The number and type of measurements needed to ascertain the amplitudes for pseudoscalar meson photoproduction are analyzed in this paper.It is found that 8 carefully selected measurements can determine the four transversity amplitudes without discrete ambiguities. That number of measurements is one less than previously believed. We approach this problem in two distinct ways: (1) solving for the amplitude magnitudes and phases directly; and (2) using a bilinear helicity product formulation to map an algebra of measurements over to the well-known algebra of the 4 × 4 Gamma matrices. It is shown that the latter method leads to an alternate proof that 8 carefully chosen experiments suffice for determining the transversity amplitudes completely. In addition, Fierz transformations of the Gamma matrices are used to develop useful linear and nonlinear relationships between the spin observables. These relationships not only help in finding complete sets of experiments, but also yield important constraints between the 16 observables for this reaction. Typeset using REVT E XRecently, Keaton and Workman (KW) [2] argued that selecting a complete set of observables is more complicated than the above BDS rule. However, KW were not able to provide sufficient conditions for resolving all ambiguities. Their work inspired us to investigate the problem of determining which experiments can provide a "complete set," e.g. those

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The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential equations is straight forward.

A dynamical coupled-channel formalism for processes πN → KY and γN → KY is presented which provides a comprehensive investigation of recent data on the γp → K + Λ reaction. The nonresonant interactions within the subspace KY ⊕ πN are derived from effective Lagrangians, using a unitary transformation method. The calculations of photoproduction amplitudes are simplified by casting the coupled-channel equations into a form such that the empirical γN → πN amplitudes are input and only the parameters associated with the KY channel are determined by performing χ 2 -fits to all of the available data for π − p → K • Λ, K • Σ • and γp → K + Λ. Good agreement between our models and those data are obtained. In the fits to πN → KY channels, most of the parameters are constrained within ±20% of the values given by the Particle Data Group and/or quark model predictions, while for γp → K + Λ parameters, ranges compatible with broken SU (6)⊗ O(3) symmetry are imposed. The main reaction mechanisms in K + Λ photoproduction are singled out and issues related to newly suggested resonances S 11 , P 13 , and D 13 are studied. Results illustrating the importance of using a coupled-channel treatment are reported. Meson cloud effects on the γN → N * transitions are also discussed.

Observables in two-body reactions such as cross sections, polarizations, and spin correlations are often of simple form at threshold, since only a few partial waves contribute. Spin observables near threshold for meson photoproduction reactions (with emphasis on the pp~K +A case) are studied in this paper. The expected nodal structure of all sixteen observables near threshold, their evolution with momentum, the role of the centrifugal barrier on threshold multipole amplitudes, and the role of resonance efFects on spin observables are discussed.PACS number(s): 24.70.+s, 25.20.Lj, 13. 60.Le, 13.88.+e M denotes a spin zero pseudoscalar meson (e.g., pion, kaon, etc. ), and b is the final state spin 1/2 baryon (e.g. , proton, neutron, A, Z, etc. ). We begin by defining the T matrix in terms of a current operator, J, and the photon polarization vector s'p(k): (q m, ]T) k m, A) = (m, )Fp( m, ) = (m,~J[m, ) eg(k) . (2.1) The scattering amplitude is (m,~P&~m, ) and the pho-46 2430