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By E.H.S. BURHOP (Eds.)

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Then the solution is obtained in a particularly simple form, namely EW(W)\{W - Af) * ( - β / / 8 π Μ ) ( μ ρ + (4/3π) Γ EtfiW) μη) dW Im M$(W')lk'q'9 (11-19) 2 » (*//4π){1 - ±[1 4- (1 - u )\2u In (1 - ιι)/(1 + u)]}, (11-20) * Hereafter referred to as CGLN. t Since the magnitude of the s-wave phase shifts is not more than 10-15° in the energy range being considered, this correction should be of the order of μ/Μ and consequently its omission is consistent with the static model assumptions. 36 A. DONNACHIE where u is the velocity of the outgoing pion E0°+\W)/(W - Μ ) » ( - * / / 8 π Μ ) ( μ ρ + μη).

Turning first to charged pion photoproduction, the contribution from the + ρ can be readily investigated using the π / π " ratio near threshold, as was done, for example, by Donnachie and Shaw (1966). In the case of the p , the p N N coupling can be obtained, for instance, from pion-nucleon scattering so that an absolute value can be obtained for the pny coupling, which can most conveniently be expressed in terms of the width for the p^ny decay. 6 MeV, obtained by Fidecaro et ah (1966). As can be gauged by these errors quoted on the p->ny width, the effect of ρ exchange in charged pion production is smaller + than the current experimental errors on the π and π~ cross sections.

2 FIG. 7. The coefficient C in the expansion (da/dQ)(yp ->ρπ°) = A + Β cos θ - f C c o s Θ. 2 FIG. 8. The ratio C/A from the expansion (da/dÜ)(yp ->ρπ°) = A + Β cos θ + C c o s 0 . 40 A. DONNACHIE The result of the integration then was added to the Born term to give a new approximation to the real part, and the procedure was repeated until a solu­ tion was found which reproduced itself sufficiently accurately. Special care had to be taken in the resonance region where the real part of the amplitude vanishes and small errors in the calculation of the real part lead to large errors in the imaginary part used in the next iteration (tan δ -* oo at resonance) and an unstable solution results.

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