Off-Shell Effects in Nuclear Matter

Abstract

We examine the binding energy of nuclear matter for exactly phase-shift-equivalent potentials. We generate these potentials by applying a short-range unitary transformation to the Reid soft-core potential. All potentials have a one-pion-exchange tail. We find that, for the potentials studied, variations of up to 9.5 MeV in the binding energy and 0.33 ${\mathrm{F}}^{\ensuremath{-}1}$ in the saturation density occur. The variations in binding energy are linearly correlated with the wound integral $\ensuremath{\kappa}$ for those potentials that give nearly the same deuteron electric form factor. An increase in $\ensuremath{\kappa}$ leads to less binding in nuclear matter. The sensitivity of the binding energy is somewhat greater to the $^{3}S_{1}+^{3}D_{1}$ contribution to $\ensuremath{\kappa}$ than to the $^{1}S_{0}$ contribution to $\ensuremath{\kappa}$. We give a theoretical explanation, based on the modified Moszkowski-Scott separation approximation, to account for the sensitivity of the binding energy to the $^{1}S_{0}$ and $^{3}S_{1}+^{3}D_{1}$ contributions to $\ensuremath{\kappa}$. We also discuss the relation of $\ensuremath{\kappa}$ and the binding energy of nuclear matter to the off-shell elements of the $T$ matrix. We discover that far-off-shell elements ($q\ensuremath{\gtrsim}6$ ${\mathrm{F}}^{\ensuremath{-}1}$) play a significant role in nuclear matter.