  We demonstrate a new approach to the analysis of extensive multi-energy data.
For the case of d + He-4, we produce a phase shift analysis covering for the
energy range 3 to 11 MeV. The key idea is the use of iterative perturbative
data-to-potential inversion which can produce potentials which reproduce the
data simultaneously over a range of energies. It thus effectively regularizes
the extraction of phase shifts from diverse, incomplete and possibly somewhat
contradictory data sets. In doing so, it will provide guidance to
experimentalists as to what further measurements should be made. This study is
limited to vector spin observables and spin-orbit interactions. We discuss
alternative ways in which the theory can be implemented and which provide
insight into the ambiguity problems. We compare the extrapolation of these
solutions to other energies. Majorana terms are presented for each potential
component.
