Study of the Reactionπ+n→pπ0π0at 2.1 GeV/c

Using the reaction ${\pi }^{+}d\to pp\left(\mathrm{MM}\right)$ at 2.13 GeV/c with photons from the final-state ${\pi }^0\text{'}\mathrm{s}$ detected by tantalum plates in the 30-in. ANL bubble chamber, a $2{\pi }^0$ mass spectrum has been obtained in several ways. This spectrum is found to be in good agreement with phase-space expectations and presents no evidence for the production of a "narrow" $\epsilon$ ($\Gamma <200\mathrm{}$ MeV). The $2{\pi }^0$ cross section for ${\Delta }^2<15\mathrm{}{\mu }^2$ is 386 ± 80 μb. $\pi \pi$ production and scattering angular distributions are presented. Good agreement with the one-pion-exchange model is noted. Assuming that the ratios of peripheral pion-production cross sections are equal to their pole values, a new method for extracting $\pi \pi$ scattering parameters is discussed. Using this method the $I=0\mathrm{}$ $s$-wave phase shift is uniquely determined from threshold to 1 GeV/${\mathit{c}}^2$ and found to be similar to the so-called UP-DOWN solutions of $s-p$ wave interference analyses. In addition, the ratios of $I=0\mathrm{}$ to $I=2\mathrm{}$ $s$-wave scattering phase shifts and scattering lengths are found to be equal to -(${3.2}_{-1.0\mathrm{}}^{+1.5\mathrm{}}$) near $\pi \pi$ threshold. Using a dispersion sum rule, the $\pi \pi$ scattering lengths are found to be $a_0=+(0.15\mathrm{}\pm 0.08){\mu }^{-1\mathrm{}}$ and $a_2=-(0.05\mathrm{}\pm 0.01){\mu }^{-1\mathrm{}}$.