Double polarization experiments at intermediate energy

At modern electron accelerators with highly polarized, intense, high duty factor beams double polarization coincidence experiments became feasible with good statistical accuracy. The strong potential towards the precise determination of small nucleon structure quantities is illustrated by two recent examples from MAMI. The measurement of $G_E^n$ in the quasifree reaction $D(\vec e, e'\vec n)p$ lead to a new parametrization of $G_E^n$ which is significantly above the previously preferred one from elastic $e-D$ scattering. A $p(\vec e, e'\vec p)\pi^0$ experiment at the energy of the $\Delta$ resonance yields preliminary results for the longitudinal quadrupole mixing. Both experimental errors and model uncertainties are complementary to unpolarized measurements.Comment: 8 pages, 6 figures, plenary talk given at PANIC'9

The role of the pion cloud in electroproduction of the Δ\Delta(1232)

We calculate the ratios $E2/M1$ and $C2/M1$ of the multipole amplitudes for electroproduction of the $\Delta$(1232) in the range of photon virtuality $0<-K^2<1$~GeV$^2$ in a chiral chromodielectric model and a linear $\sigma$-model. We find that relatively large experimental values can be explained in terms of the pion contribution alone; the contribution arising from d-state quark admixture remains below 10\%. We describe the pion cloud as a coherent state and use spin and isospin projection to obtain the physical nucleon and the $\Delta$. The $A_{1/2}$ and $A_{3/2}$ amplitudes are reasonably well reproduced in the $\sigma$-model; in the chromodielectric model, however, they are a factor of two too small.Comment: 10 pages LaTeX2e, 3 LaTeX figures within the text; Requires elsart.cls (included in the self-unpacking uuencoded gzipped file). (Accepted for publication in Phys. Lett. B

Relativistic effects in electromagnetic nuclear responses in the quasi-elastic delta region

A new non-relativistic expansion in terms of the nucleon's momentum inside nuclear matter of the current for isobar electro-excitation from the nucleon is performed. Being exact with respect to the transferred energy and momentum, this yields new current operators which retain important aspects of relativity not taken into account in the traditional non-relativistic reductions. The transition current thus obtained differs from the leading order of the traditional expansion by simple multiplicative factors. These depend on the momentum and energy transfer and can be easily included together with relativistic kinematics in non-relativistic, many-body models of isobar electro-excitation in nuclei. The merits of the new current are tested by comparing with the unexpanded electromagnetic nuclear responses in the isobar peak computed in a relativistic Fermi gas framework. The sensitivity of the relativistic responses to the isobar's magnetic, electric and Coulomb form factors and the finite width of the isobar is analyzed.Comment: 26 pages plus 6 figure

The Drell-Hearn-Gerasimov Sum Rule

The Drell-Hearn-Gerasimov (DHG) sum rule relates the helicity structure of the photoabsorption cross section to the anomalous magnetic moment of the nucleon. It is based on Lorentz and gauge invariance, crossing symmetry, causality and unitarity. A generalized DHG sum rule my be derived for virtual photons. At low momentum transfer this generalized sum rule is saturated by the resonance region, at high momentum transfer it may be expressed by the parton spin distributions measured in deep inelastic scattering. The longitudinal-transverse interference determines the Cottingham sum rule, which is related to the electric and magnetic form factors over the whole range of momentum transfer.Comment: 20 pages LATEX plus 12 figures (available by fax from the author

A unitary isobar model for pion photo- and electroproduction on the proton up to 1 GeV

A new operator for pion photo- and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances ($P_{33}(1232)$, $P_{11}(1440)$, $D_{13}(1520)$, $S_{11}(1535)$, $F_{15}(1680)$, and $D_{33}(1700)$). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The $Q^2$ dependence of electromagnetic resonance vertices is described with appropriate form factors in the electromagnetic helicity amplitudes. Within this model we have obtained good agreement with the experimental data for pion photo- and electroproduction on the nucleon for both differential cross sections and polarization observables. The model can be used as a starting point to predict and analyze forthcoming data.Comment: 32 pages LaTeX including 23 postscript figures (a few misprints have been corrected

Intrinsic quadrupole moment of the nucleon

We address the question of the intrinsic quadrupole moment Q_0 of the nucleon in various models. All models give a positive intrinsic quadrupole moment for the proton. This corresponds to a prolate deformation. We also calculate the intrinsic quadrupole moment of the Delta(1232). All our models lead to a negative intrinsic quadrupole moment of the Delta corresponding to an oblate deformation.Comment: 17 pages, 5 figure

(gamma,np) reactions in ¹²C , ⁶Li and ^3,4He

The emission of neutron-proton pairs is the most probable outcome of photon absorbtion in the energy region above the giant resonance at least up to the pion threshold, but little detailed information on the process has been obtained due to experimental difficulties. Two nucleon emission following photon absorbtion by a correlated pair is favoured compared to direct knockout of a single nucleon, which is suppressed by the large momentum mismatch between the ingoing photon and a single outgoing fast nucleon. Studies of the (gamma,np) process seek firstly to obtain a quantitative understanding of the photon interaction mechanism, and through this to open the door to investigations of nucleon correlations in nuclei [1], information about which is long sought but not readily obtainable

Measurement of the recoil polarization in the p (\vec e, e' \vec p) pi^0 reaction at the \Delta(1232) resonance

The recoil proton polarization has been measured in the p (\vec e,e'\vec p) pi^0 reaction in parallel kinematics around W = 1232 MeV, Q^2 = 0.121 (GeV/c)^2 and epsilon = 0.718 using the polarized c.w. electron beam of the Mainz Microtron. Due to the spin precession in a magnetic spectrometer, all three proton polarization components P_x/P_e = (-11.4 \pm 1.3 \pm 1.4) %, P_y = (-43.1 \pm 1.3 \pm 2.2) %, and P_z/P_e = (56.2 \pm 1.5 \pm 2.6) % could be measured simultaneously. The Coulomb quadrupole to magnetic dipole ratio CMR = (-6.4\pm 0.7_{stat}\pm 0.8_{syst}) % was determined from P_x in the framework of the Mainz Unitary Isobar Model. The consistency among the reduced polarizations and the extraction of the ratio of longitudinal to transverse response is discussed.Comment: 5 pages LaTeX, 1 table, 2 eps figure

The electroproduction of the Δ\Delta(1232) in the chiral quark-soliton model

We calculate the ratios E2/M1 and C2/M1 for the electroproduction of the $\Delta$(1232) in the region of photon virtuality $0<-q^2<1$ GeV$^2$. The magnetic dipole amplitude M1 is also presented. The theory used is the chiral quark-soliton model, which is based in the instanton vaccum of the QCD. The calculations are performed in flavor SU(2) and SU(3) taking rotational ($1/N_c$) corrections into account. The results for the ratios agree qualitatively with the available data, although the magnitude of both ratios seems to underestimate the latest experimental results.Comment: 14 pages, Latex, 3 figures, uses eps

Delta-to-N-gamma Coulomb Quadrupole Amplitude in PQCD

We present a leading-order pQCD calculation of the helicity-flip $\Delta\to N\gamma^*$ matrix element $G_0$ (Coulomb quadrupole amplitude $C2$), taking into account the transverse momenta of the quarks and the contribution from the gluons. In the large $Q^2$ limit, its scaling behavior acquires a double-logarithmic correction $\log^2{(Q^2/\Lambda^2)}$ compared with the standard scaling analysis, due to the contribution from the orbital motion of the small-$x$ partons. Based on this and on the latest JLab experimental results of the $C2-M1$ ratio $R_{SM}$ at $Q^2$ = 3 $\sim$ 4 GeV$^2$, we make a phenomenological prediction for the latter at higher values of $Q^2$.Comment: 9 pages, two figure