\Delta V_{ij} \psi_{j \mu} {\rm d} r. 
\label{eq:dS}$$ The expression (\[eq:dS\]) is the basis for the coupled-channel inversion method. The success of the inversion method in leading to a converged solution confirms the wide applicability of this equation in each step of our iteration process.

Testing couple-channel $S \rightarrow V$ inversion for spin-1 projectiles
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We carried out two contrasting tests of $S \rightarrow V$ inversion as described in Sections \[firsttest\] and \[multi\] below. First let us define the potentials and the inversion basis.

Specification of the interaction potential and basis used {#specs}
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In one respect our notation is non-standard. We write down the complete potential for spin-1 projectiles scattering from a spin-zero target. It is $$V_{\rm cen}(r) + {\rm i} W_{\rm cen}(r) + V_{\rm coul}(r) + \\
2{\bf l \cdot s}(V_{\rm so} + {\rm i}W_{\rm so}) + (V_{\rm R} + 
{\rm i}W_{\rm R})T_{\rm R}
\label{eq:defpot}$$ where $V_{\rm coul}(r)$ is the usual hard-sphere Coulomb potential. Note that our spin-orbit potentials $ V_{\rm so}$ and $W_{\rm so}$, are defined in such a way that they will be half the magnitude of those defined according to the usual convention [@satchlerbook] for spin-1 projectile.[^2] For the test cases we present, the spin-orbit 