Elastic scattering of protons by helium 4: New experiments and analysis

Abstract

Accurate measurements of $p-\alpha$ elastic scattering cross sections were made at energies of 11.157, 12.040, 13.600, and 14.230 MeV. The average relative error is about 0.6% and the scale error is 0.37%. These data and all available cross section and spin-dependent measurements of $p-\alpha$ scattering between 0 and 18 MeV were collected and prepared for input to a general purpose $R$-matrix analysis program. Strict statistical criteria were used for the elimination of data. The resulting search on 1131 data produced a unique fit with a ${\chi }^2$ per degree of freedom of 1.001 which is within one standard deviation in ${\chi }^2$ space. Arbitrary normalizations to the data were not allowed; a normalization was treated as another datum restrained by a scale error obtained from the experimental information. The parameter space was made up of background contributions in $S$, $P$, $D$, and $F$ states with an additional level each in the $P_{\frac{3}{2}}$ and $P_{\frac{1}{2}}$ states. There were 14 free parameters. For the first time, the reduced widths of the $p$-wave resonance states come out almost equal. Comparisons are made to the $R$-matrix analysis of Stammbach and Walter and to the phase shift analysis of Arndt, Roper, and Shotwell.