~ Nuelear Physics B23 (1970) 181-217. North-Holland Pablishing Company AN ANALYSIS OF SINGLE PION PHOTOPRODUCTION IN THE SECOND RESONANCE REGION R. G. MOORHOUSE and W. A. RANKIN Department of Natural Philosophy, University of Glasgow Received 11 June 1970 Abstract: We have analysed single pion photoproduetion data off protons in the second resonance region, using an isobar model, in an attempt to determine how well the electromagnetic couplings of the Sl1(1520), D13(1520 ) and P11(1470) resonances are determined by the existing data. We find that both D13 couplings can be classed as well determined and the Sll coupling as fairly well determined. Within significant limits the photonic coupling of the Roper or P11(1470) resonance is undetermined by the existing data and possible experiments to resolve the ambi- guities are discussed. 1. INTRODUCTION In this paper we present an energy-dependent multipole amplitude anal- ysis of pion photoproduction data off protons in the second resonance re- gion. There have been several analyses before [1], the most recent being those of Chau et al. [2] which hereafter we witl refer to as CDM, and of Walker [3]. The reasons for the present re-analysis are two-fold. Firstly, in view of the general importance of a knowledge of the electromagnetic couplings of resonances, it is desirable for a phenomenological analysis to present not only "best" values of the parameters representing these coup- lings, but also information on how well these "best" values are determined in fits to the data. This information was not provided by previous analyses. Secondly, there is the appearance of new experimental data, notably on the ~o asymmetry ratio for polarised photons [2]. The present analysis makes use of this new data and examines the variation of the goodness of fit with changes in the resonance parameters in order to find a "true" error on each resonance electromagnetic coupling parameter. As examples of just some of the applications of resonance electromagnetic couplings we may mention quark-model tests and calculations [5-7], sidewise dispersion re- lations [8] and current-algebra calculations [9]. Just as for the resonance parameters, we could have found a "true" error on each electromagnetic multipole. However the non-resonant multi- poles tend to be not so large, individually, as the resonant multipoles and consequently not so well determined. In the present state of the data it did not seem to be worth the effort and computing time involved to determine the "true" errors on all the multipoles. We give tables of all the multi-