Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering
National Aeronautics and Space Administration, Langley Research Center, 1995 - Science - 18 pages
A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.
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absorption cross sections approximation with exact Born approximation calculation using Eikonal carbon-nucleus systems Comparison of total constituent cross section calculation Cucinotta data are shown denote the projectile Eikonal approximation Eikonal model elastic amplitude elastic scattering energy range equation 18 equation 30 ergies exact and Eikonal exact solution first-order optical model first-order optical potential fm(q form factor FP(q free two-body Green's function GT(q Hampton Hampton University Heitler equation helium-nucleus high energies impulse approximation Langley Research Center Lippmann-Schwinger calculation Lippmann-Schwinger Eikonal Lippmann-Schwinger equation lmax low energy matrix element Maung multiple scattering n-12C scattering n-208Pb scattering n-4He scattering n-MCu scattering nucleon-nucleus system nucleons nucleus-nucleus scattering number of partial on-shell optical theorem partial-wave decomposition Pauli spin operator physical inputs projectile and target range from 25A scattering amplitude shown by error solution using equation system in energy target nuclei total and absorption total cross section total elastic transition operator two-body amplitude wave vector