Phase factors in electron-molecule collision calculations Original Research Article

At low impact energies, high quality electron-molecule collision calculations require target correlated wavefunctions representing several electronic states. Target correlation is usually introduced via a configuration interaction (CI) expansion. This approach introduces phase factors in coefficients of the target CI expansion between the N electron target calculation and the N + 1 electron scattering calculation. A method requiring radiagonalisation of the target calculation for each scattering symmetry was used (Orel et al., Phys Rev A 44 (1991) 4328) and widely copied. It is suggested that while this method accounts for the most serious phase problems, for certain calculations residual phase inconsistencies can arise. It is shown that the phase factors actually arise from different ordering of spin-orbitals in the N and N + 1 electron calculations. An alternative method based on the analysis of the electron configurations used in the scattering calculation is proposed. This method resolves all phase ambiguities and removes the need for redundant rediagonalisations of the target Hamiltonian. The price of this method is the need to understand in detail the algorithm used for generating antisymmetrised configurations. Implementation of this method as part of the UK molecular R-matrix codes which are based on the ALCHEMY package is discussed.