The unabridged momentum-space optical model potential for nucleon-nucleus scattering with non-local density-dependent effective interactions
H. F. Arellano 1*, E. Bauge 2
1 Physics Department - FCFM - University of Chile
2 CEA/DAM/DIF, F-91297 Arpajon, France
The evaluation of microscopic optical model potentials, based on density-dependent effective interactions, involve multi-dimensional integrals to account for the full Fermi motion of the bound nucleons throughout the nucleus. Under the assumption of a spherical matter distribution, each matrix element U(k',k;E) of the optical potential requires the reckoning of seven-dimensional integrals. In this work we report results when a full account of these integrals is in place, retaining the genuine off-shell structure of the nucleon-nucleon effective interaction given by solutions for the g matrix in the Brueckner-Bethe-Goldstone framework. The evaluation takes advantage of the asymptotic separation[1,2] of the optical model potential for nucleon-nucleus scattering in momentum space, where the potential is split into a free t-matrix contribution and another which depends exclusively on the gradient of the density-dependent g matrix. The calculated potentials, based on the Paris nucleon-nucleon (NN) potential, are applied to proton elastic scattering from 16O and 90Zr at beam energies between 30 and 65 MeV. Results are compared with alternative approximations to the unabridged expression, finding moderate differences among their scattering observables. Comparisons of these results with those based on the Argonne v18 NN potential, show smaller differences than the ones attainable to the choice of the internucleon potential. In this work we shall also present the coordinate-space structure of the unabridged optical potential, aiming to disclose its actual equivalence to standard r-space approaches within the local density approximation.
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