π^{+}p Elastic Scattering at 310 Mev: PhaseShift Analysis
Abstract
A comprehensive phaseshift analysis of π^{+}p elasticscattering data at 310Mev incidentpion laboratory kinetic energy has been performed. The experimental data utilized include measurements of the differential and total cross sections and of the recoilproton polarization. The Dwave phase shifts were found to be definitely needed in order to attain an adequate fit to the data. A general search for phaseshift solutions was carried out, using S, P, and Dwave phase shifts. One solutionof the Fermi typewas found that fits the data significantly better than any of the other solutions obtained. The calculated errors in the phase shifts of this set vary from 0.4 to 0.6 deg. Because it was felt that these errors might be deceivingly restrictive, the effects of small nuclear Fwave phase shifts on the results of the analysis were investigated and were found to be large: not only are the uncertainties in the original Fermitype solution increased, but additional sets of phase shifts arise that fit the data well. One of these new solutions is similar to the original Fermi set except that the magnitudes of the phase shifts in this new fit are in general larger than those in the initial solution, and the signs of the Dwave phase shifts are reversed. The nuclear phase shifts in the original Fermi solution and their rms errors are (when Fwave phase shifts are allowed): S_{3,1}=17.2+/2.6 deg, P_{3,1}=2.9+/4.0 deg, P_{3,3}=135.0+/0.6 deg, D_{3,3}=3.1+/2.6 deg, D_{3,5}=4.9+/2.1 deg, F_{3,5}=0.5+/0.6 deg, F_{3,7}=0.6+/1.4 deg. Although theory appears to favor this set, further theoretical and experimental evidence is desirable. The values given here for the first five phase shifts approximate the corresponding values obtained when the Fwave phase shifts were assumed negligible. However, all except P_{3,3} fall outside the limits set by the small original errors. Inelasticscattering processes were neglected during the phaseshift analysis. Calculations indicate that, if these processes could properly be taken into account, any changes in the quoted values of the phase shifts would probably be well within the corresponding errors given here. Extension of the phaseshift inquiries to include G waves was attempted, but it was observed that the available data and theory do not allow the Gwave interaction to be significantly incorporated into the analysis.
 Publication:

Physical Review
 Pub Date:
 May 1961
 DOI:
 10.1103/PhysRev.122.959
 Bibcode:
 1961PhRv..122..959F