General behavior of the effective nucleon-nucleon interaction as a function of the relative velocity

Abstract

We have studied volume integrals of the central part of optical potentials extracted from data analyses for a variety of light and heavy systems. The data-extracted integrals present a quite simple behavior as a function of the relative velocity between target and projectile. This behavior is system independent and, therefore, it reflects a feature of the effective nucleon-nucleon interaction itself. The overall results are in good agreement with the predictions of the São Paulo potential, which is a model for the nuclear interaction that so far has been employed mostly in analyses of heavy-ion reactions.

α+αscattering reexamined in the context of the São Paulo potential

“…The behavior of the volume integrals (J R ) of the real part of the interaction, extracted from the data analyses of many systems, including those involving light nuclei, indicates that the SPP model should be appropriate at even higher velocities (v ≈ 0.7 c) [32]. In particular, α-nucleus volume integrals that have been obtained through different models are compatible with the corresponding SPP predictions.…”

Non-local effects on the heavy-ion fusion at sub-barrier energies

“…In Refs. [7,8,9], the Jackson-Johnson idea was extended to heavier systems and the resulting potential, which is a modification of the double-folding one, was shown to be quite accurate in accounting for a large body of elastic scattering data for a wide range of systems, including 16 O + 208 Pb. The PB non-locality was originally derived for neutron-nucleus scattering.…”

“…To test the use of the SPP in tunneling problems and compare it to the exact solution of the integro-differential equation, we have considered the fusion system 16 O + 208 Pb at center of mass energies that span a region 10 MeV below the Coulomb barrier up to 10 MeV above it. In the analysis, we have assumed a Woods-Saxon shape inner imaginary potential to simulate the flux absorption by the fusion process, with the following parameters: W 0 = 200 MeV, r i0 = 0.8 fm, and a i = 0.2 fm.…”

“…In section II we give an account of the São Paulo potential. In Section III we calculate the fusion cross section for 16 O + 208 Pb and compare it with the data. We assess the effect of the Pauli non-locality and found it to be minor.…”

“…The São Paulo potential (SPP) has been in use for about one decade, especially in the analysis of heavy-ion elastic scattering data [9,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. It is based in part on the idea of single folding employed for alpha-nucleus scattering by Jackson and Johnson [27] in order to get the Perey-Buck (PB) nonlocal effects [28] extended to heavy ions.…”