Off-Shell Effects in Nuclear Matter

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 ${\mathrm{F}}^{-1\mathrm{}}$ in the saturation density occur. The variations in binding energy are linearly correlated with the wound integral $\kappa$ for those potentials that give nearly the same deuteron electric form factor. An increase in $\kappa$ 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 $\kappa$ than to the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ contribution to $\kappa$. 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 $\kappa$. We also discuss the relation of $\kappa$ and the binding energy of nuclear matter to the off-shell elements of the $T$ matrix. We discover that far-off-shell elements ($q\gtrsim 6$ ${\mathrm{F}}^{-1\mathrm{}}$) play a significant role in nuclear matter.