Off-shell structures of nucleon-nucleon<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi></mml:math>matrices and their influence on nucleon-nucleus elastic scattering observables

Abstract

The sensitivity of nucleon-nucleus elastic scattering observables to the off-shell structure of nucleon-nucleon $t$ matrices, derived from realistic $\mathrm{NN}$ potentials, is investigated within the context of a full-folding model based on the impulse approximation. Our study uses recently developed $\mathrm{NN}$ potential models, which describe a subset of the $\mathrm{NN}$ data base with a ${\ensuremath{\chi}}^{2}$ per datum $\ensuremath{\sim}1$, which means that the $\mathrm{NN}$ $t$ matrices are essentially on-shell equivalent. We calculate proton-nucleus elastic scattering observables for ${}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$ between 100 and 200 MeV laboratory energy. We find that the elastic scattering observables are insensitive to off-shell differences of the employed $\mathrm{NN}$ $t$ matrices. A more detailed investigation of the scattering equation and the optical potential as given in a factorized approximation reveals that the elastic scattering observables do not sample the $\mathrm{NN}$ $t$ matrices very far off-shell where they exhibit differences.