Electron-molecule collision calculations using the R-matrix method

摘要

The R-matrix method is an embedding procedure which is based on the division of space into an inner region where the physics is complicated and an outer region for which greatly simplified equations can be solved. The method developed out of nuclear physics, where the effects of the inner region were simply parametrized, into atomic and molecular physics, where the full problem can be formulated and hopefully solved ab initio. In atomic physics R-matrix based procedures are the method of choice for the ab initio calculation of electron collision parameters. There has been a number of R-matrix procedures developed to treat the low-energy electron-molecule collision problem or particular aspects of this problem. These methods have been extended to both positron physics and the R-matrix treatment of vibrational motion. The physical basis of the R-matrix method as well as its theoretical formulation are presented. Various electron scattering models within an R-matrix formulation including static exchange, static exchange plus polarization and close coupling are described with reference to various computational implementations of the method; these are compared to similar models used within other scattering methods. The need for a balanced treatment of the target and continuum wave functions is emphasised. Extensions of close-coupling based models into the intermediate energy regime using pseudo-states is discussed, as is the adaptation of R-matrix methods to problems involving photons. The numerical realisation of the R-matrix method is based on the adaptation of quantum chemistry codes in the inner region and asymptotic electron-atom scattering programs in the outer region. Use of bound state codes in scattering calculations raises issues involving continuum basis sets, appropriate orbitals, integral evaluation, orthogonalization, Hamiltonian construction and diagonalization which need to be addressed. The algorithms developed to resolve these issues are described as are ones associated with the outer region where methods to characterize resonances have received particular attention. Results from a few illustrative calculations are discussed: (i) electron collisions with polar systems with water as an example; (ii) electron collisions with molecular ions focusing on H_3~+; (iii) electron collisions with organic species such as methane and uracil and (iv) positron-molecule collisions. Finally some outstanding issues that need to be addressed are mentioned.