Effects of interchannel coupling on the photoionization cross sections of carbon dioxide

Abstract

The photoionization cross sections of CO2 leading to the first four electronic states of CO+2 have been computed including the effects of interchannel coupling. The results were obtained in the Tamm–Dancoff approximation using the Padé-approximant C̃-functional method to solve the resulting scattering equations. All of the required matrix elements have been computed using single-center expansions and numerical integration of the resulting radial functions. An alternative approach for computing products of single-center-expanded functions is presented where the functions are transformed into a coordinate representation, then the product is computed, and finally the product is transformed back into the angular momentum representation. The computational effort required in this approach depends on the second power of the number of partial waves in contrast to the third power dependence found in methods used previously. The photoionization cross sections are obtained in the mixed dipole representation which ensures that the Thomas–Reiche–Kuhn sum rule is satisfied. In the coupled-channel approximation, the shape resonance in the 4σg→kσu channel is found to remain at the same energy and have the same width as was found in earlier single-channel calculations. Both the total cross section in the (4σg)−1 channel and the photoelectron asymmetry parameter are somewhat less affected by the resonance than in the single-channel approximation, but there is still a substantial disagreement with experimental data. The kσu shape resonance is found to modify the cross sections and asymmetry parameters in the other channels, with the largest effect being in the (3σu)−1 ionization channel. The full coupled-channel results, which include coupling among the 1πg→kπu,1πu→kπg,3σu→kσg, and 4σg→kσu channels, are found to significantly modify the cross section in the 1πg→kπu channel leading to good agreement between theory and experiment for the total ionization cross section in the (1πg)−1 channel. However, this coupling is found to significantly perturb the other channels, and in the case of the asymmetry parameters in the (3σu)−1 channel, this leads to relatively poor agreement with experimental data.