Wigner real spin-orbit terms. In keeping with the nature of this test, the very small inversion basis of Ref.[@prl] was used. This has two Gaussians only for each component except the central components for which there were three. The centres and widths of the Gaussians were not varied during the inversion.

The ‘target’ (known) and inverted potentials are shown in Figure 2, together with the starting potential required by the IP method. The starting potential is the dot dashed line, non-zero for two components only, and corresponding to $\sigma = 10.552$ where $\sigma$, defined in Section \[ipinv\], is summed over the 11 energies. The inverted potential is shown as the dotted line, and the ‘target’ potential, from which $S^J_{l'l}$ was calculated, is the full line. We see that the qualitative features are reproduced although less well for the small components and near the nuclear centre. The value of $\sigma$ for the potential shown in the dotted line was $0.135$ which is reasonable for a low energy multi-energy case. For 10.5 MeV, this corresponds to $S^J_{l'l}$ for the target and inverted potentials being indistinguishable on a graph apart from one single term: the phase angle of the non-diagonal part of $S^J_{l'l}$ 