The 1S 0 Phase Shift for Nucleon-Nucleon Scattering by the Nambu-Salpeter-Bethe Equation. III

Abstract

The Nambu-Salpeter-Bethe equation for the 1S0 state of nucleon-nucleon scattering is solved numerically including the negative-energy intermediate states. Calculation is made for the exchange of pion, isoscalar vector meson (µV=775.0 MeV) and scalar meson (µs=556.0 MeV), respectively. Our results show that the contribution from the negative-energy intermediate states does not alter the results from only positive-energy intermediate states for the vector-meson exchange, that it alters them quantitatively but not qualitatively for the scalar-meson exchange and that it alters qualitatively them for the spin exchange in the range of coupling constant g2/4π≤15. Our results seem to show that the conjecture by Gemmel et al., which connects the appearance of a pole in tan δ to Mandelstam's condition, is not valid.