Reaction channel coupling effects for nucleons on O16 : Induced undularity and proton-neutron potential differences

Abstract

Background: Precise fitting of scattering observables suggests that the nucleon-nucleus interaction is $l$ dependent. Such $l$ dependence has been shown to be $S$-matrix equivalent to an undulatory $l$-independent potential. The undulations include radial regions where the imaginary term is emissive.Purpose: To study the dynamical polarization potential (DPP) generated in proton-$^{16}\mathrm{O}$ and neutron-$^{16}\mathrm{O}$ interaction potentials by coupling to pickup channels. Undulatory features occurring in these DPPs can be compared with corresponding features of empirical optical model potentials (OMPs). Furthermore, the additional inclusion of coupling to vibrational states of the target will provide evidence for dynamically generated nonlocality.Methods: The fresco code provides the elastic channel $S$-matrix ${S}_{lj}$ for chosen channel couplings. Inversion, ${S}_{lj}\ensuremath{\rightarrow}V(r)+\mathbf{l}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{s}\phantom{\rule{0.16em}{0ex}}{V}_{\mathrm{SO}}(r)$, followed by subtraction of the bare potential, yields an $l$-independent and local representation of the DPP due to the chosen couplings.Results: The DPPs have strongly undulatory features, including radial regions of emissivity. Certain features of empirical DPPs appear, e.g., the full inverted potential has emissive regions. The DPPs for different collective states are additive except near the nuclear center, whereas the collective and reaction channel DPPs are distinctly nonadditive over a considerable radial range, indicating dynamical nonlocality. Substantial differences between the DPPs due to pickup coupling for protons and neutrons occur; these imply a greater difference between proton and neutron OMPs than the standard phenomenological prescription.Conclusions: The onus is on those who object to undularity in the local and $l$-independent representation of nucleon elastic scattering to show why such undulations do not occur. This work suggests that it is not legitimate to halt model-independent fits to high-quality data at the appearance of undularity.