Velocity-dependent optical potential for neutron elastic scattering from1p-shell nuclei

Abstract

Background: The conventional optical model is quite successful in describing the nucleon elastic scattering data from medium and heavy nuclei. However, its success in describing the light 1p-shell nuclei is somewhat limited. The velocity-dependent optical potential resulted in a significant improvement in describing the elastic angular distributions for light nuclei in the low energy region. Purpose: To extend the formalism of the velocity-dependent potential to higher energies, and to assess its importance in describing neutron elastic scattering data from light 1p-shell nuclei at high energies. Method: We fit the angular distribution data for neutron elastic scattering from 12 C and 16 O using (i) the velocity-dependent optical potential and (ii) the conventional optical potential. The results of the two models are then compared. At low energies, we compare our angular distribution fits with the fits of other works that exist in the literature. Furthermore, the total integrated cross sections in addition to the analyzing power are calculated using the velocity-dependent optical potential and compared to the experimental data. Results: The velocity-dependent potential resulted in significant improvements in describing the angular distributions particularly in the large-angle scattering region and for certain energy ranges. This model is important where the experimental data show structural effects from nuclear surface deformations, which are important in light nuclei. Furthermore, the calculated total elastic cross sections and analyzing power are in good agreement with the experimental data. Conclusions:The velocity-dependent potential gives rise to surface-peaked real terms in the optical model. Such terms account, at least partly, for the structural effects seen in the angular distribution data. The energy range over which the surface terms are needed is found to depend on the target nucleus. Other works that have introduced real surface terms in the optical potential are discussed.

Three-body problem with velocity-dependent optical potentials: a case of (d, p) reactions

“…Eq. ( 2) can be reduced to a standard form by introducing the Perey factor P (r), Ψ(r) = P (r)ϕ(r) (5) and demanding that the equation describing ϕ should not contain first derivatives. Then P (r) satisfies the first-order differential equation…”

“…On the other hand, it is also known that a nonlocal two-body problem is equivalent to one with a potential that contains an infinite sum of powers of kinetic energy operators arising from the Taylor series expansion of an exponent that contains the nucleon kinetic energy operator [7]. Thus, from a formal point of view, the velocity dependence used in Refs [1,2,3,4,5] is just a particular case of a more general nonlocal problem, truncated to retain linear terms only.…”

Nucleon-nucleus velocity-dependent optical model: revisited

“…However, for higher energies, an additional real volume term that is proportional to the matter distribution of the [47] 24.0 [47] target nucleus was necessary to restore the good agreement with the experimental data. The importance of the added surface term over the wider 10-90 MeV range was investigated for the case of neutron scattering of the light 1p−shell 12 C and 16 O nuclei [22]. For the low 10-20 MeV energy range, the results of the VDP were compared to those of reference [23].…”

“…The VDP has been the interest of many works including nuclear physics [20][21][22][24][25][26], atomic physics [27], quantum dots [28] and others. For example, the nonlocality due to a spatially-variable effective mass of the incident nucleon introduced in [19] was considered to calculate half-lives of spontaneous one-proton emission from neutron deficient nuclei [29].…”

“…In references [19][20][21][22], the main concern was to reproduce the elastic angular distributions for nucleon scattering off nuclear targets whose surface deformations result in nonlocal effects manifested as prominent minima in the backward scattering region. The local equivalent potential was not looked at as it was not needed in the calculations.…”