outcome of inversion will be a potential with many components. We therefore label each component with an index $p$ which identifies central, spin-orbit or tensor terms, each real or imaginary. The number of components doubles when the potential is parity dependent. (Parity dependence is particularly important for light nuclei at lower energies.)

The IP method commences with a ‘starting reference potential’, SRP, and proceeds by iteratively correcting each component $p$ of the potential: $$V^{(p)} \rightarrow V^{(p)} + \sum_n \alpha^{(p)}_n v^{(p)}_n(r) \label{first}$$ where $\alpha^{(p)}_n$ are coefficients to be determined and $v^{(p)}_n(r)$ are the functions comprising the ‘inversion basis’, (which, if required, can be chosen differently for different $p$). The amplitudes $\alpha^{(p)}_n$ are determined at each iteration from linear equations, based on an SVD algorithm, which successively reduce the ‘phase shift distance’ $\sigma$ defined by: $$\sigma^2 = \sum |S^{\rm t}_k - S^{\rm c}_k|^2 \label{sigma}.$$ For each partial wave $k$, $S^{\rm t}_k$ is the ‘target’ $S$-matrix and $S^{\rm c}_k$ is for the potential at the current iteration. Here the label $k$ is a single index which identifies the partial wave angular momentum $l$ as well as the energy $E_i$ when multi energy sets of $S_l(E_i)$ are simultaneously inverted. It also includes non-diagonal elements 