A NEW APPROACH TO THE RANDOM-PHASE-APPROXIMATION

With the aim of obtaining a practical approach to molecular photoioniz ation continua, a new formulation is given for the random phase approx imation (RPA). This development is based on the so-called algebraic-di agrammatic construction (ADC) used previously to derive higher-order a pproximations to the polarization and other propagators. In the ADC re formulation the RPA pseudo-eigenvalue equations split into two equival ent, generally Hermitian, secular problems of half dimension. Here the elements of the resulting ADC secular matrices are given in the form of 'regular' perturbation expansions. Similar perturbation expansions result for the 'effective' transition amplitudes required to calculate spectral intensities. Approximation schemes converging to the full RP A are obtained by truncating these perturbation expansions at successi vely higher-order n. For the lowest orders n = 1 and 2 the ADC(n)/RPA schemes are specified explicitly. In addition to the perturbation-theo retical approach, direct closed-form expressions are given for the ADC secular matrix and effective transition amplitudes relating these qua ntities to the RPA eigenvalues and eigenvectors. As shown by these rel ations, the ADC reformulation can be viewed as a specific form of quas i-degenerate perturbation theory (QDPT) applied to the RPA pseudo-eige nvalue problem. In the single-channel (SC) approximation the ADC secul ar equations reduce to a one-electron eigenvalue problem for an energy -independent non-local potential. A particularly useful method is the single-channel ADC(1) scheme combining the scattering solutions of the familiar frozen-core Hartree-Fock (FCHF) model with a simple first-or der expression for the transition moments. Illustrative applications o f the SC-ADC(I) method to the photoionization in H-2 (1 sigma(g)) and N-2 (3 sigma(g)) are reported. These calculations show that Wound stat e correlation can quite substantially influence both the magnitude and the shape of the cross sections as a function of energy.