Nucleon–nucleus real potential of Woods–Saxon shape between  60 and  60 MeV for the 40  A  208 nuclei

Abstract

The nucleon differential elastic scattering cross sections, the total proton reaction cross sections, and the single-particle energies of nucleon bound states for 40 Ca, 90 Zr, and 208 Pb nuclei are reanalyzed in terms of the dispersive optical model at energies ranging from -75 MeV to 60 MeV. The resultant real effective Woods-Saxon potential, which corresponds to the dispersive potential, is studied as dependent on A, Z, and E and on projectile specie (proton or neutron). For the first time, a parameterization of the Woods-Saxon real part of the nucleonnucleus optical potential is proposed for the 208 40 A nuclei at energy ranging from -60 MeV to +60 MeV, including a range near the Fermi energy. The parameterization reflects the dispersion relation between the real and imaginary parts of the optical model potential through the energy dependence of the radius parameter of the real part of the potential. The method to determine the imaginary part of the optical model potential, which is symmetrical relative to the Fermi energy, is also proposed for the 208 40 A nuclei. The differential elastic scattering cross sections, the total neutron interaction cross sections, the total proton reaction cross sections, and the single-particle energies of the nucleon bound states calculated in terms of the proposed nucleon-nucleus potential parameterization for some of the n,p+A ( 40 A) systems are compared with the available experimental data, yielding a fairly good agreement.

Accurate analytic presentation of solution of the Schrödinger equation with arbitrary physical potential

“…In the Schrödinger equation (4) with WS potential, m = 938 MeV is a vacuum value of the nucleon mass. Numerous experimental data is fitted by the following A dependence of the characteristics of the WS potential [8], [9] …”

“…Anyway, the accuracy obtained by the first iteration overshoots the one, expected by employing WS potential in calculations. Already in the calculations with a 10 À3 -10 À4 precision, improvement of the accuracy is connected with employing of the potentials of more complicated form [9,18,20].…”

“…The binding energy was determined by Eqs. (9) or (24), (25), where the right hand side contained dependence on E n in terms of the wave functions or their logarithmic derivatives.…”

“…This is just a smooth version of a spherical well. Nowadays the WS potential is used as a real part of the nuclear optic-model potential, describing the nucleon single particle bound states in nuclei, as well as nucleon-nucleus scattering [8,9]. The Schrö dinger equation with the potential (30) can be, in principle, solved exactly [17].…”

The Woods–Saxon potential with point interactions

“…The Woods-Saxon potential is a reasonable potential for nuclear shell models and hence attracts lots of attention in nuclear physics and it is used to represent the distribution of nuclear densities [2][3][4][5][6][7][8][9][10][11][12][13][14].…”