potential is defined as in Eq. \[eq:defpot\].

For notational simplicity, Eq. \[eq:defpot\] has not been written to reflect parity dependence. There are two alternative methods of representing parity dependence. The code IMAGO can apply either of these to each of the components in Eq. \[eq:defpot\] except $V_{\rm coul}$. The first representation defines Wigner and Majorana components for each term, say $V_{\rm x}$: $$V_{\rm x} = V_{\rm x, W} + (-1)^l V_{\rm x, M}$$ where $l$ is the partial wave angular momentum. With this form the inversion procedure can be made to determine $V_{\rm x, W}$ and $V_{\rm x, M}$ for any or all $V_{\rm x}$. An alternative approach is to determine independent positive or negative parity components for $V_{\rm x}$. In many cases, the Wigner-Majorana representation is most natural and has been shown [@kuk-new] to be preferable where the odd parity term may otherwise be ill-determined. However, sometimes the odd-even representation is more appropriate, for example where a particular $V_{\rm x}$ has completely different shapes and magnitudes for the different parities, as we believe can be the case for $V_{\rm R}$. The code IMAGO offers the freedom to represent the parity dependence of each component $V_{\rm x}$ in either way.

