Nuclear applications of inverse scattering, present ... and future?

Abstract

There now exists a practical method (IP) for the routine inversion of $S$-matrix elements to produce the corresponding potential. It can be applied to spin-1/2 and spin-1 projectiles. We survey the ways that IP inversion can be applied in nuclear physics by inverting $S_{lj}$ derived from theory or from experiment. The IP inversion method can be extended to invert $S_{lj}(E)$ over a range of energies to produce a potential $V(r,E) + \vect{l}\vdot\gvect{\sigma} V_{\rm ls}(r,E)$. It also yields parity-dependent potentials between pairs of light nuclei and can be convoluted with a direct search on the $S$-matrix to produce `direct data $\to V$ inversion'. The last is an economical alternative form of optical model search to fit many observables (e.g. for polarized deuterons) for many energies, producing an energy-dependent potential with many parameters (e.g. $T_{\rm R}$ for deuterons).