The variations of the cross sections with temperature are normally fairly simple. Earlier versions of TRANSX used a $N$-th order Lagrangian interpolation scheme on $\sigma(T)$ and $T$, where $T$ is the temperature and $N$ is the number of values in the temperature grid. However, this scheme would sometimes give unphysical or negative cross sections due to oscillations in the interpolation function. This version of TRANSX reverts to using simple linear interpolation for its stability.
For $\sigma_0$, the shielding curve has a shape similar to the tanh function (see Kidman, Ref. 18). Like tanh, it has a limited radius of convergence, and no single polynomial can be used to represent it for all $\sigma_0$. Earlier versions of TRANSX used a combination of $1/\sigma_0$, Lagrangian, and quadratic interpolation for different $\sigma_0$ ranges. Just as for temperature interpolation, this scheme sometimes led to large unphysical oscillations in the interpolated cross sections. Therefore, this version of TRANSX uses simple linear interpolation based on $\log(\sigma_0)$, except for very large $\sigma_0$ values, where it uses $1/\sigma_0$ interpolation. The lowest cross-section value is used for $\sigma_0$ less than the lowest grid point in the self-shielding table. This approach is stable and reliable, but it requires that data be given on a finer $\sigma_0$ grid than the older method for equivalent accuracy. Note also that linear interpolation preserves the condition that the total cross section be equal to the sum of its parts.
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