Woods-Saxon Equivalent to a Double Folding Potential

Abstract

A Woods-Saxon equivalent to a double folding potential in the surface region is obtained for the heavy-ion scattering potential. The Woods-Saxon potential has fixed geometry and was used as a bare potential in the analysis of elastic scattering angular distributions of several stable systems. A new analytical formula for the position and height of the Coulomb barrier is presented, which reproduces the results obtained using double folding potentials. This simple formula has been applied to estimate the fusion cross section above the Coulomb barrier. A comparison with experimental data is presented.

B8+Al27 scattering at low energies

“…energies by V b , where R b is the position of the Coulomb barrier and V b is its height. Both R b and V b have been calculated using the formula presented in [38], which provide Coulomb barrier positions and heights in very good agreement with those obtained using numerical double folding nuclear potential calculations.…”

“…The Coulomb barrier for this system is at V lab B = 13.42 MeV using the formula deduced in Ref. [38]. …”

“…We performed optical model calculations using two different types of nuclear potentials, the usual São Paulo Potential (SPP) [39] and a Woods-Saxon (WS) potential described below [38]. At near barrier energies, the São Paulo potential is essentially an usual double folding potential that has no free parameters, since it has been derived from the systematics of nuclear matter densities in the region.…”

“…The index p, t stands for the projectile and the target, respectively. This potential has a fixed geometry r 0v = r 0w = 1.3 fm and a v = a w = 0.65 fm and, the depths V 0 and W 0 are varied to fit the data [38]. In reference [38] it has been shown that a Woods-Saxon form factor with this geometry and depths between 10 − 20 MeV can reproduce quite well the tail of the double folding potential for a number of stable systems.…”

“…This potential has a fixed geometry r 0v = r 0w = 1.3 fm and a v = a w = 0.65 fm and, the depths V 0 and W 0 are varied to fit the data [38]. In reference [38] it has been shown that a Woods-Saxon form factor with this geometry and depths between 10 − 20 MeV can reproduce quite well the tail of the double folding potential for a number of stable systems. We used the same procedure here and obtained again good agreement between the WoodsSaxon and double folding potentials in the tail region, the important region for the description of the elastic scattering.…”