Dispersive coupled-channel analysis of nucleon scattering from ${}^{232}\mathrm{Th}$ up to 200 MeV

An isospin-dependent coupled-channels optical model potential containing a dispersive term (including nonlocal contribution) is used to simultaneously fit the available experimental database (including strength functions and scattering radius) for neutron and proton scattering on strongly deformed ${}^{232}\mathrm{Th}$ nucleus. The energy range 0.001–200 MeV is covered. A dispersive coupled-channel optical model potential with parameters that show a smooth energy dependence and energy independent geometry are determined from fits to the entire data set. Dispersive contribution is shown to be the dominant Coulomb correction to the proton real potential below the Coulomb barrier. Inclusion of nonlocality effects in the absorptive volume potential and its corresponding dispersive contribution to the real potential is needed to achieve an excellent agreement above 100 MeV.

Figure 1

Neutron total cross sections for ${}^{232}\mathrm{Th}$ for energies 0.001 to 1 MeV (top panel) and 1 to 200 MeV (bottom panel). Solid lines are the result of present calculations, whereas dotted lines correspond to the nondispersive OMP of Ref. 37. Experimental data are shown by various symbols.

Figure 2

Selected neutron scattering cross sections on ${}^{232}\mathrm{Th}$ in center of mass (c.m.) system. Solid lines are the result of present calculations. Experimental data are shown by various symbols. The scattering cross sections to the resolved $0^{+}$, $2^{+}$, and $4^{+}$ levels of ${}^{232}\mathrm{Th}$ at 3.4 MeV are shown in the left column. The scattering cross sections for excitation of a sum of $0^{+}$, $2^{+}$, $4^{+}$, $6^{+}$, and $8^{+}$ levels of ${}^{232}\mathrm{Th}$ from 4.5 to 15.2 MeV are shown in the right column. Incident energy for plots appearing on the right pannel is indicated by a number on top of each plot.

Figure 3

Selected proton scattering cross sections on ${}^{232}\mathrm{Th}$ from 20 to 65 MeV in c.m. system. Solid lines are the result of present calculations. Experimental data are shown by various symbols. The corresponding excited level of the Th${}^{232}$ rotational band is indicated in the top right corner of each pannel (ELASTIC corresponds to the $0^{+}$ ground state). Incident energy is indicated by a number on top of each plot.

Figure 4

Reaction cross section for protons incident on ${}^{232}\mathrm{Th}$. Solid bold line is the result of present calculations, whereas thin line corresponds to the nondispersive OMP of Ref. 37. Experimental data are shown by various symbols. Barashenkov systematic [72] is represented by dotted line (systematic is given for U${}^{238}$ reaction cross section, which was corrected by the 0.9832$\hspace{1em}=\hspace{1em}{232}^{1/3}/{238}^{1/3}$ ratio). Uncertainty of 6% was assumed, equal to the difference between total cross section measured by Abfalterer et al. [34] and predicted by systematic [72].

Figure 5

Energy dependence of the average volume integrals per nucleon of the imaginary (top) and real (bottom) components of the mean field both for protons (left) and neutrons (right). Bold lines correspond to present calculations, whereas empty circles for protons and triangles for neutrons correspond to the nondispersive OMP of Ref. 37. The volume (dashed) and surface (dotted) contributions to the imaginary volume integral for the present DCC OMP are shown for protons and neutrons in the top panels. The volume (dashed) and surface (dotted) dispersive contributions to the real volume integral are shown in the bottom panel. Expanded low-energy region of the real neutron volume integral is included in the inset.

Figure 6

Energy dependence of partial contributions (in percentages) of the dispersive potentials to the real-volume integral per nucleon $J_V(E)/A$ for the proton (top) and neutron (bottom) DCCOM potential of this work. Solid lines correspond to the full dispersive contribution in each panel. The volume-dispersive contribution $J_{\Delta {\tilde{V}}_v(E)}/J_V\hspace{1em}(E)$ is shown by a dashed line and the asymmetric part $J_{\Delta V_{<}+\Delta V_{>}}/J_V\hspace{1em}(E)$ by dotted line. The dispersive surface contribution to the real-volume integral $J_{\Delta V_s}/J_V\hspace{1em}(E)$ is displayed with a dot-dashed line. The volume $J_{\Delta V_v^{\mathrm{Coul}}}/J_V\hspace{1em}(E)$ (open circles) and surface $J_{\Delta V_s^{\mathrm{Coul}}}/J_V\hspace{1em}(E)$ (solid circles) Coulomb correction's contributions to the real-volume integral for protons, including dispersive Coulomb correction, are also shown in the upper panel.

Figure 7

Energy dependence of the volume integral per nucleon for the Coulomb correction to the real potential calculated for the nondispersive OMP of Ref. 37 (dashed line) and for DCCOM potential (solid line). The volume $J_{\Delta V_v^{\mathrm{Coul}}/A}(E)$ (dotted line) and surface $J_{\Delta V_s^{\mathrm{Coul}}/A}(E)$ (solid circles) Coulomb correction's contributions to the real-volume integral for protons are also shown. The dispersive volume Coulomb correction, included into $J_{\Delta V_v^{\mathrm{Coul}}/A}(E)$, is shown by open circles.