1 Introduction

For electron impact with ions, the collision strength is finite at threshold and in the high energy asymptotic limit it displays logarithmic, constant or inverse square behaviour depending on whether the transition is of dipole, non-dipole, non-spin change or spin change type. There are also intermediate cases of small oscillator strength. It was pointed out by Burgess & Tully (1992) that, with the emphasis on large collision calculations, such as those using the R-matrix method, and with the focus on resonance structure, attention was often not given to ensuring the correct continuation of the collision strength from low energies into the Born and Born/Ochkur regime at high energy. While this did not matter for forbidden line formation in nebulae, it certainly did for fusion plasma applications. In the latter case, inflowing impurity species can find themselves in temperature regimes spanning from well below the ionisation energy to far above it. The high energy behaviour is of course simply prescribed, given the atomic structure, in terms of oscillator strength or first Born coefficients. Properly, the whole energy range of collision strength data should be provided for applications and the Burgess-Tully method of mapping the energy from threshold to infinity onto [0, 1] emphasised this. With the finite behaviour at threshold, the scaled collision strength for ions, as a function of scaled energy, displayed small variation over the whole independent variable range such that it could be well represented by a simple five-point equally-spaced knot spline. A single parameter, C, allowed a scale distortion in the independent variable by which the spline could be optimised. The plots became known as "C-plots'' and often showed up embarrassing deficiencies in the original data. With the introduction of divertor technology into magnetically confined fusion plasma design and the resurgence of discharge devices for plasma processing, neutral atoms and molecules are now very much the focus of interest in the laboratory environment (Behringer & Fantz 1996) as well as of continuing importance in astrophysics (see, for example, the recent first observation of the neutral helium intercombination line in the solar atmosphere by Brooks et al. 1999). Collision strengths for neutrals are zero at threshold, with the behaviour near threshold dependent on the dominant partial wave in the N+1 electron system. Also, collision data is usually presented on scales which conceal the threshold region. The problem is analogous to that for the high energy region and a similar opening out of the threshold region as Burgess & Tully did for the high energy region is desirable. There is a second issue. The Burgess-Tully method is not a faithful representation of the original data but a considered (and hopefully) improved conversion of the data. A second path of fitting data is that of strict interpolation on the assumption that the source data is exact. For this it is helpful to prepare an analytic approximate form $\Omega^{\rm (approx)}$ which can be compared with the tabulated collision strength $\Omega$. It is useful if optimised fitting and interpolative fitting run side by side. Within the Atomic Data and Analysis Structure (ADAS) Project, established in support of the SOHO spacecraft and solar astrophysics (Mason et al. 1997; Summers et al. 1998; Summers 1993, 1999), both methods are used with the latter designed also to highlight misprints and errors of data entry.