Photoproduction Amplitudes Research Articles

Theory of Photoproduction of Pions from Nucleons

A resonance theory of the pion-nucleon system based on a very general static model is extended to give an expression for the pion photoproduction amplitude. It is found that for photon energies less than 500 Mev there are just two important terms in the amplitude, one of them describing direct photoejection of the pion and the other, photoexcitation of the $J=\frac{3}{2}$, $I=\frac{3}{2}$ resonance state of the nucleon. The first term is estimated by means of a weak-coupling, finite-source theory which is made gauge-invariant by introducing line currents in the source. Comparison with the threshold ${\ensuremath{\pi}}^{+}$ production leads to a coupling constant (without recoil correction) ${f}^{2}=0.049$. The behavior of the cross section at high energies does not appear to be consistent with this result. Much better agreement with the data above threshold is obtained for the uncorrected coupling constant ${f}^{2}=0.07$. However, serious discrepancies within the data make it impossible to resolve this difficulty at present.The behavior of the photoejection part of the ${\ensuremath{\pi}}^{+}$ cross section above the resonance is found to be sensitive to the form of the source function. With ${f}^{2}=0.049$ and a Gaussian source function, infinite cutoff comes closest to fitting the data. However a considerably better fit is obtained with ${f}^{2}=0.07$ and a cutoff of about 4 pion masses. The resonance term is sensitive to the form of the pion-nucleon phase shift ${\ensuremath{\alpha}}_{33}$ above the resonance. We find that the simple one-level form for the energy dependence of ${\ensuremath{\alpha}}_{33}$ (Chew-Low curve) is not adequate to account for the data for high-energy photoproduction of pions; it is necessary to take account of the residue of higher resonances. Good agreement with the resonance term is obtained in terms of just two constant parameters, $\mathfrak{M}$, the strength of the resonance matrix element, and $Q$, the contribution of higher resonances to the phase shift. We find no supporting evidence for a previously suggested $S$ wave, $I=\frac{1}{2}$ resonance.

Transition Amplitudes for Photoproduction of Mesons from Nucleons and Photodisintegration of the Deuteron

An elementary technique of general applicability is applied to the explicit construction as operators in the spin space of the particles involved, of the transition matrices for photoproduction of mesons from nucleons and photodisintegration of the deuteron.

Photoproduction processes and dispersion relations

Abstract Dispersion relations for photoproduction of π-mesons on nucleons are obtained. The role of “bound states” is discussed in connection with an analysis of the unobservable energy region. The matrix structure of the photoproduction amplitude is considered. The dispersion relations are presented in a form convenient for phase shift analysis.