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Register a new userFixed-t analyticity as a constraint in single energy partial wave analyses of meson photoproduction reactions
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Partial wave amplitudes of meson photoproduction reactions are an important source of information in baryon spectroscopy. We investigate a new approach in single-energy partial wave analyses of these reactions. Instead of using a constraint to theoretical models in order to achieve solutions which are continuous in energy, we enforce the analyticity of the amplitudes at fixed values of the Mandelstam variable $t$. We present an iterative procedure with successive fixed-$t$ amplitude analyses which constrain the single-energy partial wave analyses and apply this method to the $gamma p to eta p$ reaction. We use pseudo data, generated by the EtaMAID model, to test the method and to analyze ambiguities. Finally, we present an analytically constrained partial wave analysis using experimental data for four polarization observables recently measured at MAMI and GRAAL in the energy range from threshold to $sqrt{s}=1.85$ GeV.
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High precision data of the $gamma p to pi^0 p$ reaction from its threshold up to $W=2$~GeV have been used in order to perform a single-energy partial wave analysis with minimal model dependence. Continuity in energy was achieved by imposing constraints from fixed-$t$ analyticity in an iterative procedure. Reaction models were only used as starting point in the very first iteration. We demonstrate that with this procedure partial wave amplitudes can be obtained which show only a minimal dependence on the initial model assumptions.
Amplitude and partial wave analyses for pion, eta or kaon photoproduction are discussed in the context of `complete experiments. It is shown that the model-independent helicity amplitudes obtained from at least 8 polarization observables including beam, target and recoil polarization can not be used to determine underlying resonance parameters. However, a truncated partial wave analysis, which theoretically requires only 5 observables will be possible with minimal model input.
An R-matrix model for three-body final states is presented and applied to a recent measurement of the neutron energy spectrum from the T+T->2n+alpha reaction. The calculation includes the n-alpha and n-n interactions in the final state, angular momentum conservation, antisymmetrization, and the interference between different channels. A good fit to the measured spectrum is obtained, where clear evidence for the 5He ground state is observed. The model is also used to predict the alpha-particle spectrum from T+T as well as particle spectra from 3He+3He. The R-matrix approach presented here is very general, and can be adapted to a wide variety of problems with three-body final states.
This paper combines the graph-theoretical ideas behind Moravcsiks theorem with a completely analytic derivation of discrete phase-ambiguities, recently published by Nakayama. The result is a new graphical procedure for the derivation of certain types of complete sets of observables for an amplitude-extraction problem with $N$ helicity-amplitudes. The procedure is applied to pseudoscalar meson photoproduction ($N = 4$ amplitudes) and electroproduction ($N = 6$ amplitudes), yielding complete sets with minimal length of $2N$ observables. For the case of electroproduction, this is the first time an extensive list of minimal complete sets is published. Furthermore, the generalization of the proposed procedure to processes with a larger number of amplitudes, i.e. $N > 6$ amplitudes, is sketched. The generalized procedure is outlined for the next more complicated example of two-meson photoproduction ($N = 8$ amplitudes).
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V.V.Kotlyar (National Science Center
, ``Kharkov Institute of Physicsn
, Technology Institute of Theoretical Physics
1999
We develop an approach for calculating matrix elements of meson exchange currents between 3N basis states in (jJ)-coupling and a 3N bound state. The contribution generated by $pi$- and $rho$-exchange are included in the consideration. The matrix elements are expressed in terms of multiple integrals in the momentum space. We apply a technique of the partial wave decompositions and carry out some angular integrations in closed form. Different representations appropriate for numerical calculations are derived for the matrix elements of interest. The momentum dependences of the matrix elements are studied and benchmark results are presented. The approach developed is of interest for the investigations of deuteron- proton radiative capture and ^3He photo- and electrodisintegration when the interaction in the initial or final nuclear states is taken into account by solving the Faddeev equations.
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