Charge symmetry of the nuclear force as off-shell constraint

Abstract

Off-shell changes are generated in the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ nucleon-nucleon interaction using the Reid soft-core potential and unitary transformations of short range. Charge symmetry is assumed for the nuclear force. The same off-shell variations of the Reid potential are employed as the hadronic part of the proton-proton interaction and as neutron-neutron interaction. The Reid potential fits the experimental proton-proton data. It also accounts for the neutron-neutron scattering length with satisfying accuracy. The off-shell behavior of the Reid potential is varied in two different ways. First, off-shell changes are performed which preserve the fit to the proton-proton data. Most transformed potentials of the type attempted here are unable to yield the correct experimental value of the neutron-neutron scattering length and have to be rejected. A simple practical rule is given according to which the off-shell changes consistent with the neutron-neutron scattering length can be selected. Second, off-shell changes are performed which leave the neutron-neutron scattering length unaltered. Transformed potentials of this type have usually been employed in nuclear-structure calculations. The potentials which exhibit large off-shell effects in nuclear structure are unable to account for the experimental proton-proton data. Their off-shell effects are therefore of no physical significance, and the potentials have to be rejected. A simple practical rule is given according to which the off-shell changes consistent with the experimental proton-proton data can be selected.