance, and the corresponding imaginary frequencies, fall in the range of convergence that has been observed for the dynamic polarizability. In this range, a moderate number of terms accounts for nine decimal figure results for dipole, quadrupole and octopole FDPs of H(1s).