Photopion Production From Deuterium Near Threshold

The reactions $\gamma d\to {\pi }^{-}2p, {\pi }^{+}2n$ were studied near threshold with the Berkeley electron synchrotron. A 4-in. liquid-deuterium bubble chamber served as target and detector in a 194-MeV bremsstrahlung beam hardened by about one radiation length of LiH. A total of 1309 ${\pi }^{-}$ and 447 ${\pi }^{+}$ events was analyzed. The experimental data for the minus-to-plus ratio $R$ were corrected for final-state Coulomb interactions by the method of Baldin, with the results $R=1.28\mathrm{}\pm 0.13$ for $160 \mathrm{MeV}<k<\mathrm{}175\mathrm{} \mathrm{MeV}$ and ${\theta }^{*}>110\mathrm{}$ deg (c.m.); $R\ge 1.13\pm 0.13$ for $152 \mathrm{MeV}<k<\mathrm{}160\mathrm{} \mathrm{MeV}$ and ${\theta }^{*}<110\mathrm{}$ deg (c.m.). The theory of Chew, Goldberger, Low and Nambu (CGLN), modified by Ball to include the $\rho$-exchange parameter $\Lambda$, predicts $R=1.28(1-0.14\mathrm{} \frac{\Lambda }{e})$. This relation was used with our values of $R$ to obtain $\frac{\Lambda }{e}=0.0\mathrm{}\pm 0.7$ and $\frac{\Lambda }{e}\le 0.8\pm 0.7$ for the above two photon-energy ranges. The Chew-Low extrapolation technique was used to obtain the value of the squared matrix element ${a_0}^{-}$ for the reaction $\gamma n\to {\pi }^{-}p$. It was found to be a satisfactory method to apply to the deuteron for deriving reaction cross sections for free neutrons. We obtain ${a_0}^{-}=27.3\mathrm{}\pm 2.8$ μb/sr at threshold with a slope of -0.30±0.16 μb/sr MeV. Our most accurate value is ${a_0}^{-}=23.3\mathrm{}\pm 1.9$ μb/sr at $k_{\gamma n}=162\mathrm{}$ MeV. These results have been corrected for the final-state ${\pi }^{-}p$ interaction, by means of the Coulomb penetration factor. The threshold value of the squared matrix element for the reaction $\gamma p\to {\pi }^{+}n$ was determined to be ${a_0}^{+}=21.5\mathrm{}\pm 0.9$ μb/sr by McPherson et al. using the same apparatus. Combining these results gives the values $R=\frac{{a_0}^{-}}{{a_0}^{+}}=1.27\mathrm{}\pm 0.13$ at threshold and $\frac{\Lambda }{e}=0.06\mathrm{}\pm 0.7$. The results are in good agreement with the CGLN theory, and consistent with a value $\Lambda =0\mathrm{}$.