The Effective Range of Nuclear Forces. Effect of the Potential Shape

Abstract

Corrections to the theory of the effective range, which take account of the shape of the neutron-proton potential, are discussed. The following quantities are calculated for a Yukawa, exponential, and square well potential: (a) various triplet ranges compatible with the value obtained for ${\rho }_t(0,-\epsilon )$ from the latest experiments, (1.72±0.035)×${10}^{-13\mathrm{}}$ cm. (b) The singlet effective range $r_{0s}$ from neutron-proton scattering cross sections at energies up to 6 Mev. (c) $r_{0s}$ from neutron absorption cross sections by hydrogen. (d) Photoelectric and photomagnetic disintegration cross sections for the deuteron for various $\gamma$-rays.