Phonon coupling effects in proton scattering fromCa40

Abstract

Background: Formal optical model theory shows that coupling to vibrational nuclear states generates a nonlocal and l-dependent dynamical polarization potential (DPP). Little is established concerning the DPP, yet its properties are crucial for explaining the departures of optical model potentials (OMPs) from global behavior and for the rigorous extraction of spectroscopic information from direct reactions. Purpose: To appraise the application of channel coupling followed by S-matrix inversion for the systematic exploration of the contribution of the coupling of collective states to the nucleon OMP and to identify properties of nuclear potentials indicative of l-dependence. Methods: S-matrix to potential, S lj → V (r) + l · s V SO (r), inversion provides local potentials that precisely reproduce the elastic channel S-matrix from coupled channel (CC) calculations. Subtracting the elastic channel uncoupled (bare) potential yields a local and l-independent representation of the DPP. The dependence of this local DPP upon the nature of the coupled states and upon other parameters can be studied. Results: All components of the DPP arising from coupling to vibrational states are substantially undulatory with a point-by-point magnitude therefore disproportionate to their contribution to volume integrals. Information relating to dynamical nonlocality is found. The proton charge leads to a substantial difference between DPPs for protons and neutrons. Conclusions: Undulatory features in potentials found in precision fits to elastic scattering data are significant, are a consequence of coupling to inelastic channels and must be allowed for in phenomenology; they are indirect evidence of l-dependence. Within the model, coupling to excited states magnifies the effect of the proton charge on the difference between proton-nucleus and neutron-nucleus interactions. Coupled channel plus inversion is a procedure of wide applicability, complementary to evaluation of the Feshbach formalism.

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

“…The present calculations employ the same set of excitations of 40 Ca and the local equivalent potentials presented in Ref. [41] are those employed herein. We remark that the true DPPs are l-dependent as well as nonlocal, so that this work is actually studying the impact of both l-dependence and nonlocality that is generated by the coupling to collective states.…”

“…[41], we treat nucleons as spinless, omitting spin-orbit interactions; a study of the effect of nonlocality on analyzing powers must await later studies. Consistently with this, we also omit spin in our treatment of the stripping process and this, of course, includes omitting the D state of the deuteron.…”

“…An account of the relevant inversion calculations is given in Ref. [41], which includes volume integrals and other characteristics of the local DPPs generated by the coupling. The local DPPs are the inverted potentials 044602-5 with the bare potentials of the CC calculations subtracted.…”

“…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.…”

“…The collective coupling, by design, produces a large part of the absorption of a realistic OMP for this case. However, transfer contributions were omitted [41] so the CC calculation employed a bare potential with a nonzero imaginary component. The effect of the coupling on the elastic scattering angular distribution is large, as can be seen in Fig.…”