Integrated Cross Section for a Velocity-Dependent Potential

Abstract

For a possible distinction between a velocity-dependent two-nucleon potential, and a static potential with an infinite repulsive core, we study their contributions to the integrated cross section (${\sigma }_{\mathrm{int}}$) for the deuteron photoeffect. Both potentials considered are central, with square shapes, and have Serber mixtures for the attractive parts. (They have Wigner character for the repulsive core, and for the velocity-dependent term, respectively.) These potentials are adjusted to give (1) the observed binding energy of the deuteron, (2) the same effective range $\rho (-\epsilon , -\epsilon )=1.76\mathrm{}$ fermis; and (3) the same value (260 Mev) at which the ${}_{}{}^3{}_{}{}^{}S$ phase shift changes sign. Using sum-rule calculations, in the electric-dipole approximation, we find that ${\sigma }_{\mathrm{int}}$ for the static case is 37.7 Mev-mb, while for the velocity-dependent case it is very nearly the same: namely, 38.8 Mev-mb.