Nonlocal Nucleon-Nucleon Interaction

It has been explicitly demonstrated that the proton-proton scattering data require that the singlet even parity nucleon-nucleon interaction be nonlocal. This result comes from an examination of the energy dependence of both the ¹S₀ and ¹D₂ phase shifts. A nonlocal singlet even parity potential of the form $V(r, {r}^{{'}})={V{(r)}1/2V{({r}^{{'}})}1/2{R}^{{-}3}[exp({-}{R}^{{-}1}|r{-}{r}^{{'}}|)]}{(4{π}{R}^{{-}1}|r{-}{r}^{{'}}|)}$ is examined. The potential function $V(r)$ is taken to have the form of a monotonic attraction outside a "hard core." The radius of the "hard core," the depth and range of $V(r)$, and the nonlocal distance $R$ provide four parameters which can be adjusted to fit the experimental values of the singlet scattering length and effective range, and the 310-MeV $¹S₀$ and $¹D₂$ phase shifts. For a long-range attractive potential function, such as the Yukawa, the energy dependence of the $¹S₀$ and $¹D₂$ phase shifts is strikingly similar to that suggested by the phase-shift analysis of the Yale group. Although the radius of the "hard core" is decreased somewhat from the local value, a "hard core" is still required.