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

Abstract

Accurate measurements of $p\ensuremath{-}\ensuremath{\alpha}$ 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 $p\ensuremath{-}\ensuremath{\alpha}$ 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 ${\ensuremath{\chi}}^{2}$ per degree of freedom of 1.001 which is within one standard deviation in ${\ensuremath{\chi}}^{2}$ 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.NUCLEAR REACTIONS $^{4}\mathrm{He}(p, p)$, $E=11\ensuremath{-}14$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$, $\ensuremath{\theta}(\mathrm{c}.\mathrm{m}.)=19\ensuremath{-}167\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\theta}=0.03\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\sigma}=0.06%$; calculated $R$-matrix parameters for all $^{4}\mathrm{He}(p, p)^{4}\mathrm{He}$ data, $E=0\ensuremath{-}17$ MeV.