Pion production in pion-nucleon collisions in the Chew-Low-Wick formalism (original) (raw)
The produc~ion of a single p-wave pion in pion-nucleon collisions has been studied using the Chew-Low-Wick formalism. This theory is a low-energy, static-source theory. The purposes of this study are: to determine the ability of the theory to handle high-energy processes; to determine the effects of high-energy processes upon the low-energy predictions of the theory; a.nd to obtain information on the behavior of the production cross-section. An equation has been derived which, in the one-intermediatemeson approximation, gives the matrix element for meson production in terms of the matrix element for scattering. This equations exhibits a crossing symmetry under a time reversal of one of the outgoing mesons. The angular momentum a.nd isotopic spin dependences have been extracted. This allows one to take advantage of the conservation of the total angular momentum and total isotopic spin, and to use the symmetry of the theory between angular momentum and isotopic spin. The resulting equations have the form of twenty coupled integral equations; they are uncoupled by neglecting integrals containing non-resonant denominators. Solutions have been obtained by including scattering 1n only the T = J = 3/2 state. The resulting production cross-section for ff-incident on protons shows a peak. for an incident energy of 700 Mev. For energies in this region, each outgoing meson can attain the 33-resonant energy relative to the nucleon. The peak is the result of this "two-particle resonance". The one-meson approximation does not maintain the requirements of unitarity. It is found that the production cross-sections violate unitarity in the region of 500 Mev. This is attributable to the inadequacies of the one-meson approximation and to the fact that high-energy scattering effects are important. The equation for the production matrix element shows that the high-energy scattering amplitudes act to damp the production cross-section. The solutions for meson production have been used to examine the two-meson corrections to the equation for the scattering matrix element. These corrections are small relative to the scattering amplitude for the 33-state, but large relative to the amplitudes for the 11-and 13-atates. The equation for the matrix element describing the photoproduction of two p-wave pions has been derived. All quantities involved have been expressed 1n terms of multipoles. The structure of the equation is identical with the equation for meson production, leading to the belief that double photoproduction will show a peak for incident photon energies of about 800 Mev.
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