Reaction channel coupling effects for nucleons on ${}^{16}\mathrm{O}$: Induced undularity and proton-neutron potential differences

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, $S_{lj}\to V\left(r\right)+\mathbf{l}·\mathbf{s}{V}_{\mathrm{SO}}\left(r\right)$, 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.

Figure 1

For 30.1 MeV protons on ${}^{16}\mathrm{O}$, the effects on the differential cross section (upper panel) and analyzing power (lower panel) of coupling successively more channels to the elastic channel. The dashed line (Bare) is for no coupling, the dotted line shows the effect of coupling to the $2^{+}$ state (GQR), the dash-dotted line is with coupling to the $3^{-}$ state added, and the solid line is with the full pickup coupling added. The large dots represent the experimental measurements [2, 3].

Figure 2

For 30.1 MeV neutrons on ${}^{16}\mathrm{O}$, the effects of coupling successively more channels to the elastic channel on the differential cross section (upper panel) and analyzing power (lower panel). The dashed line (Bare) is for no coupling, the dot-dashed line shows the effect of coupling to the $2^{+}$ and $3^{-}$ states, and the solid line is with the full pickup coupling added to the collective states. (No experimental measurements are available.)

Figure 3

For 30.1 MeV protons on ${}^{16}\mathrm{O}$, the DPPs arising from coupling to the $2^{+}$ and $3^{-}$ vibrational states of ${}^{16}\mathrm{O}$. The dotted line (CC2) is for coupling to the $2^{+}$ state, the dash-dotted line (CC3) is for coupling to the $3^{-}$ state, the dashed line presents the numerical sum of the CC2 and CC3 DPPs, and the solid line is the DPP for the CC23 case in which both vibrational states are coupled to the elastic channel. Panels (a)–(d) present the real central, imaginary central, real spin-orbit, and imaginary spin-orbit terms, respectively.

Figure 4

For 30.1 MeV protons and neutrons on ${}^{16}\mathrm{O}$, the DPPs arising from coupling to both the $2^{+}$ and $3^{-}$ vibrational states of ${}^{16}\mathrm{O}$. The solid lines present the CC23 DPP shown in Fig. 3, the dashed lines present the DPP for the same case in which the Coulomb excitation is turned off, and the dot-dashed lines show the DPP for neutron scattering with coupling to the same pair of vibrational states. Panels (a)–(d) present the real central, imaginary central, real spin-orbit, and imaginary spin-orbit terms, respectively.

Figure 5

For 30.1 MeV protons on ${}^{16}\mathrm{O}$, inverted potentials, labeled pot3 (dashed) and pot4 (solid), for the CRC case together with the bare potential; dotted lines. Pot3 and pot4 are successive solutions to IP inversion, as explained in the text. The CRC cases include coupling to two pickup states together with the two vibrational states. Panels (a)–(d) present the real central, imaginary central, real spin-orbit, and imaginary spin-orbit terms, respectively.

Figure 6

For 30.1 MeV protons on ${}^{16}\mathrm{O}$, the DPP pot4 for the CRC calculation, solid lines, together with the numerical sum of the DPP for CRC-noInel and the CC23 DPP, dashed lines. Panels (a)–(d) present the real central, imaginary central, real spin-orbit, and imaginary spin-orbit terms, respectively.

Figure 7

For 30.1 MeV protons on ${}^{16}\mathrm{O}$, inverted potentials for CRC coupling. The dashed lines present the DPP for the CRC case for neutrons. For comparison, the solid lines present the DPP pot4 for protons, as also shown in Fig. 6. Panels (a)–(d) present the real central, imaginary central, real spin-orbit, and imaginary spin-orbit terms, respectively.

Figure 8

For 30.1 MeV protons and neutrons on ${}^{16}\mathrm{O}$, inverted potentials for CRC coupling without inelastic scattering (cases CRC-noInel and CRCn-noInel). The solid lines present the DPP for protons and the dashed lines present the DPP for neutrons. Panels (a)–(d) present the real central, imaginary central, real spin-orbit, and imaginary spin-orbit terms, respectively.

Figure 9

For 30.1 MeV protons on ${}^{16}\mathrm{O}$, inverted potentials for CRC coupling without inelastic scattering (cases CRC-noInel and CRC-noInelwxp5). The solid lines present the DPP for protons for case CRC-noInel and the dashed lines present the DPP for protons when the imaginary part of the deuteron OMP is halved, CRC-noinelwxp5. Panels (a)–(d) present the real central, imaginary central, real spin-orbit, and imaginary spin-orbit terms, respectively.

Figure 10

For 30.1 MeV protons on ${}^{16}\mathrm{O}$, comparing inverted potentials for the CRC case for alternative inversion bases. The dotted lines give the four components of the bare potential: Panels (a)–(d) present the real central, imaginary central, real spin-orbit, and imaginary spin-orbit terms, respectively. The solid lines present the inverted potential obtained using IP inversion with a Gaussian function basis; the dashed lines present the result of IP inversion using a Bessel-function basis.