# A microscopic complex potential description of elastic, inelastic cross section in the Coulomb nuclear interference region in the 28Si on 28Si system

TL;DR: In this article, the Coulomb nuclear interference dip observed in the inelastic excitation functions could not be fitted satisfactorily with calculation, and an energy dependent term of Gaussian shape was added to the associated matrix element with the reorientation coupling in the phenomenological calculations.

Abstract: Elastic and inelastic angular distribution and excitation functions were measured for the 28 Si + 28 Si system in the vicinity of the Coulomb barrier. While the elastic data could be described very well by using fully microscopic complex potential, the inelastic cross sections were found to be more sensitive to small variations in the potential. In particular the Coulomb nuclear interference dip observed in the inelastic excitation functions could not be fitted satisfactorily with calculation. Inclusion of an energy dependent term of Gaussian shape to the associated matrix element with the reorientation coupling in the phenomenological calculations leads to a better fit the inelastic excitation functions.

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TL;DR: In this paper, the elastic scattering cross-sections of 28Si projectile by 27Al, 28Si, 58Ni, 64Ni and 208Pb targets were analyzed using the double folding model based on the effective M3Y interaction.

Abstract: The elastic scattering cross-sections of 28Si projectile by 27Al, 28Si, 58Ni, 64Ni and 208Pb targets are analyzed using the double folding model based on the effective M3Y interaction which is know...

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TL;DR: In this article, a new formulation of the theory of nuclear reactions based on the properties of a generalized "optical" potential is presented, where the real and imaginary part of this potential satisfy a dispersion type relation while its poles give rise to resonances in nuclear reactions.

Abstract: A new formulation of the theory of nuclear reactions based on the properties of a generalized “optical” potential is presented. The real and imaginary part of this potential satisfy a dispersion type relation while its poles give rise to resonances in nuclear reactions. A new derivation of the Breit-Wigner formula is given in which the concept of channel radius is not employed. This derivation is extended to the case of overlapping resonances. These results can then be employed to obtain the complex potential well model for pure elastic scattering. This potential well is shown to become real as the average width of the resonances increases. Reactions as well as elastic scattering are treated. Considering the former process in an isolated resonance, we obtain a nonresonant term analogous to the familiar potential scattering term of elastic scattering. This is just the direct interaction term which thus appears automatically in this formalism. Upon performing the appropriate energy averages over resonances, the complex potential well model is generalized so as to include inelastic scattering. The effects of the identity of nucleons is investigated. It is shown that our formalism is valid as long as the exit channels can at most contain one nucleon.

2,140 citations

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999 citations

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TL;DR: In this article, an effective local interaction for inelastic scattering is derived by fitting the matrix elements of a sum of Yukawas and, for the tensor force, other closely related forms, to three selected sets of G-matrix elements.

Abstract: An effective local interaction for inelastic scattering is derived by fitting the matrix elements of a sum of Yukawas and, for the tensor force, other closely related forms, to three selected sets of G-matrix elements. The ranges were selected to ensure OPEP tails in the relevant channels as well as a short-range part which simulates the “σ-exchange” process. Some of the implications of the various parts of the interaction are discussed in a distorted-wave context.

790 citations

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TL;DR: In this paper, the energy and density dependence of the isoscalar, isovector, and Coulomb components of the complex optical-model potential in infinite nuclear matter, for energies up to 160 MeV.

Abstract: Starting from the Brueckner-Hartree-Fock approximation and Reid's hard core nucleon-nucleon interaction, we calculate and parametrize the energy---and the density---dependence of the isoscalar, isovector, and Coulomb components of the complex optical-model potential in infinite nuclear matter, for energies up to 160 MeV. We then construct the optical-model potential in a finite nucleus. In a first step, we adopt a local density approximation which implies that the value of the complex potential at each point of the nucleus is the same as in a uniform medium with the local density. We compute the corresponding volume integrals per nucleon and mean square radii of the real and of the imaginary parts of the optical-model potential, in particular for protons scattered by $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, $^{58}\mathrm{Ni}$, $^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. We compare these results with a compilation of empirical values and find that the calculated and experimental volume integrals are in good agreement but that the theoretical mean square radii are too small. We ascribe this discrepancy to the fact that our local density approximation does not include accurately the effect in a nonuniform medium of the range of the effective interaction. We include this range in a semiphenomenological way suggested by the Hartree approximation. With a reasonable value for this range parameter, which is the only one occurring in our work, good agreement is obtained between the theoretical and the empirical values of the volume integrals and mean square radii of the real and, to a lesser extent, of the imaginary parts of the optical-model potential, for mass numbers $12\ensuremath{\le}A\ensuremath{\le}208$ and for energies $E$ up to 160 MeV. Our results are given in analytic form and can thus be used in analyses of experimental data. We also discuss the difference between the optical-model potentials for protons and for neutrons.[NUCLEAR REACTIONS Calculation of the complex optical-model potential for finite nuclei from Reid's hard core interaction; comparison with a compilation of empirical potentials.]

415 citations

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TL;DR: The double-folding model is generalized for the calculation of nucleus-nucleus potential using the new version of the density-dependent M3Y interaction which reproduces consistently the equilibrium density and binding energy of the normal nuclear matter as well as the density and energy dependence of the nucleon optical potential.

Abstract: The double-folding model is generalized for the calculation of nucleus-nucleus potential using the new version of the density-dependent M3Y interaction which reproduces consistently the equilibrium density and binding energy of the normal nuclear matter as well as the density and energy dependence of the nucleon optical potential. The exchange part of the heavy-ion optical potential is evaluated within a local density formalism, using the finite-range exchange components of the same interaction. The model is used successfully to describe the elastic $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ scattering data at low and medium energies. The influence of different density-dependent parameters (which determine different nuclear equations of state) on the description of heavy-ion scattering is also discussed.

141 citations