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 ${\ensuremath{\rho}}_{t}(0,\ensuremath{-}\ensuremath{\epsilon})$ from the latest experiments, (1.72\ifmmode\pm\else\textpm\fi{}0.035)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ 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 $\ensuremath{\gamma}$-rays.It is shown that a comparison of the values obtained for ${r}_{0s}$ from (b) and (c) could, with a slight increase in experimental accuracy, give an estimate of the potential shape. Present, very tentative, indications are for a short-tailed potential and a value for ${r}_{0s}$ of about (2.7\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm.