Optical-Model Analysis of Elastic Scattering of Protons on Carbon at Intermediate Energies

Abstract

Differential cross sections and polarizations for the elastic scattering of protons by carbon at energies between 7 and 20 Mev have been analyzed according to the diffuse-surface optical model of the nucleus. The model parameters were varied systematically, the best fits to the experimental data being determined by a method of least squares. Various forms of the absorptive part of the potential were investigated, although the main part of the analysis was carried out with a surface-plus-volume absorption potential. It was found that the model could not account satisfactorily for the data below about 12 Mev, and the presentation of results is limited to the region 11.85 Mev^Eiab^ 19.4 Mev. Excellent fits can be obtained over the latter region with generally reasonable values of the model parameters, although some features of their behavior as a function of energy remain to be explained. The most striking feature of the results is the thin absorptive shell and small volume absorption which characterizes the potential. Although the predicted reaction cross sections appear generally too low, the experimental data are not sufficiently precise to warrant drawing a definite conclusion.

Nuclear Mean-Field Description of Proton Elastic Scattering by \(^{12,13}\)C at Low Energies

“…In the previous results [7], the elastic scattering on intermediate-mass and heavy nuclei can be analyzed successfully without renormalization of the strength of the real folded potential. To evaluate the validity of this argument for the case of light nuclei 12,13 C, we remained unchanged N R = 1 and only adjusted slightly the strength of imaginary potentials, while the phenomenological spin-orbit potential was used [11]. From the optical model results obtained with the CDM3Y6 interaction shown in Fig.…”

“…It is pointed out that the limitation of the present microscopic approach. Within the phenomenological optical model approach, Nodvik et al [11] indicated that the absorbed (imaginary) surface potential at these energies is more dominant than the absorbed volume potential, while the imaginary folded potential based on JLM interaction is only defined as a central volume potential. The addition of imaginary surface potential is necessary due to the fact that it is characterized by the effect of strong coupling at low energies.…”

“…Optical model description of the elastic p + 12 C scattering data measured at the proton incident energies in the range of 14.0 -19.4 MeV [21] given by the folded optical potential obtained with the CDM3Y6 interaction with RT and without RT, using the imaginary potential fitted to JLM interaction and the spin-orbit potential taken from Ref. [11]. The real folded potential was used with N R = 1, while the imaginary folded potential was renormalized by the factor N I given in Table 1.…”

“…However, for the energies below 10 MeV for lighter nuclei, there are a wide diversity of difficulties in consistent study of dispersion relation between the real and imaginary parts. With the use of absorbed surface potential, Nodvik et al [11] reported the sets of parameters of WS and Gaussian potentials to analyze the differential cross sections at the bombarding energies from about 12 MeV to 20 MeV. Recently, the WS parameters have been updated via nucleon scattering upon light nuclei (A < 13) from 65 MeV to 75 MeV [10].…”

“…For instance, the elastic scattering of proton from 12 C and 13 C targets at astrophysical energies is related to the first proton radiative capture reactions (p, γ) occurring in the carbon-nitrogen-oxygen (CNO) cycle in asymptotic giant branch (AGB) stars after the nucleus 12 C is formed by the 3α process. The mean-field potential models applied to these elastic scattering 12 C(p, p) and 13 C(p, p) are regularly of the WS form [10,11] with the parameters adjusted to obtain best fits in comparison with experimental data. Nevertheless, these phenomenological potential models are still relatively simple and depend on the parameters of a function instead of starting from NN interactions.…”