3 Electronic matrix elements

We have used the ab-initio matrix elements calculated by Wolniewicz and Dressler ([1988]) as functions of the internuclear distance (B.O. Potential and adiabatic corrections for diagonal elements, radial coupling and rotational coupling for off diagonal elements) to solve the coupled equations. However we have slightly modified the diagonal matrix elements as indicated by Abgrall et al. ([1994]) by fitting them to experimental levels which are not affected by the rotational coupling (i.e. levels with J=0 and levels with J=1 belonging to C^- and D^-). This procedure was necessary because the wavefunctions and energy levels are very sensitive to the relative position of zero order energy levels (i.e. the solutions of the uncoupled equations). With this method, almost all energy levels are obtained within 0.5 wavenumber of the experimental value up to high rotational quantum numbers, and the mixing between the electronic B.O. wavefunctions is improved. The electronic transition moment $M_{{\rm BX}}$ and $M_{{\rm CX}}$ are those of Dressler & Wolniewicz ([1985]), $M_{{\rm B'X}}$ is taken from Ford et al. ([1975]) and $M_{{\rm DX}}$ from Rothenberg & Davidson ([1967]). In this latter case, only few points were available with poor claimed accuracy. Drira ([1999]) has recently recalculated $M_{{\rm DX}}$with a precise interaction configuration method (MRCI) and a fine grid of internuclear distances. We have thus introduced her value in our calculations. Particular care was taken in the calculations that all matrix elements involve wavefunctions with coherent values of the relative phases and we have explicitly verified these properties with the MOLPRO software package (Knowles & Werner [1992]).