January IS, 1951 I N a recent paper Wentzel 1 has proposed a theory in which the M-meson field is strongly coupled to the nucleon field by a pair type interaction similar to that used to explain beta-decay. This interaction provides forces between a ;u-M° pair, and the resulting bound state is identified with the ir-meson. However, besides coupling 7r-mesons and nucleons, the pair theory also predicts processes in which the ^-mesons appear in unbound states, one example of such a process being photo-production, for which Wentzel estimates a ratio of n-p 0 production cross section to 7r-production cross section of 0.1-0.01 at photon energies of 350 Mev. This is about the energy available on the Berkeley synchrotron, and since experiments of Peterson 2 have already placed an upper limit on the number of /x-mesons produced from this machine, it seemed worthwhile to recalculate this ratio more precisely.The calculations were carried out to the lowest order in the coupling constant using the Feynman-Dyson methods, and, since the theory is not covariant, all matrix elements were evaluated in the rest system of the 7r-meson and then assumed to transform covariantly on returning to the center-of-mass system. Furthermore, in this problem, the usual plane wave solutions for a pair of ju-mesons in the field are no longer correct, because of the presence of binding forces, so two approximate sets of wave functions were adopted. The first consisted of all plane waves plus the single bound level; the second was the same except that each plane wave was corrected by addition of some of the bound solution, the amount being so chosen that the corrected waves were orthogonal to the bound state. Finally, because of the noncovariance, it was necessary to neglect binding effects in the intermediate states and to treat all intermediate particles as being free.With these approximations the cross section for the production of a x + meson by a 7-ray incident on a proton is e 2 l^l 2 (PA( mc ) * T 2UMc\Mc*+hu)\mc/\hr where | U | 2 is the parameter used by Wentzel, p v is the momentum of the outgoing meson in the center-of-mass system, and m and M axe the masses of the x-meson and nucleon, respectively. For the pair cross section, using the first set of wave functions mentioned above, the following expression was obtained:where M is the mass of the pair meson, ij the coupling constant, and A the total kinetic energy in the center-of-mass system of the three outgoing particles. A similar calculation using the second set of wave functions yields a formula with the same form, but the numerical coefficient of which is approximately half as great. It should be noted that these expressions were derived under the assumption that outgoing particles were nonrelativistic, and they are, therefore, incorrect for energies far from threshold.From the cross sections the relative yield of /A-fi° pairs to x's is calculated by integrating over a bremsstrahlen (dE/E) spectrum. For a maximum photon energy of 322 Mev and using the value |(7|2/^2=2.4x(/^) 3 ...