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We present a phenomenological discussion of spin-independent, generalized dipole polarizabilities of hadrons entering the virtual Compton scattering process gamma* h -> gamma h. We introduce a new method of obtaining a tensor basis with appropriate Lorentz-invariant amplitudes which are free from kinematical singularities and constraints. We then motivate a gauge-invariant separation into a generalized Born term containing ground-state properties only, and a residual contribution describing the model-dependent internal structure. The generalized dipole polarizabilities are defined in terms of Lorentz-invariant residual amplitudes. Particular emphasis is laid on a physical interpretation of these quantities as characterizing the spatial distributions of the induced electric polarization and magnetization of hadrons. It is argued that three dipole polarizabilities, namely the longitudinal electric alpha_L(q^2), the transverse electric alpha_T(q^2), and the magnetic beta(q^2) ones are required in order to fully reconstruct local polarizations induced by soft external fields in a hadron. One of these polarizabilities, alpha_T(q^2), describes an effect of higher order in the soft final-photon momentum q'. We argue that the associated spatial distributions obtained via the Fourier transforms in the Breit frame are meaningful even for such a light particle as the pion. The spatial distributions are determined at large distances r ~ 1/m_pi for pions, kaons, and octet baryons by use of ChPT., 41 pages, 5 figures, RevTex file

Differential cross-sections for quasi-free $\pi^0$ photoproduction from the proton and neutron bound in the deuteron have been measured for $E_\gamma= 200 - 400$ MeV at $\theta^{\rm lab}_\gamma = 136.2^\circ$ usind the Glasgow photon tagger at MAMI, the Mainz 48 cm $\varnothing$ $\times$ 64 cm NaI(Tl) photon detector and the G\"ottingen SENECA recoil detector. For the proton measurements made with both liquid deuterium and liquid hydrogen targets allow direct comparison of "free" $\pi^0$ photoproduction cross-sections as extracted from the bound proton data with experimental free cross sections which are found to be in reasonable agreement below 320 MeV. At higher energies the "free" cross sections extracted from quasifree data are significantly smaller than the experimental free cross sections and theoretical predictions based on multipole analysis. For the first time, "free" neutron cross sections have been extracted in the $\Delta$-region. They are also in agreement with the predictions from multipole analysis up to 320 MeV and significantly smaller at higher photon energies.

Experimental differential cross sections for Compton scattering by the proton measured with the LARge Acceptance arrangement at the tagged-photon facility MAMI (Mainz) are interpreted in terms of the nonsubtracted dispersion theory based on the SAID-SM99K parameterization of photo-meson amplitudes. Using the new global average for the difference of electric and magnetic polarizabilities of the proton α β= (10:5 0:9stat+syst 0:7model) 10 4fm3 a backward spin-polarizability of γπ = ( 37:1 0:6stat+syst 3:5model) 10 4fm4 and a E2/M1 ratio of EMR(340 MeV)=( 1:7 0:4stat+syst 0:2model) % have been obtained.

Photoproduction of e{sup +}e{sup {minus}} pairs at small angles is investigated as a tool to determine the functions f{sub 1} and f{sub 2} entering the real-photon forward Compton scattering amplitude. The method is based on an interference of the Bethe-Heitler and the virtual Compton scattering mechanisms, generating an azimuthal asymmetry in the e{sup +} versus e{sup {minus}} yield. The general case of a circularly polarized beam and a longitudinally polarized target allows one to determine both the real and imaginary parts of f{sub 1} as well as f{sub 2}. The imaginary part of f{sub 2} requires target polarization only. We calculate cross sections and asymmetries of the reaction p({gamma},e{sup +}e{sup {minus}})p, estimate corrections and backgrounds, and propose suitable kinematical regions to perform the experiment. Our investigation shows that photoproduction of e{sup +}e{sup {minus}}-pairs off the proton and light nuclei may serve as a rather sensitive test of the validity of the Gerasimov-Drell-Hearn sum rule. {copyright} {ital 1998} {ital The American Physical Society}

Differential cross sections for Compton scattering by the proton have been measured in the energy interval between 200 and 500 MeV at scattering angles of θcms = 75° and θcms = 90° using the CATS, the CATS/TRAJAN, and the COPP setups with the Glasgow Tagger at MAMI (Mainz). The data are compared with predictions from dispersion theory using photo-meson amplitudes from the recent VPI solution SM95. The experiment and the theoretical procedure are described in detail. It is found that the experiment and predictions are in agreement as far as the energy dependence of the differential cross sections in the Δ-range is concerned. However, there is evidence that a scaling down of the resonance part of the M 1+ 3 2 photo-meson amplitude by (2.8 ± 0.9)% is required in comparison with the VPI analysis. The deduced value of the M 1+ 3 2 - photoproduction amplitude at the resonance energy of 320 MeV is: |M 1+ 3 2 | = (39.6 ± 0.4) × 10 −3 m π + −1 .

Dispersion theory of proton Compton scattering is extended to energies up to {approximately}1 GeV where excitations of higher resonances and nonresonance double-pion photoproduction become important photoabsorption mechanisms. To saturate s-channel dispersion relations, the VPI partial-wave analysis of single-pion photoproduction and resonance photocouplings is used. Models for double-pion photoproduction and dispersion asymptotic contributions are constructed. The latter are mainly given by {pi}{sup 0} and {sigma}(600) exchanges. Being used in dispersion calculations, they result in a reasonable agreement with all available data on both differential cross sections and polarization observables in Compton scattering. Some unsolved problems are outlined. {copyright} {ital 1997} {ital The American Physical Society}

Using the tagged-photon beam of MAMI (Mainz) differential cross-sections for Compton scattering by the proton through θcms = 75° have been measured for the Δ-resonance region from 200 to 410 MeV. The data put a new constraint on the M1+32 photoproduction amplitude in the resonance, |M1+32| = (39.6 ± 0.4) · 10−3mπ+−1 at 320 MeV, which is (2.8 ± 0.9) % less than given by the recent analysis SM95 of the Virginia group.

Two aspects of the nucleon electromagnetic polarizabilities, αN and βN, are discussed. The first one is the interrelation between static and Compton polarizabilities. Relativistically consistent treatment of the polarization effects based on effective Lagrangians results in the conclusion that the Compton polarizabilities, rather than the static ones, drive the energy shift of the nucleon in external fields. The cluster substructure of the static polarizabilities is shown to be crucial for consistent calculations of the polarizabilities. The second aspect concerns the dominant role of pion degrees of freedom in αN as seen through dispersion relations, chiral perturbation theory, and constituent models. The reported calculations of αN within soliton models are shown to be inconsistent with gauge invariance. The difficulties in explaining the observed large diamagnetic component of βN are emphasized.

Dispersion relations are used to re-derive and explain the recent one-loop results of the chiral perturbation theory (CHPT) for nucleon polarizabilities and spin-dependent part of the Compton scattering amplitude and to estimate contributions lying beyond. The conclusion is made that the CHPT expansion over m π is convergent too slowly to provide a thrust for the one-loop results.

Differential cross section of deuteron Compton scattering has been calculated using the Bonn NN-potential, a consistent set of meson-exchange currents and seagulls, and lowest- and higher-order electromagnetic polarizabilities of the nucleon. Estimates of the polarizabilities of the neutron are obtained from recent experimental data., 3 pages, 2 figures, Latex2e with ps fonts. Talk at the FB16 Conference, Taipei, March 6-10, 2000. To appear in proceedings

Kinematic effects due to binding have been studied for the electric and magnetic polarizabilities of the nucleon within a nonrelativistic quark model. A specific unitary transformation of the model hamiltonian has been applied to disentangle nucleon and quark degress of freedom. It is shown that the naive guess of a vanishing or modification of the recoil diamagnetism βrec = −〈D2〉/2M for the bound nucleon is not correct. Instead, the same total magnetic polarizability β is shown to appear for the free and bound nucleon in the energy shift of the nucleon under the action of a static homogeneous magnetic field, as well as in the amplitude of αA scattering. The corresponding result can be formulated as a generalized low-energy theorem for Compton scattering by the bound nucleon. This results agrees also with the findings of a recent αA-scattering experiment carried out to study the polarizability of the bound nucleon. Generalization taking into account higher multipoles and ω-dependent terms in the polarizabilities are also provided.

Differential cross sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz tagging spectrometer at the Mainz MAMI accelerator together with the Mainz 48 cm $\oslash$ $\times$ 64 cm NaI(Tl) photon detector and the G\"ottingen SENECA recoil detector. The data cover photon energies ranging from 200 MeV to 400 MeV at $\theta^{LAB}_\gamma=136.2^\circ$. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction $p(\gamma,\pi^+ n)$. The "free" proton Compton scattering cross sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross section for free scattering from quasi-free data. Differential cross sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron have been obtained to be $\alpha-\beta= 9.8\pm 3.6(stat){}^{2.1}_1.1(syst)\pm 2.2(model)$ in units $10^{-4}fm^3$. In combination with the polarizability sum $\alpha +\beta=15.2\pm 0.5$ deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, $\alpha_n=12.5\pm 1.8(stat){}^{+1.1}_{-0.6}\pm 1.1(model)$ and $\beta_n=2.7\mp 1.8(stat){}^{+0.6}_{-1.1}(syst)\mp 1.1(model)$ are obtained. The backward spin polarizability of the neutron was determined to be $\gamma^{(n)}_\pi=(58.6\pm 4.0)\times 10^{-4}fm^4$.

Differential cross sections for Compton scattering from the deuteron were measured at MAX-lab for incident photon energies of 55 MeV and 66 MeV at nominal laboratory angles of $45^\circ$, $125^\circ$, and $135^\circ$. Tagged photons were scattered from liquid deuterium and detected in three NaI spectrometers. By comparing the data with theoretical calculations in the framework of a one-boson-exchange potential model, the sum and difference of the isospin-averaged nucleon polarizabilities, $\alpha_N + \beta_N = 17.4 \pm 3.7$ and $\alpha_N - \beta_N = 6.4 \pm 2.4$ (in units of $10^{-4}$ fm$^3$), have been determined. By combining the latter with the global-averaged value for $\alpha_p - \beta_p$ and using the predictions of the Baldin sum rule for the sum of the nucleon polarizabilities, we have obtained values for the neutron electric and magnetic polarizabilities of $\alpha_n= 8.8 \pm 2.4$(total) $\pm 3.0$(model) and $\beta_n = 6.5 \mp 2.4$(total) $\mp 3.0$(model), respectively., Comment: 4 pages, 2 figures, revtex. The text is substantially revised. The cross sections are slightly different due to improvements in the analysis

Using the Mainz $48\mathrm{cm}\ensuremath{\emptyset}\ifmmode\times\else\texttimes\fi{}64\mathrm{cm}$ NaI(Tl) detector and the segmented G\"ottingen recoil detector SENECA in coincidence, Compton scattering by the proton at ${\ensuremath{\theta}}_{\ensuremath{\gamma}}^{\mathrm{lab}}=136\ifmmode^\circ\else\textdegree\fi{}$ has been measured at MAMI (Mainz) in the energy range from 200 to 470 MeV. The new data confirm the previous observation that there is a systematic discrepancy between MAMI and LEGS (Brookhaven) data leading to different spin polarizabilities ${\ensuremath{\gamma}}_{\ensuremath{\pi}}=\ensuremath{-}38.7\ifmmode\pm\else\textpm\fi{}1.8$ and $\ensuremath{-}27.2\ifmmode\pm\else\textpm\fi{}3.1$ $(\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{\mathrm{fm}}^{4}),$ respectively.

Measuring Compton scattered photons and recoil neutrons in coincidence, quasifree Compton scattering by the neutron has been investigated at MAMI (Mainz) at ${\ensuremath{\theta}}_{\ensuremath{\gamma}}^{\mathrm{lab}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}136\ifmmode^\circ\else\textdegree\fi{}$ in an energy range from 200 to 400 MeV. From the data a polarizability difference of ${\ensuremath{\alpha}}_{n}\ensuremath{-}{\ensuremath{\beta}}_{n}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}9.8\ifmmode\pm\else\textpm\fi{}3.6(\mathrm{stat}{)}_{\ensuremath{-}1.1}^{+2.1}(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}2.2(\mathrm{model})$ in units of ${10}^{\ensuremath{-}4}{\mathrm{fm}}^{3}$ has been determined. In combination with the polarizability sum ${\ensuremath{\alpha}}_{n}+{\ensuremath{\beta}}_{n}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}15.2\ifmmode\pm\else\textpm\fi{}0.5$ deduced from photoabsorption data, the first precise results for the neutron electric and magnetic polarizabilities, ${\ensuremath{\alpha}}_{n}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}12.5\ifmmode\pm\else\textpm\fi{}1.8(\mathrm{stat}{)}_{\ensuremath{-}0.6}^{+1.1}(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}1.1(\mathrm{model})$ and ${\ensuremath{\beta}}_{n}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2.7\ensuremath{\mp}1.8(\mathrm{stat}{)}_{\ensuremath{-}1.1}^{+0.6}(\mathrm{syst})\ensuremath{\mp}1.1(\mathrm{model})$, are obtained.

Compton scattering by the proton has been measured over a wide range covering photon energies 250 MeV lt or approximately=E/sub gamma / lt or approximately=800 MeV and photon scattering angles 30 degrees lt or approximately= theta /sub gamma //sup lab/ lt or approximately=150 degrees , using the tagged-photon facility at MAMI (Mainz) and the large-acceptance arrangement LARA. The previously existing data base on proton Compton scattering is greatly enlarged by more than 700 new data points. The new data are interpreted in terms of dispersion theory based on the SAID-SM99K parametrization of photo-meson amplitudes. It is found that two-pion exchange in the t-channel is needed for a description of the data in the second resonance region. The data are well represented if this channel is modeled by a single pole with the mass parameter m/sub sigma / approximately=600 MeV. The asymptotic part of the spin-dependent amplitude is found to be well represented by pi /sup 0/ exchange in the t-channel. No indications of additional effects were found. Using the mass parameter m/sub sigma / of the two-pion exchange determined from the second resonance region and using the new global average for the difference of the electric and magnetic polarizabilities of the proton, alpha - beta =(10.5+or-0.9/sub stat+syst/+or-0.7/sub model/)*10/sup -4/ fm/sup 3/, as obtained from a recent experiment on proton Compton scattering below pion photoproduction threshold, a backward spin polarizability of gamma /sub pi /=(-37.1+or-0.6/sub stat+syst/+or-3.0/sub model/)*10/sup -/$ u4 fm/sup 4/ has been determined from data of the first resonance region below 455 MeV. This value is in a good agreement with predictions of dispersion relations and chiral perturbation theory. From a subset of data between 280 and 360 MeV, the resonance pion photoproduction amplitudes were evaluated leading to a E2/M1 multipole ratio of the p to Delta radiative transition of EMR (340 MeV)=(-1.7+or-0.4/sub stat+syst/+or-0.2/sub model/)%. It was found that this number is dependent on the parameterization of photo-meson amplitudes. With the MAID2K parameterization, an E2/M1 multipole ratio of EMR (340 MeV)=(-2.0+or-0.4/sub stat+syst/+or-0.2/sub model/)% is obtained.

Compton scattering by the proton has been measured over a wide range covering photon energies 250 MeV < E_\gamma < 800 MeV and photon scattering angles 30^0 < \theta^{lab}_\gamma < 150^0, using the tagged-photon facility at MAMI (Mainz) and the large-acceptance arrangement LARA. The data are in good agreement with the dispersion theory based on the SAID-SM99K parameterization of photo-meson amplitudes. From the subset of data between 280 and 360 MeV the resonance pion-photoproduction amplitudes were evaluated leading to the multipole E2/M1 ratio EMR(340 MeV) =(-1.6 \pm 0.4(stat+syst) \pm 0.2(model)%. From all data below 455 MeV the proton's backward spin polarizability was determined to be \gamma_\pi=(-37.9 \pm 0.6(stat+syst) \pm 3.5(model))x10^{-4}fm^4.

The concept of Compton scattering by even-even nuclei from giant-resonance to nucleon-resonance energies and the status of experimental and theoretical researches in this field are outlined. Nuclear Compton scattering in the giant-resonance energy-region provides information on the dynamical properties of the in-medium mass of the nucleon. The electromagnetic polarizabilities of the nucleon in the nuclear medium can be extracted from nuclear Compton scattering data obtained in the quasi-deuteron energy-region. Recent results are presented for two-body effects due to the mesonic seagull amplitude and due to the excitation of nucleon internal degrees of freedom accompanied by meson exchanges. Due to these studies the in-medium electromagnetic polarizabilities are by now well understood, whereas the understanding of nuclear Compton scattering in the Delta-resonance range is only at the beginning. Phenomenological methods how to include retardation effects in the scattering amplitude are discussed and compared with model predictions., 146 pages, 37 figures, submitted to Phys. Reports

Recently, a longitudinal sum rule for the electric polarizability of nuclei was used to revise a relativistic correction in a dipole sum rule for the polarizability (nucl-th/9802011). This revision is shown to be wrong because of neglecting an asymptotic contribution in the underlying dispersion relation. The status and correct use of the longitudinal sum rule is clarified., Comment: 9 pages, revtex, minor clarifications added. To appear in Nucl. Phys. A

Elastic scattering of photons in a Lorentz-scalar potential via virtual spin-zero particle-antiparticle pairs (`` Delbr\"uck scattering") is considered. An analytic expression for the Delbr\"uck amplitude is found exactly in case of an oscillator potential. General properties of the amplitude and its asymptotics are discussed., Comment: 8 pages, LATEX, BINP 94-65

It has been found that the reaction of Grignard reagents and organolithium compounds with barenic ketones containing the direct bond between carbonyl group and barene carbon atom proceeds abnormal and does not give barenic tertiary alcohols. Instead of this, cleavage of the carbon-carbon bond between the carbonyl group and the carbon atom of the barenic nucleus and the reduction of barenic ketones to barenic secondary alcohols take place. The reduction of barenic ketones under the action of CH 3 MgI and PhMgBr proceeds through the formation of free radicals. The action of Grignard reagents and n -butyllithium on esters of barenecarboxylic acids results also in the cleavage of carbon-carbon bond between the carboxyl group and the results also in the cleavage of carbon-carbon bond between the carboxyl group and the carbon atom of barenic nucleus.

The differential cross sections for Compton scattering from the proton have been measured at MAMI with three different detector setups. There is a good agreement among all the results. The theoretical calculation based on dispersion relations shows that there is no drastic change necessary in the parameters of this approach.