A Study of Repulsive Core Potentials in the Neutron-Proton System at Low Energies

Abstract

The variational parameters, ro,P,Q, in the expansion k cotσ = -1/a + rok^2-Pr^3ok^4+Qr^5ok^6 link theory and experiment. Using "experimental" values of a and ro, P is calculated in both the 1s and 3s neutron-proton states, for the square, gaussian, exponential, and Yukawa wells with repulsive cores. Comparison of the theoretical values of f with values derived from experiment indicates that the potential shape is at least as singular as the Yukawa (1/r), and that if a core exists, it is small, of the order of .1 or .2x10-^13cm. Q is calculated in the 1s state for the square and Yukawa wells with repulsive cores, and found to be so small as to be undefined by the present experimental data.