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The Compton double-polarization observable \\(\\Sigma_{2z}\\) has been measured for the first time in the \\(\\Delta(1232)\\) resonance region using a circularly polarized photon beam incident on a longitudinally polarized target at the Mainz Microtron. This paper reports these results, together with the model-dependent extraction of four proton spin polarizabilities from fits to additional asymmetry data using dispersion relation and chiral perturbation theory calculations, with the former resulting in: \\(\\gamma_{E1E1} = -3.18 \\pm 0.52\\), \\(\\gamma_{M1M1} = 2.98 \\pm 0.43\\), \\(\\gamma_{E1M2} = -0.44 \\pm 0.67\\) and \\(\\gamma_{M1E2} = 1.58 \\pm 0.43\\), in units of \\(10^{-4}~\\mathrm{fm}^{4}\\).

A new data set for the helicity-dependent differential cross section of the single-meson photoproduction reaction \\(\\gamma p \\to p \\pi^{0}\\) was obtained for the photon energy interval 150-400 MeV. The experiment was performed at the A2 tagged photon facility of the Mainz Microtron MAMI using a circularly polarized photon beam and a longitudinally polarized proton target. The reaction products were detected with the large acceptance Crystal Ball/TAPS calorimeter covering 97\\% of the full solid angle. These new results, obtained with a fine energy and polar angle binning, greatly increase both the existing quantity and quality of the data available for this observable. A moment analysis, based on a finite expansion in Legendre polynomials, was applied to these data by using a bootstrap-based fitting method to correctly account for their systematic uncertainties. From the resulting decomposition of the differential cross sections, the \\(E2/M1\\) ratio for the \\(N\\to \\Delta(1232)\\) transition was determined to be \\([-2.38 \\pm 0.16{\\hbox{ (stat.+sys.)}} \\pm 0.10 {\\hbox{ (model)}}] \\%\\). Combining this value with previous results also allowed us to evaluate the most precise available estimate of the \\(E2/M1\\) ratio to be used for all further reference and model comparisons.

Photoproduction of \\(\\pi^0\\pi^{\\pm}\\)-pairs from quasifree nucleons bound in the deuteron has been investigated to study the helicity dependence of this reaction. Measurements with a liquid deuterium target were used to extract the unpolarized cross sections for reactions on protons and neutrons. A deuterated, longitudinally polarized solid-butanol target, together with a circularly polarized photon beam, determined the double polarization observable \\(E\\). From these results the spin-dependent cross sections \\(\\sigma_{1/2}\\) and \\(\\sigma_{3/2}\\), corresponding to the anti-parallel and parallel spin configurations of the beam photon and target nucleon, have been derived. The measurements were performed at the Mainz MAMI accelerator with tagged, circularly-polarized photon beams produced via bremsstrahlung from longitudinally polarized electron beams. The reaction products were detected with an almost \\(4\\pi\\) solid-angle covering calorimeter composed of the Crystal Ball and TAPS detectors, supplemented by plastic scintillation detectors for charged particle identification. The results are sensitive to sequential decays of nucleon resonances via intermediate states and also to the decay of nucleon resonances by emission of charged \\(\\rho\\) mesons, and are compared to recent model results.

We report the measurement of the helicity asymmetry \\(E\\) for the \\(p\\pi^0\\) and \\(n\\pi^+\\) final states using, for the first time, an elliptically polarized photon beam in combination with a longitudinally polarized target at the Crystal Ball experiment at MAMI. The results agree very well with data that were taken with a circularly polarized photon beam, showing that it is possible to simultaneously measure polarization observables that require linearly (e.g.~\\(G\\)) and circularly polarized photons (e.g.~\\(E\\)) and a longitudinally polarized target. The new data cover a photon energy range 270 - 1400 MeV for the \\(p\\pi^0\\) final state (230 - 842 MeV for the \\(n\\pi^+\\) final state) and the full range of pion polar angles, \\(\\theta\\), providing the most precise measurement of the observable \\(E\\). A moment analysis gives a clear observation of the \\(p\\eta\\) cusp in the \\(p\\pi^0\\) final state.

A first measurement of the polarisation transfer from a circularly-polarised photon to the final state neutron (\\(C^n_{x'}\\)) in deuterium photodisintegration has been carried out. This quantity is determined over the photon energy range 370~--~700~MeV and for neutron centre-of-mass breakup angles \\(\\sim45-120^{\\circ}\\). The polarisation of the final state neutrons was determined by an ancillary large-acceptance nucleon polarimeter, surrounding a cryogenic liquid deuterium target within the Crystal Ball detector at MAMI. The polarimeter characterised \\((n,p)\\) charge exchange of the ejected neutrons to determine their polarisation. The new \\(C^n_{x'}\\) data are also compared to a theoretical model based on nucleonic and nucleon resonance degrees of freedom constrained by the current world-database of deuterium photodisintegration measurements. Structures in \\(C^n_{x'}\\) observed in the region of the \\(d^*(2380)\\) could not be explained by conventional models of deuteron photodisintegration.

The helicity-dependent cross sections for the photoproduction of \\(\\pi^0\\eta\\) pairs have been measured for the first time. The experiment was performed at the tagged photon facility of the Mainz MAMI accelerator with the combined Crystal Ball - TAPS calorimeter. The experiment used a polarized deuterated butanol target and a circularly polarized photon beam. This arrangement allowed the \\(\\sigma_{1/2}\\) (photon and target spin antiparallel) and \\(\\sigma_{3/2}\\) (parallel spins) components to be measured for quasi-free production of \\(\\pi^0\\eta\\) pairs off protons and neutrons. The main finding is that the two helicity components contribute identically, within uncertainties, for both participant protons and neutrons. The absolute couplings for protons and neutrons are also identical. This means that nucleon resonances contributing to this reaction in the investigated energy range have almost equal electromagnetic helicity couplings, \\(A_{1/2}^{n,p}\\) and \\(A_{3/2}^{n,p}\\). Identical couplings for protons and neutrons are typical for \\(\\Delta\\) resonances and identical \\(A_{1/2}\\) and \\(A_{3/2}\\) components are only possible for \\(J\\geq 3/2\\) states, which constrains possible contributions of nucleon resonances.

We report a first measurement of the double-polarisation observable, \\(C_{x'}\\), in \\(\\pi^+\\) photoproduction off the proton. The \\(C_{x'}\\) double-polarisation observable represents the transfer of polarisation from a circularly polarised photon beam to the recoiling neutron. The MAMI circularly polarised photon beam impinged on a liquid deuterium target cell, with reaction products detected in the Crystal Ball calorimeter. Ancillary apparatus surrounding the target provided tracking, particle identification and determination of recoil nucleon polarisation. The \\(C_{x'}\\) observable is determined for photon energies 800-1400 MeV, providing new constraints on models aiming to elucidate the spectrum and properties of nucleon resonances. This is the first determination of any polarisation observable from the beam-recoil group of observables for this reaction, providing a valuable constraint and systematic check of the current solutions of partial wave analysis based theoretical models.

Background: Photoproduction of pion pairs allows to study sequential decays of nucleon resonances via excited intermediate states. Such decays are important e.g. for states which in the quark model have both oscillators excited and de-excite them in a two-step process. However, analyses of multi-meson final states is difficult and requires more than unpolarized cross section measurements. Purpose: Experimental study and model analysis in view of resonant contributions of target and beam-target polarization observables for the reaction \\(\\gamma p \\to \\pi^0 \\pi^0 p\\). Methods: Investigated were target (single) and beam-target (double) polarization asymmetries in dependence of several parameters. The experiments were performed at the Mainz Microtron (MAMI) using circularly polarized photon beams and transversally polarized solid-state butanol targets. The reaction products were analyzed with the Crystal Ball and TAPS detectors. Results: Studied were the polarization observables Py (unpolarized beam, target polarized in y direction) and Px (circularly polarized beam, target polarized in x direction), which are similar to T (target asymmetry) and F (beam-target asymmetry) for single pion production. The asymmetries were analyzed with three independent methods, revealing systematic uncertainties.

A precise measurement of the differential cross-sections \\(d\\sigma/d\\Omega\\) and the linearly polarized photon beam asymmetry \\(\\Sigma_3\\) for Compton scattering on the proton below pion threshold has been performed with a tagged photon beam and almost \\(4\\pi\\) detector at the Mainz Microtron. The incident photons were produced by the recently upgraded Glasgow-Mainz photon tagging facility and impinged on a cryogenic liquid hydrogen target, with the scattered photons detected in the Crystal Ball/TAPS set-up. Using the highest statistics Compton scattering data ever measured on the proton along with two effective field theories (both covariant baryon and heavy-baryon) and one fixed-\\(t\\) dispersion relation model, constraining the fits with the Baldin sum rule, we have obtained the proton electric and magnetic polarizabilities with unprecedented precision: \\begin{align*} &{}\\alpha_{E1} = 10.99 \\pm 0.16 \\pm 0.47 \\pm 0.17 \\pm 0.34 &{}\\beta_{M1} = 3.14 \\pm 0.21 \\pm 0.24 \\pm 0.20 \\pm 0.35 \\end{align*} in units of \\(10^{-4}\\)\\,fm\\(^3\\) where the errors are statistical, systematic, spin polarizability dependent and model dependent.

The helicity-dependent single \\(\\pi^{0}\\) photoproduction cross section on the deuteron and the angular dependence of the double polarisation observable \\(E\\) for the quasi-free single \\(\\pi^0\\) production off the proton and the neutron have been measured for the first time from the threshold region up to the photon energy 1.4 GeV. The experiment was performed at the tagged photon facility of the MAMI accelerator and used a circularly polarised photon beam and longitudinally polarised deuteron target. The reaction products were detected using the large acceptance Crystal Ball/TAPS calorimeter, which covered 97% of the full solid angle. Comparing the cross section from the deuteron with the sum of free nucleon cross sections provides a quantitative estimate of the effects of the nuclear medium on pion production. In contrast, comparison of \\(E\\) helicity asymmetry data from quasi-free protons off deuterium with data from a free proton target indicates that nuclear effects do not significantly affect this observable. As a consequence, it is deduced that the helicity asymmetry \\(E\\) on a free neutron can be reliably extracted from measurements on a deuteron in quasi-free kinematics.