# L Dependence

This is a study of the l-dependence of the total cross section, total elastic cross section and total reaction cross section for neutron scattering off 90Zr. The density of 90Zr is a Dirac-Hartree density (Horowitz-Serot). The free NN interaction used to construct the microscopic optical potential is AV18. Calculations are carried out at 160 and 65 MeV laboratory projectile kinetic energy.

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The KONING Potentials in the figures are slightly off due to a compilation issue (the TALYS software gave erroneous results while on APOLLO when the fast option is set with the SUN compiler)

## Effect of Medium modification to the NN t-matrix

Local stands for a local t*rho $(t\;\rho)$ approximation. Here only the diagonal density is used together with a local NN t-matrix. "Medium" stands for the propagator modification due to the nuclear mean field as given in

 Microscopic Formulation of Medium Contributions to the First Order Optical Potential,
C.R.~Chinn, Ch.~Elster, R.M.~Thaler, Phys. Rev. C48, 2956 (1993)
and
Propagator Modifications in Elastic Nucleon-Nucleus Scattering within the Spectator Expansion,
C.R.~Chinn, Ch.~Elster, R.M.~Thaler, S.P.~Weppner, Phys. Rev. C52, 1992 (1995).


The curve labeled Koning is a calculation with the phenomenological Koning optical potential

## Effect of Off-shell

Different Off-shell structures of the microscopic optical potential are considered. FF stands for a full-folding calculation as given in e.g.

Full-Folding Optical Potentials for Elastic Nucleon-Nucleus Scattering based on Realistic Densities,
Ch.~Elster, S.P.~Weppner, and C.R.~Chinn, Phys. Rev. C56, 2080 (1997).


Successively approximations are introduced: first optimum factorization (i.e. taking only the off-shell NN t-matrix into account, and then local, which uses a local NN t-matrix. In our case adding more off-shell character had some effect but it was not dramatic.

## Our simplest vs. our best

This shows that our best calculation, Fullfolding with medium (FF+med) approaches the phenomenological when summed over all partial waves. The t

## Dividing by (2l + 1)

A different look at the previous figure. Here we have isolated the partial wave amplitudes only without their projection weighting factor of 2l + 1

## Nucleon-Nucleon Wolfenstein amplitudes for the AV18 potential

Compared are here the Wolfenstein amplitudes A and C (central and spin-orbit) derived from the free NN t-matrix of AV18 with the corresponding amplitudes which have been calculated taking the propagator modification due to the nuclear medium into account. The summary is that the medium affects both energies but the lower energy differences are more significant.