Neutron scattering off spherical nuclei with a global nonlocal dispersive optical model

We present a global nonlocal and dispersive optical model potential for neutron scattering off spherical nuclei with incident energies up to 250 MeV. This optical model is an extension of the nondispersive Perey-Buck potential. The imaginary components are chosen to be energy dependent and the dispersive constraints are taken into account. The surface imaginary part is nonlocal, whereas the volume imaginary part above 10 MeV is local, allowing one to reproduce total cross sections and scattering data for high energies. We obtain a good description of scattering observables for target nuclei ranging from $A=16$ up to 209. The inclusion of a nonlocal spin-orbit term enables a better description of the analyzing power data relative to the local dispersive model.

Figure 1

Total cross section (in logarithmic scale) for neutron-nucleus scattering as functions of the beam energy. The data (symbols) are from Ref. [19]. Red solid curves correspond to the PB potential [5] and blue dashed curves to that of TPM [10].

Figure 2

Differential cross sections (in logarithmic scale) for neutron elastic scattering as functions of the c.m. scattering angle. Red solid curves correspond to the PB potential [5] while blue dashed curves denote TPM [10] results. Data are denoted by symbols [19].

Figure 3

Depths $W$ (red curve) and dispersive contribution $\mathrm{\Delta }V$ of surface (a), volume (b), and spin-orbit (c) imaginary potentials as functions of the energy. Dashed, solid, and dotted curves denote results for ${}^{40}\mathrm{Ca}$, ${}^{89}\mathrm{Y}$, and ${}^{208}\mathrm{Pb}$, respectively.

Figure 4

Reduced radius $r_0$ (a) and diffuseness $a$ (b) as functions of the target mass $A$ for the nonlocal dispersive model.

Figure 5

Total cross section for neutron-nucleus scattering as function of the energy. The data (symbols) are from Ref. [19]. Red solid curves correspond to NLD potential (this work) and blue dashed curves to LD potential [3].

Figure 6

Differential cross sections (in logarithmic scale) for neutron elastic scattering. Data are denoted by symbols [19]. Red solid curves correspond to NLD potential (this work) and blue dashed curves to LD potential [3].

Figure 7

Relative differences experimental vs calculation expressed as percentages for each nucleus (dashed curves) for total cross section (a) and differential cross section (b). Results are for NLD potentials (red circles), LD potential [3] (blue square), and KD potential [6] (black triangle).

Figure 8

Analyzing powers (in linear scale) for neutron scattering at 10 and 17 MeV. Data are denoted by symbols. Red solid curves are obtained with NLD potential and the blue dashed curves with LD potential.

Figure 9

Neutron single-particle energies for ${}^{208}\mathrm{Pb}$, ${}^{90}\mathrm{Zr}$, and ${}^{40}\mathrm{Ca}$ determined with LD and NLD potentials and from experiment.

Figure 10

Uncertainties ($\pm 1\sigma$) in the total (red), reaction (black) and elastic (blue) cross sections for neutron scattering of ${}^{208}\mathrm{Pb}$.