Morse Function and Velocity-Dependent Nucleon-Nucleon Potentials

We investigate a static soft-core potential (the Morse potential) and three representative velocity-dependent $N-N$ potentials. First we study the problem of adjusting potentials to maintain the $1S$ state bound near zero energy, and we test two integral criteria. For the Morse potential we derive a convenient analytical expression for the $S$-wave phase shifts. By fitting experimental phase shifts in the energy range $E_{\mathrm{lab}}\le 400$ MeV for elastic nucleon-nucleon scattering, we evaluate the potential parameters for the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ states. We then examine and compare a phenomenological and two-meson-theoretic one-boson-exchange potentials in $S$ states which are representative of a number of $N-N$ potentials in current use. We point to ways of characterizing these potentials which are helpful in assessing their scattering consequences. We show that different mechanisms embodied in such potentials can account equally well for the negative $S$-wave phase shifts observed at higher energies.