6 Assessing the reliability

Although in Tables 2 - 5 we give results with 4 significant figures we need to warn the reader against believing that this reflects the reliability of our data.

At low temperatures the value obtained for $\Upsilon(T)$ depends quite critically on the energy dependence of the cross section near threshold. Since the target is a neutral atom, $\Omega(E_j) \propto E_j^{1/2}$for sufficiently small E_j, but, for most of the transitions, the data produced by the CCC calculations are not sufficiently detailed at low energies to delineate this. The numbers given here for $\Upsilon(T)$were obtained by assuming that $\Omega(E_j)$ falls linearly to zero in the interval between E_j = 0 and the lowest value of E_j at which the cross section was calculated. For our tabulated range, we have $\log T \geq 3.75$, where the error due to this threshold effect does not exceed a few percent. Further details will be given elsewhere.

The CCC approximation takes full account of continuum states, whereas the R-matrix method used by both BK and SB does not. Allowing for the continua has two opposite effects: (a) part of the flux which would go to discrete states is now diverted towards continuum states, so reducing collision strengths for transitions between discrete states; (b) intermediate continuum states may provide alternative routes for flux to reach discrete states, thereby increasing collision strengths. By comparing effective collision strengths we reach the following conclusions: for transitions $1 \to j$, $2 \to j$, $3 \to j$ the ratio $\Upsilon({\rm BBFT})/\Upsilon({\rm SB})$ is close to one for $j\leq11$, and is significantly less than one if $j\geq12$ (i.e. n=4). This we interpret to mean that (a) is the dominant effect for these latter transitions. However, for some of the $4 \to j$ transitions the ratio is appreciably greater than one, indicating that (b) dominates. This suggests that the continuum states are capable of either decreasing or increasing collision strengths particularly if both the initial and final levels are close to the ionisation threshold.