Determination of the

We report the first measurement of the parity-violating elastic electron scattering asymmetry on ^{27}Al. The ^{27}Al elastic asymmetry is A_{PV}=2.16±0.11(stat)±0.16(syst) ppm, and was measured at ⟨Q^{2}⟩=0.02357±0.00010 GeV^{2}, ⟨θ_{lab}⟩=7.61°±0.02°, and ⟨E_{lab}⟩=1.157 GeV with the Q_{weak} apparatus at Jefferson Lab. Predictions using a simple Born approximation as well as more sophisticated distorted-wave calculations are in good agreement with this result. From this asymmetry the ^{27}Al neutron radius R_{n}=2.89±0.12 fm was determined using a many-models correlation technique. The corresponding neutron skin thickness R_{n}-R_{p}=-0.04±0.12 fm is small, as expected for a light nucleus with a neutron excess of only 1. This result thus serves as a successful benchmark for electroweak determinations of neutron radii on heavier nuclei. A tree-level approach was used to extract the ^{27}Al weak radius R_{w}=3.00±0.15 fm, and the weak skin thickness R_{wk}-R_{ch}=-0.04±0.15 fm. The weak form factor at this Q^{2} is F_{wk}=0.39±0.04.

Precision Measurement of the Beam-Normal Single-Spin Asymmetry in Forward-Angle Elastic Electron-Proton Scattering.

A beam-normal single-spin asymmetry generated in the scattering of transversely polarized electrons from unpolarized nucleons is an observable related to the imaginary part of the two-photon exchange process. We report a 2% precision measurement of the beam-normal single-spin asymmetry in elastic electron-proton scattering with a mean scattering angle of θ_{lab}=7.9° and a mean energy of 1.149 GeV. The asymmetry result is B_{n}=-5.194±0.067(stat)±0.082 (syst) ppm. This is the most precise measurement of this quantity available to date and therefore provides a stringent test of two-photon exchange models at far-forward scattering angles (θ_{lab}→0) where they should be most reliable.

First determination of the weak charge of the proton.

The Q(weak) experiment has measured the parity-violating asymmetry in ep elastic scattering at Q(2)=0.025(GeV/c)(2), employing 145 µA of 89% longitudinally polarized electrons on a 34.4 cm long liquid hydrogen target at Jefferson Lab. The results of the experiment's commissioning run, constituting approximately 4% of the data collected in the experiment, are reported here. From these initial results, the measured asymmetry is A(ep)=-279±35 (stat) ± 31 (syst) ppb, which is the smallest and most precise asymmetry ever measured in ep scattering. The small Q(2) of this experiment has made possible the first determination of the weak charge of the proton Q(W)(p) by incorporating earlier parity-violating electron scattering (PVES) data at higher Q(2) to constrain hadronic corrections. The value of Q(W)(p) obtained in this way is Q(W)(p)(PVES)=0.064±0.012, which is in good agreement with the standard model prediction of Q(W)(p)(SM)=0.0710±0.0007. When this result is further combined with the Cs atomic parity violation (APV) measurement, significant constraints on the weak charges of the up and down quarks can also be extracted. That PVES+APV analysis reveals the neutron's weak charge to be Q(W)(n)(PVES+APV)=-0.975±0.010.

Probing the high momentum component of the deuteron at high Q2.

The (2)H(e,e'p)n cross section at a momentum transfer of 3.5 (GeV/c)(2) was measured over a kinematical range that made it possible to study this reaction for a set of fixed missing momenta as a function of the neutron recoil angle θ(nq) and to extract missing momentum distributions for fixed values of θ(nq) up to 0.55 GeV/c. In the region of 35°≤θ(nq)≤45° recent calculations, which predict that final-state interactions are small, agree reasonably well with the experimental data. Therefore, these experimental reduced cross sections provide direct access to the high momentum component of the deuteron momentum distribution in exclusive deuteron electrodisintegration.

Transverse beam spin asymmetries in forward-angle elastic electron-proton scattering.

We have measured the beam-normal single-spin asymmetry in elastic scattering of transversely polarized 3 GeV electrons from unpolarized protons at Q2=0.15, 0.25 (GeV/c)2. The results are inconsistent with calculations solely using the elastic nucleon intermediate state and generally agree with calculations with significant inelastic hadronic intermediate state contributions. A(n) provides a direct probe of the imaginary component of the 2gamma exchange amplitude, the complete description of which is important in the interpretation of data from precision electron-scattering experiments.

Precision measurements of the nucleon strange form factors at Q2 approximately 0.1 GeV2.

We report new measurements of the parity-violating asymmetry A(PV) in elastic scattering of 3 GeV electrons off hydrogen and 4He targets with approximately 6.0 degrees . The 4He result is A(PV)=(+6.40+/-0.23(stat)+/-0.12(syst))x10(-6). The hydrogen result is A(PV)=(-1.58+/-0.12(stat)+/-0.04(syst))x10(-6). These results significantly improve constraints on the electric and magnetic strange form factors G(E)(s) and G(M)(s). We extract G(E)(s)=0.002+/-0.014+/-0.007 at =0.077 GeV2, and G(E)(s)+0.09G(M)(s)=0.007+/-0.011+/-0.006 at =0.109 GeV2, providing new limits on the role of strange quarks in the nucleon charge and magnetization distributions.

Noise-stabilized random attractor.

A two-dimensional flow model is introduced with deterministic behavior consisting of bursts that become successively larger, with longer interburst time intervals between them. The system is symmetric in one variable and there are bursts on either side of , separated by the presence of an invariant manifold at . In the presence of arbitrarily small additive noise in the direction, the successive bursts have bounded amplitudes and interburst intervals. This system with noise is proposed as a model for edge-localized modes in tokamaks. With noise, the bursts can switch from positive to negative and vice versa. The probability distribution of burst heights and interburst periods is studied, as is the dependence of the statistics on the noise variance. The modification of this behavior as the symmetry in is broken is studied, showing qualitatively similar behavior if the symmetry breaking is small enough. Experimental observations of a nonlinear circuit governed by the same equations are presented, showing good agreement.

Parity-violating electron scattering from 4He and the strange electric form factor of the nucleon.

We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from 4He at an average scattering angle = 5.7 degrees and a four-momentum transfer Q2 = 0.091 GeV2 . From these data, for the first time, the strange electric form factor of the nucleon G(E)s can be isolated. The measured asymmetry of A(PV) = (6.72 +/- 0.84(stat) +/- 0.21(syst) x 10(-6) yields a value of G(E)s = -0.038 +/- 0.042(stat) +/- 0.010(syst), consistent with zero.

Q2 dependence of the neutron spin structure function g2(n) at low Q2.

We present the first measurement of the Q2 dependence of the neutron spin structure function g2(n) at five kinematic points covering 0.57 (GeV/c)2 < or = Q2 < or = 1.34 (GeV/c)2 at x approximately = 0.2. Though the naive quark-parton model predicts g2 = 0, nonzero values occur in more realistic models of the nucleon which include quark-gluon correlations, finite quark masses, or orbital angular momentum. When scattering from a noninteracting quark, g2(n) can be predicted using next-to-leading order fits to world data for g1(n). Deviations from this prediction provide an opportunity to examine QCD dynamics in nucleon structure. Our results show a positive deviation from this prediction at lower Q2, indicating that contributions such as quark-gluon interactions may be important. Precision data obtained for g1(n) are consistent with next-to-leading order fits to world data.

Strange-quark contributions to parity-violating asymmetries in the forward g0 electron-proton scattering experiment.

We have measured parity-violating asymmetries in elastic electron-proton scattering over the range of momentum transfers 0.12 < or =Q2 < or =1.0 GeV2. These asymmetries, arising from interference of the electromagnetic and neutral weak interactions, are sensitive to strange-quark contributions to the currents of the proton. The measurements were made at Jefferson Laboratory using a toroidal spectrometer to detect the recoiling protons from a liquid hydrogen target. The results indicate nonzero, Q2 dependent, strange-quark contributions and provide new information beyond that obtained in previous experiments.

Quasielastic 3He(e,e'p)2H reaction at Q2 = 1.5 GeV2 for recoil momenta up to 1 GeV/c.

We have studied the quasielastic 3He(e,e(')p)2H reaction in perpendicular coplanar kinematics, with the energy and the momentum transferred by the electron fixed at 840 MeV and 1502 MeV/c, respectively. The 3He(e,e(')p)2H cross section was measured for missing momenta up to 1000 MeV/c, while the A(TL) asymmetry was extracted for missing momenta up to 660 MeV/c. For missing momenta up to 150 MeV/c, the cross section is described by variational calculations using modern 3He wave functions. For missing momenta from 150 to 750 MeV/c, strong final-state interaction effects are observed. Near 1000 MeV/c, the experimental cross section is more than an order of magnitude larger than predicted by available theories. The A(TL) asymmetry displays characteristic features of broken factorization with a structure that is similar to that generated by available models.

Measurement of the 3He(e,e'p)pn reaction at high missing energies and momenta.

Results of the Jefferson Lab Hall A quasielastic 3He(e,e'p)pn measurements are presented. These measurements were performed at fixed transferred momentum and energy, q=1502 MeV/c and omega=840 MeV, respectively, for missing momenta p(m) up to 1 GeV/c and missing energies in the continuum region, up to pion threshold; this kinematic coverage is much more extensive than that of any previous experiment. The cross section data are presented along with the effective momentum density distribution and compared to theoretical models.

Measurement of the generalized forward spin polarizabilities of the neutron.

The generalized forward spin polarizabilities gamma(0) and delta(LT) of the neutron have been extracted for the first time in a Q2 range from 0.1 to 0.9 GeV2. Since gamma(0) is sensitive to nucleon resonances and delta(LT) is insensitive to the Delta resonance, it is expected that the pair of forward spin polarizabilities should provide benchmark tests of the current understanding of the chiral dynamics of QCD. The new results on delta(LT) show significant disagreement with chiral perturbation theory calculations, while the data for gamma(0) at low Q2 are in good agreement with a next-to-leading-order relativistic baryon chiral perturbation theory calculation. The data show good agreement with the phenomenological MAID model.

Measurement of the generalized polarizabilities of the proton in virtual Compton scattering at Q2=0.92 and 1.76 GeV2.

We report a virtual Compton scattering study of the proton at low c.m. energies. We have determined the structure functions P(LL)-P(TT)/epsilon and P(LT), and the electric and magnetic generalized polarizabilities (GPs) alpha(E)(Q2) and beta(M)(Q2) at momentum transfer Q(2)=0.92 and 1.76 GeV2. The electric GP shows a strong falloff with Q2, and its global behavior does not follow a simple dipole form. The magnetic GP shows a rise and then a falloff; this can be interpreted as the dominance of a long-distance diamagnetic pion cloud at low Q2, compensated at higher Q2 by a paramagnetic contribution from piN intermediate states.

Precision measurement of the neutron spin asymmetryA(n)(1) and spin-flavor decomposition in the valence quark region.

We have measured the neutron spin asymmetry A(n)(1) with high precision at three kinematics in the deep inelastic region at x=0.33, 0.47, and 0.60, and Q(2)=2.7, 3.5, and 4.8 (GeV/c)(2), respectively. Our results unambiguously show, for the first time, that A(n)(1) crosses zero around x=0.47 and becomes significantly positive at x=0.60. Combined with the world proton data, polarized quark distributions were extracted. Our results, in general, agree with relativistic constituent quark models and with perturbative quantum chromodynamics (PQCD) analyses based on the earlier data. However they deviate from PQCD predictions based on hadron helicity conservation.

Measurements of GnE/GnM from the 2H(e-->,en-->)1H Reaction to Q2=1.45 (GeV/c)2.

We report new measurements of the ratio of the electric form factor to the magnetic form factor of the neutron, G(n)(E)/G(n)(M), obtained via recoil polarimetry from the quasielastic 2H(e-->,e(')n-->)1H reaction at Q2 values of 0.45, 1.13, and 1.45 (GeV/c)(2) with relative statistical uncertainties of 7.6% and 8.4% at the two higher Q2 points, which points have never been achieved in polarization measurements.

Polarization transfer in the 4He(e-->,e'p-->)3H reaction up to Q2=2.6 (GeV/c)2.

We have measured the proton recoil polarization in the 4He(e-->,e(')p-->)4H reaction at Q(2)=0.5, 1.0, 1.6, and 2.6 (GeV/c)(2). The measured ratio of polarization transfer coefficients differs from a fully relativistic calculation, favoring the inclusion of a medium modification of the proton form factors predicted by a quark-meson coupling model. In addition, the measured induced polarizations agree reasonably well with the fully relativistic calculation indicating that the treatment of final-state interactions is under control.

Estimation of entropies and dimensions by nonlinear symbolic time series analysis.

Symbolic nonlinear time series analysis methods have the potential for analyzing nonlinear data efficiently with low sensitivity to noise. In symbolic nonlinear time series analysis a time series for a fixed delay is partitioned into a small number (called the alphabet size) of cells labeled by symbols, creating a symbolic time series. Symbolic methods involve computing the statistics of words made from the symbolic time series. Specifically, the Shannon entropy of the distribution of possible words for a range of word lengths is computed. The rate of increase of the entropy with word length is the metric (Kolmogorov-Sinai) entropy. Methods of computing the metric entropy for flows as well as for maps are shown. A method of computing the information dimension appropriate to symbolic analysis is proposed. In terms of this formulation, the information dimension is determined by the scaling of entropy as alphabet size is modestly increased, using the information obtained from large word length. We discuss the role of sampling time and the issue of using these methods when there may be no generating partition.

2H(e,e(')p)n reaction at high recoil momenta.

The 2H(e,e(')p)n cross section was measured in Hall A of the Thomas Jefferson National Accelerator Facility near the top of the quasielastic peak (x(Bj)=0.964) at a four-momentum transfer squared, Q(2)=0.665 (GeV/c) (2) (omega=0.368 GeV, W=2.057 GeV), and for recoil momenta up to 550 MeV/c. The measured cross section deviates by 1-2sigma from a state-of-the-art calculation at low recoil momenta. At high recoil momenta the cross section is well described by the same calculation; however, in this region, final-state interactions and interaction currents are predicted to be large, and alternative choices of nucleon-nucleon potential and nucleon current operator may result in significant spread in the calculations.

Precision measurement of the spin-dependent asymmetry in the threshold region of 3He(e, e').

We present the first precision measurement of the spin-dependent asymmetry in the threshold region of 3He(e,e') at Q2 values of 0.1 and 0.2 (GeV/c)2. The agreement between the data and nonrelativistic Faddeev calculations which include both final-state interactions and meson-exchange current effects is very good at Q2 = 0.1 (GeV/c)2, while a small discrepancy at Q2 = 0.2 (GeV/c)2 is observed.