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Empirical Partial-Wave Analysis ofπ+pElastic Scattering Above 1 GeV/c

1964; American Institute of Physics; Volume: 136; Issue: 3B Linguagem: Inglês

10.1103/physrev.136.b787

1536-6065

M. L. Perl, Mary C. Corey,

Particle Accelerators and Free-Electron Lasers

The partial-wave equation $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}=|[\frac{1}{2ik}]\ensuremath{\Sigma}\stackrel{L}{l=0}(2l+1)(1\ensuremath{-}{a}_{l}){P}_{l}(cos\ensuremath{\theta}){|}^{2}$ has been used to fit most of the recent $\ensuremath{\pi}+p$ differential cross-section measurements above 1 GeV/c. The ${a}_{l}$ were determined by the method of weighted least squares, with the further requirement that they be real and they satisfy either constraints of the form $1\ensuremath{\ge}1\ensuremath{-}{a}_{l}\ensuremath{\ge}0$ (which allows the scattering to be interpreted as purely absorptive) or the more relaxed constraints $2\ensuremath{\ge}1\ensuremath{-}{a}_{l}\ensuremath{\ge}0$. This equation with the requirements does not allow the scattering amplitude to have a spin-flip part or a real part, but for one set of data further terms were added to allow these additional parts of the scattering amplitude. For each differential cross section at the various energies, a set of ${a}_{l}$ values was determined which in almost all cases fit the measured cross sections quite well. These sets of ${a}_{l}$ parameters have two properties in common. First, all ${a}_{l}$ except ${a}_{0}$ satisfy $1\ensuremath{\ge}1\ensuremath{-}{a}_{l}\ensuremath{\ge}0$. The ${a}_{0}$ parameters ($s$-wave amplitudes) required $1\ensuremath{-}{a}_{0}\ensuremath{\ge}1$ except for the higher energies where $1\ensuremath{\ge}1\ensuremath{-}{a}_{0}\ensuremath{\ge}0$ was obtained. Second, graphs of $1\ensuremath{-}{a}_{l}$ versus $l$ (one graph for each different cross-section measurement) show that $1\ensuremath{-}{a}_{l}$ decreases rather smoothly with increasing $l$ and that the curve is either roughly linear or concave upward. No striking variations in the ${a}_{l}$ parameters are observed when the energy is close to one of the $\ensuremath{\pi}+p$ total cross section resonances. The ${a}_{l}$ parameters are interpreted using $1\ensuremath{-}{a}_{l}$ as a measure of the absorption of the $l\mathrm{th}$ partial wave by inelastic processes. Differential cross section measurements of ${\ensuremath{\pi}}^{\ensuremath{-}}+p$ at 2.01 GeV/c and of ${\ensuremath{\pi}}^{+}+p$ at 2.02 GeV/c, previously published only in graphical form, are given in the Appendix.