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Potential inversion with subbarrier fusion data revisited
Abstract
We invert experimental data for heavy-ion fusion reactions at energies well below the Coulomb barrier in order to directly determine the internucleus potential between the colliding nuclei. In contrast to the previous applications of the inversion formula, we explicitly take into account the effect of channel couplings on fusion reactions, by assuming that fusion cross sections at deep subbarrier energies are governed by the lowest barrier in the barrier distribution. We apply this procedure to the $^{16}$O +$^{144}$Sm and $^{16}$O +$^{208}$Pb reactions, and find that the inverted internucleus potential are much thicker than phenomenological potentials. A relation to the steep fall-off phenomenon of fusion cross sections recently found at deep subbarrier energies is also discussed.
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We propose a new mechanism to explain the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier. The saturation properties of nuclear matter are causing a hindrance to large overlap of the reacting nuclei and consequently a sensitive change of the nuclear potential inside the barrier. We report in this Letter a good agreement with the data of coupled-channels calculation for the 64Ni + 64Ni combination using the double-folding potential with Michigan-3-Yukawa-Reid effective N - N forces supplemented with a repulsive core that reproduces the nuclear incompressibility for total overlap.
The double-folding model, with “realistic” nucleon-nucleon interactions based upon a G-matrix constructed from the Reid potential, is used to calculate the real part of the optical potential for heavy-ion scattering. The resulting potentials are shown to reproduce the observed elastic scattering for a large number of systems with bombarding energies from 5 to 20 MeV per nucleon. Some representative inelastic transitions are also reproduced. Exceptions are the elastic scattering of 6Li and 9Be for which the folded potentials must be reduced in strength by a factor of about two.The same effective interactions are shown to give a good account of two particular cases of alpha scattering as well as some cases of nucleon-nucleus scattering. Some typical examples of inelastic heavy-ion scattering are also predicted successfully.Some general properties of the folding model are reviewed and its theoretical basis is discussed. An explicit density-dependence is examined for one particular realistic interaction and found not to change the results. Single nucleon exchange is included in an approximate way and its importance is studied.In addition to being a study of the folding model, this work also provides a systematic and comprehensive optical model analysis of heavy-ion elastic scattering in this energy range.
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