Analysis of proton-Be9,10,11,12scattering using an energy-, density-, and isospin-dependent microscopic optical potential

Abstract

The proton elastic scattering of 9,10,11,12 Be isotopes at a wide energy range from 3 to 200 MeV/nucleon is analyzed using the optical model with the partial-wave expansion method. The microscopic optical potential (OP) is taken within the single-folded model. The density-and isospin-dependent M3Y-Paris nucleon-nucleon (NN) interaction is used for the real part and the NN-scattering amplitude of the high-energy approximation is used for the imaginary one. The surface contribution to the imaginary part is included. The analysis reveals that the partial-wave expansion with this microscopic OP reproduces well the basic scattering observables at energies up to 100 MeV/nucleon. For higher energies, the eikonal approximation with the same OP gives results better than the partial-wave expansion calculations. The volume integrals of the OP parts have systematic energy dependencies, and they are parameterized in empirical formulas. In addition, the volume integral's parametrizations determine the true energy dependence for the depths of the OP parts. The study of increasing the number of neutrons for a given isotope shows that the imaginary volume integrals and reaction cross sections depend on the matter radii of the scattered nuclei. Further, they are found to have larger values for the halo nucleus scattering ( 11 Be + p) than those for the scattering of their isotopes.

Analysis of proton scattering of stable and exotic light nuclei using an energy-dependent microscopic optical potential

“…1(b). The renormalization factors for the eikonal approximation calculations are listed in Table IV in our work [3]. It is clear that the eikonal approximation gives a good agreement with the data than the partial-wave expansion at energies ≥ 50 MeV/nucleon over all the angular range.…”

“…1. The best-fit renormalization factors are listed in Table II in our work [3]. The differential crosssection data for energies up to 100 MeV/nucleon are reproduced well.…”

“…The present problem considers a proton with an energy E incident upon a target with a mass number A and scattered by a microscopic spherical optical potential U OP (r) which a e-mail: h.maridi@gmail.com can be written as [1][2][3] …”

“…The forms of effective M3Y-Paris NN interactions v D and v EX , their energy and density dependencies, the realistic local approximation of the density matrix, as well as necessary explanations and values of calculation parameters can be found in Refs. [3,4]. The imaginary OP using the HEA model is expressed in Ref.…”

“…[5] as (5) where v is the velocity of the nucleon-nucleus relative motion, ρ(q) is the form factor corresponding to the point-like nucleon density distribution of the nucleus, and f NN (q) is the NN scattering amplitude.σ NN is the average over isospin total NN cross section. The Green's function Monte Carlo (GFMC) density [6] is used for 9,10 Be and the Gaussian-Oscillator (GO) distribution is used for 11,12 Be (see [3]). …”