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

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

A brief overview of various approaches to the optical-model description of nuclei is presented. A survey of some of the formal aspects is given which links the Feshbach formulation for either the hole or particle Green's function to the time-ordered quantity of many-body theory. The link between the reducible self-energy and the elastic nucleon-nucleus scattering amplitude is also presented using the development of Villars. A brief summary of the essential elements of the multiple-scattering approach is also included. Several ingredients contained in the time-ordered Green's function are summarized for the formal framework of the dispersive optical model (DOM). Empirical approaches to the optical potential are reviewed with emphasis on the latest global parametrizations for nucleons and composites. Various calculations that start from an underlying realistic nucleon-nucleon interaction are discussed with emphasis on more recent work. The efficacy of the DOM is illustrated in relating nuclear structure and nuclear reaction information. Its use as an intermediate between experimental data and theoretical calculations is advocated. Applications of the use of optical models are pointed out in the context of the description of nuclear reactions other than elastic nucleon-nucleus scattering.

Recent developments for the optical model of nuclei

High Resolution Measurement of Neutron Inelastic Scattering and (n,2n) Cross-Sections for 209Bi

We develop for the first time a microscopic global nucleon-nucleus optical potential with quantified uncertainties suitable for analyzing nuclear reaction experiments at next-generation rare-isotope beam facilities. Within the improved local density approximation and without any adjustable parameters, we begin by computing proton-nucleus and neutron-nucleus optical potentials from a set of five nuclear forces from chiral effective field theory for 1800 target nuclei in the mass range $12\ensuremath{\le}A\ensuremath{\le}242$ for energies between $0\text{ }\text{ }\mathrm{MeV}lE\ensuremath{\lesssim}150\text{ }\text{ }\mathrm{MeV}$. We then parameterize a global optical potential for each chiral force that depends smoothly on the projectile energy as well as the target nucleus mass number and isospin asymmetry. Uncertainty bands for elastic scattering observables are generated from a full covariance analysis of the parameters entering in the description of our global optical potential and benchmarked against existing experimental data for stable target nuclei. Since our approach is purely microscopic, we anticipate a similar quality of the model for nucleon scattering on unstable isotopes.

Global Microscopic Description of Nucleon-Nucleus Scattering with Quantified Uncertainties.

High-accuracy measurements of ${\mathit{A}}_{\mathit{y}}$(\ensuremath{\theta}) data for elastic scattering for n${+}^{209}$Bi have been performed at 6 and 9 MeV. The data are incorporated into a large database of \ensuremath{\sigma}(\ensuremath{\theta}), ${\mathit{A}}_{\mathit{y}}$(\ensuremath{\theta}), and ${\mathrm{\ensuremath{\sigma}}}_{\mathit{T}}$ for n${+}^{209}$Bi covering the energy range 1.0--80 MeV. A complementary database is constructed for n${+}^{208}$Pb and a dispersive optical-model analysis is performed for both scattering systems while constraining many of the parameters to be identical for both systems. A good representation of both databases is obtained with conventional geometry and spin-orbit parameters. The $^{208}\mathrm{Pb}$ model predicts quite well the measured energies of valence single-particle and single-hole bound states. Occupation probabilities and spectroscopic factors for the same bound states are also calculated. Finally, a fully constrained model is presented in which the only differences between the n${+}^{208}$Pb and the n${+}^{209}$Bi systems are the Fermi energy and the isospin dependence in the real volume potential. \textcopyright{} 1996 The American Physical Society.

Analyzing power measurements for 209Bi(n,n) at 6 and 9 MeV and consistent dispersive optical-model analyses for n+209Bi and n+208Pb from -20 to +80 MeV.

Angular distributions of the tensor analyzing powers [ital A][sub [ital z][ital z]] and [ital A][sub [ital x][ital x]][minus][ital A][sub [ital y][ital y]] for the reactions [sup 2]H([ital d],[ital p])[sup 3]H and [sup 2]H([ital d],[ital n])[sup 3]He are presented at deuteron energies of 25, 40, 60, and 80 keV. The analyzing powers for the two reaction channels are quite similar at these energies. The data have been included in an [ital R]-matrix analysis of the four nucleon system. According to this analysis, transitions from entrance-channel quintet-[ital S] states are important in these reactions, so that the use of polarized fuels would not result in a neutron-lean fusion reactor.

Tensor analyzing powers for 2H(d,p)3H and 2H(d,n)3He at deuteron energies of 25, 40, 60, and 80 keV.

The dispersive optical model (DOM) provides a natural connection between the shell model potential for bound states and the optical model for nucleon scattering at positive energies. At TUNL we have developed DOMs for neutron scattering for ten nuclei between 27Al and 209Bi. In these studies we rely on TUNL measurements of differential cross-section (σ(θ)) and analyzing power, as well as a wealth of σ(θ) and total cross section measurements from numerous other laboratories. In this paper we briefly outline the DOM method and the achievements in describing scattering data for n + 208Pb and n + 209Bi and single-particle bound-state data for neutrons in 208Pb.

The dispersive optical model for n + 208Pb and n + 209Bi

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Analyzing power measurements for 209Bi(n,n) at 6 and 9 MeV and consistent dispersive optical-model analyses for n+209Bi and n+208Pb from -20 to +80 MeV.

Tensor analyzing powers for 2H(d,p)3H and 2H(d,n)3He at deuteron energies of 25, 40, 60, and 80 keV.

The dispersive optical model for n + 208Pb and n + 209Bi