F_l(kr);$$ where $F_l$ and $G_l$ are regular and irregular Coulomb wavefunctions respectively. Note that the boundary conditions given in Eq. \[eq:boundary\] differ by a factor from those adopted by Satchler. Where there is no ambiguity, we suppress the $J$ superscript. When $\pi= (-1)^J$, $V$ is diagonal and Eq. \[eq:cde\] is uncoupled.

In general, $S$ will not be unitary, but will be subject to the unitarity limits: $|S_{11}|^2 + |S_{12}|^2 \le 1$ and $|S_{22}|^2 + |S_{21}|^2 \le 1$, where, of course $S_{12}=S_{21}$. These limits present no particular problem for $S \rightarrow V$ inversion where $S$ can be assumed to satisfy them, but they can represent a significant problem in the case of data to potential inversion, see Section \[datatp\].

The $T_{\rm R}$ interaction and its effect. {#matrixele}
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Non-diagonal matrix elements $(l'J|V|l''J)$ occur in Eqn. \[eq:cde\] for elastic scattering of spin-1 projectiles with certain types of tensor force. The possible forms of local tensor interaction have been classified by Satchler [@satchler; @satchlerbook] who defined , $T_{\rm L}$ and $T_{\rm P}$ interactions. The $T_{\rm L}$ interaction is believed [@stamp] to be very small, at least below 50 MeV/u, and is in any case diagonal in $l$. The $T_{\rm P}$ interaction could well 