http://nrv.jinr.ru/nrv/webnrv/elastic_scattering/KoningP.pdf

Local and global nucleon optical models from 1 keV to 200 MeV

A review is given of our present knowledge of collective spin-isospin excitations in nuclei. Most of this knowledge comes from intermediate-energy charge-exchange reactions and from inelastic electron- and proton-scattering experiments. The nuclear-spin dynamics is governed by the spin-isospin-dependent two-nucleon interaction in the medium. This interaction gives rise to collective spin modes such as the giant Gamow-Teller resonances. An interesting phenomenon is that the measured total Gamow-Teller transition strength in the resonance region is much less than a model-independent sum rule predicts. Two physically different mechanisms have been discussed to explain this so-called quenching of the total Gamow-Teller strength: coupling to subnuclear degrees of freedom in the form of $\ensuremath{\Delta}$-isobar excitation and ordinary nuclear configuration mixing. Both detailed nuclear structure calculations and extensive analyses of the scattering data suggest that the nuclear configuration mixing effect is the more important quenching mechanism, although subnuclear degrees of freedom cannot be ruled out. The quenching phenomenon occurs for nuclear-spin excitations at low excitation energies ($\ensuremath{\omega}\ensuremath{\sim}10\ensuremath{-}20$ MeV) and small-momentum transfers ($q\ensuremath{\le}0.5$ ${\mathrm{fm}}^{\ensuremath{-}1}$). A completely opposite effect is anticipated in the high ($\ensuremath{\omega}$, $q$)-transfer region ($0\ensuremath{\le}\ensuremath{\omega}\ensuremath{\le}500$ MeV, $0.5\ensuremath{\le}q\ensuremath{\le}3$ ${\mathrm{fm}}^{\ensuremath{-}1}$). The nuclear spin-isospin response might be enhanced due to the attractive pion field inside the nucleus. Charge-exchange reactions at GeV incident energies have been used to study the quasifree peak region and the $\ensuremath{\Delta}$-resonance region. An interesting result of these experiments is that the $\ensuremath{\Delta}$ excitation in the nucleus is shifted downwards in energy relative to the $\ensuremath{\Delta}$ excitation of the free proton. The physical origin of this shift is discussed, and it is shown that it may be related to the energy-dependent, attractive one-pion exchange interaction in the medium.

Nuclear spin and isospin excitations

A global nucleon optical model potential

Energy levels of light nuclei A = 12

Strangeness production close to the threshold in proton–nucleus and heavy-ion collisions

Accurate and extensive measurements have been made of the differential cross sections for the elastic scattering of protons from $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ targets over an energy range of 80-180 MeV, in the angular range from about 6\ifmmode^\circ\else\textdegree\fi{} to about 90\ifmmode^\circ\else\textdegree\fi{} (to 126\ifmmode^\circ\else\textdegree\fi{} for $^{90}\mathrm{Zr}$ at 135 MeV) in 0.5\ifmmode^\circ\else\textdegree\fi{} to 2.5\ifmmode^\circ\else\textdegree\fi{} steps. The most prominent general feature of the data, namely strong damping of the diffractive oscillations in the mid-angle region (roughly 30-60\ifmmode^\circ\else\textdegree\fi{}), was found to arise from the complex spin-orbit interaction which has a considerably greater influence on the differential cross section at these energies than at lower energies. These data, together with data of comparable quality from other sources in the energy range 60-180 MeV, were analyzed in terms of a 10-parameter phenomenological optical-model potential using relativistic kinematics and a relativistic extension of the Schr\"odinger equation. Analyses with various parameter constraints were performed. A logarithmic energy dependence was found for the strengths of the real potentials (central and spin-orbit terms); the corresponding imaginary potentials were found to be essentially independent of energy. While individual model parameters were generally not uniquely defined by the cross section data, volume integrals of the central potentials were well determined. The spin-orbit parameterization was found to be relatively more uncertain, despite the enhanced sensitivity of the cross section to spin dependent terms in the potential at these energies and the inclusion of some existing polarization data in the analysis. Some features of the phenomenological potentials were compared with the predictions of microscopic potential models, and certain aspects of the proton-nucleus interaction at the higher energies have been found to be describable in terms of the free nucleon-nucleon interaction.

Elastic scattering of 80-180 MeV protons and the proton-nucleus optical potential

The energy dependence of a relativistic optical model potential consisting of a mixture of Lorentz scalar and Lorentz vector components is determined from the analysis of p-/sup 40/Ca elastic scattering experiments from 26 to 1040 MeV.

Energy dependence of the p ca-40 optical potential: a dirac equation perspective

The analyzing power ${\mathit{A}}_{\mathit{y}}$ for proton elastic scattering on $^{12}\mathrm{C}$ has been precisely and absolutely determined at three scattering angles (${\mathrm{\ensuremath{\theta}}}_{\mathrm{lab}}$=16.3\ifmmode^\circ\else\textdegree\fi{}, 17.3\ifmmode^\circ\else\textdegree\fi{}, and 18.3\ifmmode^\circ\else\textdegree\fi{}) at an incident proton energy of 188.9 MeV. The technique employed requires statistically high quality polarization transfer measurements, combined with the constraints imposed on polarization observables for reactions with the spin structure 1/2+0\ensuremath{\rightarrow}1/2+0. These results represent some of the most accurately known spin observables at intermediate energies and serve as calibration points for secondary standards.

Determination of analyzing powers for 189 MeV proton elastic scattering on 12C.

We have measured proton elastic scattering cross sections and analyzing power angular distributions on Ca and 208Pb at 200, 300, 400, and 500 MeV. The 400 MeV data from 208Pb have been fitted by an optical model and also compared with results of Impulse Approximation calculations.

P. Schwandt

Papers

Elastic scattering of 80-180 MeV protons and the proton-nucleus optical potential

Energy dependence of the p ca-40 optical potential: a dirac equation perspective

Determination of analyzing powers for 189 MeV proton elastic scattering on 12C.

Elastic scattering of polarized protons at 200 to 500 MeV