Reaction channel contributions to the proton +Pb208 optical potential at 40 MeV

Abstract

Background: Reaction channel coupling substantially modifies the real and imaginary nucleon-nucleus interactions for nuclei of $Z=20$ or less in ways that cannot be represented as uniform renormalizations of folding model potentials. For such nuclei coupling to inelastic channels also contributes. This raises the question of the effect of these couplings for heavier target nuclei.Purpose: To establish and characterize the contribution to the proton-nucleus interaction generated by coupling to neutron pickup (outgoing deuteron) channels for 40 MeV protons on the heavy closed shell nucleus $^{208}\mathrm{Pb}$. To identify and evaluate the consequent dynamical non-locality.Methods: Coupled reaction channel (CRC) calculations provide the elastic channel $S$-matrix ${S}_{lj}$ due to the included processes. Inversion of ${S}_{lj}$ will produce the local potential that would yield, in a single channel calculation, the elastic scattering observables from the CRC calculation. Subtracting the bare potential of the CRC calculations gives a local and $l$-independent representation of the dynamical polarization potential (DPP). From the DPPs due to various combinations of channel couplings, the influence of dynamically generated nonlocality can be identified.Results: Coupling to deuteron channels generates a repulsive component for the real potential and an absorptive component for the imaginary term. The radial shapes of both terms were modified in ways that could not be represented by uniform renormalization; the rms radius of the real part was substantially altered. Evidence of the dynamical nonlocality of the DPP due to pickup is provided by the nonadditivity of contributions of different couplings and other effects. For the doubly closed shell $^{208}\mathrm{Pb}$ coupling to low-lying (nongiant) collective states has a very small effect on elastic scattering, making a negligible contribution compared with pickup, and was not included.Conclusions: The DPPs established here strongly challenge the notion that folding models, in particular local density models, provide a satisfactory description of elastic scattering of protons from heavy nuclei. Coupling to neutron pickup channels induces dynamical nonlocality in the proton optical model potential with implications for direct reactions.