Two-photon transitions in hydrogen: A test of pseudostate summation

We make another application of a remarkably efficient technique, in which the intermediate states of conventional second-order perturbation theory are replaced by a finite set of pseudostates, and the energy denominators are replaced by the expectation values of the unperturbed Hamiltonian with respect to those pseudostates. In previous calculations (of van der Waals coefficients and frequency-dependent polarizabilities) in which the pseudostates were determined by diagonalization of the unperturbed Hamiltonian, excellent converged results were obtained with as few as five to ten terms representing both bound and continuum states. Following the work of Bassani, Forney, and Quattropani [Phys. Rev. Lett. 39, 1070 (1977)], we use the method to investigate the 2S-1S transition rate using both the E·x and A·p forms of the interaction. The results mirror closely those obtained in the conventional way, even when only a small number of terms are used, and they are not strongly dependent on the exact form of the basis functions used