Positive Photopion Production from Hydrogen Near Threshold

Differential cross sections for photopion production from protons were measured for 32 photon energies from 154 to 185 MeV with the Alvarez 4-in. liquid-hydrogen bubble chamber in the bremsstrahlung beam of the Berkeley electron synchrotron. High photon intensities of 1.5×${10}^7$ MeV/pulse were used by collimating the beam down to a narrow "ribbon" which was viewed edge on by the camera. Although the pion origins were obscured by the heavy electron background, the remainder of the $\pi$ track was visible for most events. Of 5000 $\pi -\mu$ decays seen, 3400 were deemed suitable for calculations. The results are in excellent agreement with the theoretical calculations by Ball, who applied the Mandelstam representation to the process. The measured values of the square of the matrix element, averaged over c.m. angles, are: All data are subject to an additional correlated error of 4.1% because of the uncertainty in the beam normalization. The cross section for the process is the product of the square of the matrix element times the kinematic factor $\frac{p^{*}}{k^{*}}$, where $p^{*}$ and $k^{*}$ are the c.m. momenta of the pion and the photon. Also a value of $\Lambda =(+0.931\mathrm{}\pm 0.59)e$ was obtained, where $\Lambda$ is the multiplicative factor associated with the matrix element for photopion production from pions as calculated by Wong.