The application of inversion to nuclear scattering

Abstract

We review the application of inverse scattering in nuclear physics. We emphasize the various ways in which inversion can be used to understand nuclear interactions, and survey the results that have been obtained. We discuss S → V inversion from both theoretical and experimentally fitted S-matrices as well as a new method for direct observable →V inversion. The various alternative approaches to inverse scattering are briefly reviewed, and their range of applicability is discussed. This is not a review of formal inversion methods, but the iterative perturbative (IP) approach is described in some detail together with a discussion of the physics results which have been obtained using it and other inversion methods. The case of p+4He scattering is presented in some detail as a case study exemplifying the kind of information which can now be obtained by the application of inverse scattering techniques. It also brings out the comparative properties of different inversion methods.

Phonon coupling effects in proton scattering fromCa40

“…We have shown that the application of exact S lj → V (r) + l · s V SO (r) inversion [16][17][18] relates coupling effects to local potential phenomenology. We first presented a local potential model of realistic GQR coupling that improved the fit to angular distribution data in a specific case.…”

“…This is done by applying S lj → V (r) + l · s V SO (r) inversion [16][17][18] to the elastic channel S-matrix output by the CC code FRESCO [19]. The local, l-independent dynamic polarization potential (DPP) generated by the coupling is obtained by subtracting the elastic channel ("bare") potential used in the CC calculation from the potential found by inversion.…”

Influence of single-neutron stripping on near-barrier He6+Pb208 and HeMarquínez-Durán1, Keeley2, Kemper3 et al. 2017Phys. Rev. C77390View full textAdd to dashboardCite

“…Before considering the DPPs, which were obtained by inversion of the elastic scattering S-matrix S L using the iterative-perturbative (IP) S L → V (r) inversion method [11], we examine the coupling effect on S L . It is important for such inversion to eliminate any small-amplitude numerical "noise" from S L ; such noise does not affect the observables, the angular distributions in this case, but can cause difficulties in the inversion process.…”

Dynamic polarization potential and dynamical nonlocality in nuclear potentials: Nucleon-nucleus potential

“…(We use "CC" to include coupled reaction channel, CRC, and continuum-discretized coupled-channel, CDCC.) An earlier variation of this approach involved refitting the observables rather than the S-matrix produced by the CC code [6,12,13], but this procedure was superseded with the advent of S-matrix-to-potential inversion techniques [14][15][16][17][18][19].…”

“…4 and 5, the two alternative ADs for the local equivalent potentials are for alternative solutions [41] to the S l → V (r) inversion [17][18][19]. As the iterative inversion process converges, the resulting potentials may become somewhat oscillatory and although the two potentials shown both give elastic scattering ADs that are indistinguishable from the elastic channel AD from the CC calculation, these figures In each case, the dotted line is the AD with the bare nucleon optical potential, the solid line is with induced nonlocality due to coupling to the 10 collective states and the dashed line is for the local equivalent nucleon OMP.…”