3 The scattering calculation

The R-matrix method used in this calculation is described fully elsewhere (Hummer et al. 1993 and references therein). As outlined above, we include mass and Darwin relativistic energy shifts, but not the one- and two-body fine-structure interactions. For the calculation in the resonance region, we use an R-matrix boundary radius of 4.66 a.u., to encompass the most extended target orbital (4d), while in the open channel region a boundary radius of only 2.84 a.u. was required. The expansion of each scattered electron partial wave is over a basis of 22 functions within the R-matrix boundary, and the partial wave expansion extends to a maximum of l=15. The outer region calculation is carried out using the program STGFJ (Hummer et al. 1993), which calculates reactance matrices in LS-coupling and then transforms them into the ${\bf Jk}$-coupling scheme (Saraph 1972, 1978), including the effects of intermediate coupling between the target terms, using the so-called term-coupling coefficients (TCCs).

Collision strengths in the resonance region are computed at 10000 points equally spaced in energy. We do not, therefore attempt to delineate all resonance structures fully. The accuracy of this sampling approach was discussed in IP XIV, where it was concluded that this number of points should lead to a purely statistical error of less than 1%. In the region of all channels open, a further 125 points span the energy range from the highest threshold up to 100 Ryd.

For energies above the highest threshold, the partial wave expansion extends to $l\,=\,18$ and the collision strengths are corrected for missing partial waves using the method described by Binello et al. (1998). In brief, for optically allowed transitions contributions from partial waves l > 18 are calculated in the Coulomb-Bethe approximation, using oscillator strengths taken from the Basis 1 target calculation including fine-structure effects. For the remaining transitions, the contribution from the high partial waves is estimated by assuming that the partial collision strengths are declining geometrically as a function of partial wave. Once all collision strengths have been corrected for missing partial waves, they are extrapolated to energies higher than 100 Ryd using the high energy behaviours discussed by Burgess & Tully (1992). Further details are given in Binello et al. (1998).