Calculation of electron-impact and photoionization cross sections of methane using analytical Gaussian integrals

The ionization by photon or electron impact of the inner (2a₁) and outer (1t₂) valence orbitals of the CH₄ molecule is investigated theoretically. In spite of a number of approximations, including a monocentric approach and a rather simple distorting molecular potential, the calculated cross sections are overall similar to those of other theoretical methods and in reasonable agreement with experimental data. The originality of the present approach stands in the way we evaluate the transition matrix elements. The key ingredient of the calculation scheme is that the continuum radial wave function of the ejected electron is represented by a finite sum of complex Gaussian-type orbitals. This numerically expensive optimization task is then largely compensated by rather simple and rapid analytical calculations of the necessary integrals, and thus all ionization observables, including cross section angular distributions. The proposed and implemented Gaussian approach is proved to be numerically very reliable in all considered kinematical situations with ejected electron energy up to 2. 7 a. u. The analytical formulation of the scheme is provided here for bound molecular states described by monocentric Slater-type orbitals; alternatively, one may also use monocentric Gaussian-type orbitals for which the formulation is even simpler. In combination with complex Gaussian functions for the continuum states, an all-Gaussian approach with multicentric bound states can be envisaged.