Resonance Model for Photoproduction ofKMesons on Nucleons

An approximate one-dimensional dispersion relation of the Cini-Fubini type is assumed for the invariant amplitudes of the photoproduction of $K$ mesons on nucleons on the supposition that among the various intermediate states in the three related channels only the single-particle states and the resonant states make appreciable contributions. The resonant states that are taken into account are the following: the three-pion-nucleon resonances, the pion-kaon resonance, and the three pion-hyperon resonances. The expressions for the spectral functions are derived by applying the unitarity conditions to each of the three related channels. By the conservation of angular momentum and parity only certain multipole amplitudes determined by the spin and parity of the resonances contribute to the spectral functions, and for these nonvanishing multipole amplitudes the Breit-Wigner formula is assumed.