Analysis of Experiments on the Scattering of Protons by Protons

Abstract

The new observations of Herb, Kerst, Parkinson and Plain and of Heydenburg, Hafstad and Tuve are analyzed. No definite indication of a $p$ wave anomaly or higher phase shifts is found. The $s$ wave anomaly is the major effect observed. The phase shift ${K}_{0}$ responsible for it is compared with theoretical expectation using potentials which are constant (except for their Coulombian part) within distances 0.75, 1, 1.25 in units $\frac{{e}^{2}}{m{c}^{2}}=2.81\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm. The first of these gives a too rapid and the last a too slow variation of ${K}_{0}$ with energy. The interaction radius $\frac{{e}^{2}}{m{c}^{2}}$ agrees with experiment much better than the others. The potential energy giving the best agreement with experiment, when superposed on the Coulomb energy within this distance, is determined within a few tenths of a percent and is 11.3 Mev. The Gauss error potential $A{e}^{\ensuremath{-}\ensuremath{\alpha}{r}^{2}}$ with $\ensuremath{\alpha}=16$ and with 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm as the unit of length gives a too slow variation of ${K}_{0}$ with $E$. Experiment agrees decidedly better with $\ensuremath{\alpha}\ensuremath{\sim}20$. An over-all fit can be obtained with $\ensuremath{\alpha}=21.6$, $A=51.4 m{c}^{2}$. The shortening of the range of force is about the same as that previously suggested by Rarita and Present from calculations on the binding energy of ${\mathrm{H}}^{3}$. This is surprising since the discovery of the electric quadrupole moment of ${\mathrm{H}}^{2}$ necessitates a revision of binding energy calculations. Conclusions about the range of force derivable from proton-proton scattering experiments are shown to be sensitive to a possible velocity dependence of the nuclear potential. The proton-proton and proton-neutron forces in $^{1}S$ states are compared and it is found that for both types of potentials the proton-proton interaction is less by approximately two percent. This difference is definitely outside the probable errors in the scattering experiments and is not very sensitive to velocity dependence.The absence of $p$ wave anomalies in the data from 1830 to 2400 kev is not sufficiently clear cut to claim a definite disagreement with Feenberg's inequality derived from saturation requirements with exchange forces. The effects expected are close to the consistency of the measurements.The paper includes formulas and tables for the calculation of anomalies due to phase shifts, discussions of geometrical corrections and of some of the effects of experimental errors on the conclusions. Some of the features that may be learned by extensions to higher and lower energies are pointed out. An outline is given in the introduction.