Nuclear Radius and Nuclear Forces

Abstract

The difference between the radius of the nuclear matter distribution and the nuclear force radius, ${R}_{N}\ensuremath{\simeq}1.4{A}^{\frac{1}{3}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm, for heavy nuclei ($Ag100$) is interpreted as a consequence of the finite range of nuclear forces. Assuming that the nuclear matter distribution coincides with the charge distribution as determined at Stanford (${R}_{C}=1.12{A}^{\frac{1}{3}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm is the distance at which the charge density falls to one half value) we sum up the nuclear interactions of an incident nucleon for various proposed internucleon potentials, $V(r)$. We also evaluate contributions from the spin, charge, and matter polarizations induced in the nuclear distributions by the incident nucleon as a test of the convergence of these calculations. The aim here is to infer some features of nuclear forces which satisfy saturation requirements and at the same time give rise to an appreciable nuclear attraction for an incident nucleon at ${R}_{N}$. Analyses of the scattering of neutrons and protons by heavy nuclei suggest a nuclear attraction \ensuremath{\gtrsim}14 Mev at a distance ${R}_{N}$.These considerations are primarily sensitive to the long range behavior of the direct, central part of $V(r)$. The key point which emerges from them is that the nuclear forces must contain long range (~ meson Compton wavelength) direct, central attractions which will be felt by an incident nucleon at ${R}_{N}$ before the shorter range repulsions (hard cores, many-body forces, or exchange interactions), which are responsible for saturation, become effective. Such interactions can be constructed phenomenologically, but are not found in recent meson-theoretically deduced potentials.