range of Si abundances found in our snapshot survey (Gänsicke et al. in prep).

Other points worth mentioning are that the determination of an effective ion charge with the simple pressure ionisation description of @paquetteetal86-1 is not appropriate in the absence of deep convection. We have used the usual Saha equation (with a small lowering of the ionisation potential from non-ideal interactions) to determine the abundances of different ions from an element. The diffusion velocity is then calculated as a weighted average of the ionisation stages. This procedure was already used in @koester+wilken06-1 and @koester09-1 for the models without or with only a shallow convection zone, although not explicitly stated in those papers. New in our present calculation is the consideration of neutral particles, following the discussion and methods outlined in @vennesetal11-2.

The main results of our calculations are the diffusion fluxes, $X \rho
v$, for each element, which are assumed (in steady state) to be the abundances of the accreted matter. These are summarised for the four objects in Table \[t-fluxes\]. The total diffusion fluxes (=accretion rates) are obtained by multiplying these fluxes with $4 \pi R_\mathrm{wd}^2$, where we used the cooling tracks of [@wood95-1] to obtain the white 