Up: Extension of the BurgessTully
Subsections
The production of Maxwellaveraged collision strengths is straightforward. The
BurgessTully GaussLaguerre based approach remains valid for the high energy
region. The finite range of the lowenergy region is treated similarly but with the
Gaussian quadrature, in this case tuned to the usual
behaviour. The switch
in energy between the two quadratures is not set at the E_{0} of Sect. 2 or the X_{k} of
Sect. 4 but, rather, where the threshold collision strength and Maxwellian exponential energyscale
lengths are equal.
For the strict interpolative approach, it is noted that the approximate forms
are integrable in terms of known functions. Thus, setting
with
the Rydbery energy unit, the Maxwell
averaged collision strength is



(10) 
where
,
is the incomplete gamma
function and E_{1} is the first exponential. Note that in ,
the
principal value of the logarithm must be taken for negative values of the
argument A.
Since the quadrature in the threshold region is tuned to the
behaviour, modest improvement in the threshold region is achieved by numerical
integration of the difference of the interpolated exact data and the
approximate form and then completing the integral with the analytic integral of the
approximate form. For neutral atoms and molecules in plasmas, distortions of
the electron distribution function are common and so dedicated quadrature
routines for particular cases are usually required. The optimised spline and
fitting algorithms given here are readily integrated into such routines.
Up: Extension of the BurgessTully
Copyright The European Southern Observatory (ESO)