Aufbau des GDH-Experiments und Messung der Helizitätsabhängigkeit von gamma p p pi + pi- von der Schwelle bis 800 MeV

Das Experiment zur Überprüfung der Gerasimov-Drell-Hearn(GDH)-Summenregel am Mainzer Mikrotron diente zur Messunghelizitätsabhängiger Eigenschaften der Photoproduktion amProton. Hierbei konnten neben den totalen Photoabsorptionswirkungsquerschnitten auch Querschnitte partieller Kanäle der Einpion-, Zweipion- und Eta-Produktion bestimmt werden. Für die möglichen Doppel-Pion-Reaktionen sind zur Zeit nur wenig Information vorhanden. Daher sind die Reaktionsmechanismen der Doppel-Pion-Photoproduktion weitgehend noch unverstanden. Aus diesem Grund ist die Untersuchung weiterer Observablenerforderlich. Die Helizitätsabhängigkeit stellt eine solcheneue Observable dar und kann dadurch gemessen werden, daßein zirkular polarisiertes Photon mit einem longitudinalpolarisierten Nukleon wechselwirkt. Der Photonspin beträgt1 und der Fermionenspin des Nukleons beträgt 1/2.Die Spins koppeln zu 3/2 und 1/2. Dies liefert diehelizitätsabhängigen Wirkungsquerschnitte.Diese Dissertation beschreibt den Aufbau des Mainzer GDH-Experiments und die technische Realisation der Messung helizitätsabhängiger Photoabsorptionswirkungsquerschnitte. Die Helizitätsabhängigkeit der doppelt geladenen Doppel-Pion-Photoproduktion am Proton wurde anhand der gemessenen Daten untersucht. Diese Reaktion ist ein Zweistufenprozeß, wobei das angeregte Nukleon resonant oder nicht-resonant in die Endzustandsteilchen zerfällt. Durch die helizitätsabhängigen Daten wurden Freiheitsgradein der Doppel-Pion-Photoproduktion eingeschränkt, wodurch eine Verbesserung der Modelle der Gent-Mainz- und der Valencia-Gruppe ermöglicht wurde. Die im Rahmen dieser Arbeit ermittelten Daten haben zusätzlich eine Motivation für weitere Interpretationsansätze durch die genanntenTheoriegruppen geschaffen.

Measurement of the helicity dependence of deuteron photodisintegration for photon energies below 450 MeV

In 1998 a pilot experiment was carried out to study the helicity dependence of photoreaction cross sections using circularly polarized real photons on longitudinally polarized deuterons in a deuterated butanol target. The knowledge of these cross sections is required to test the validity of the Gerasimov-Drell-Hearn sum rule on the deuteron and the neutron. The focus of this thesis is on the results for the differential and total cross sections for the photodisintegration reaction for various photon energies in the range from 200 to 450 MeV using data taken with the detector system DAPHNE. The current understanding of the NN interaction as represented by the calculations by M. Schwamb could be confirmed within the given uncertainties. In addition, the detector DAPHNE has been prepared for the main experiment in 2003. The according work is presented together with results of the quality-test measurements of the renewed detector components.

Study of the helicity dependence of single pion photoproduction on the deuteron

Der erste experimentelle Test der GDH-Summenregel für das Proton wurde 1998 am MAMI-Beschleuniger der Universität Mainz durchgeführt. Ferner wurde ein Pilot-Experiment mit einem polarisierten Deuteron-Target vorgenommen. Dieselbe Kollaboration führte 2003 ein auf das Deuteron ausgerichtetes Experiment durch mit der Absicht, die GDH-Summenregel für das Neutron zu untersuchen. Der in beiden Experimenten verwendete Aufbau erlaubt nicht nur die Messung des totalen Wirkungsquerschnitts, sondern auch gleichzeitig einzelne Teilreaktionen zu studieren. In dieser Arbeit werden die Daten des Deuteron-Pilot-Experiments von 1998 analysiert. Desweiteren wird eine Studie der Helizitätsabhängigkeit der differenziellen Wirkungsquerschnitte für drei Pion-Photoproduktionskanäle des Deuterons in der oberen Hälfte der Delta-Resonanz präsentiert. Diese Ergebnisse werden mit einem theoretischen Modell verglichen. Dabei wurde eine hinreichend gute Übereinstimmung für die unpolarisierten Reaktionen gefunden, während für die polarisierten Kanäle kleinere Diskrepanzen beobachtet wurden. Der Targetpolarisationsgrad ist einer der relevanten Parameter, der für eine absolute Normalisierung der Wirkungsquerschnitte notwendig ist. Die Analyse dieses Parameters für die 2003er Daten wird in der vorliegenden Arbeit vorgestellt. Zur Zeit ist in Mainz ein Frozen-Spin-Target im Bau. Es wird als Target für polarisierte Protonen oder polarisierte Deuteronen für zukünftige Experimente mit dem Crystal Ball zur Verfügung stehen. Die Vorbereitungen der verschiedenen Subsysteme dieses Aufbaus stellten einen wichtigen Teil dieser Arbeit dar. Die fundamentalen Grundlagen der Methode und deren technische Umsetzung, sowie der momentane Status der Aufbauarbeiten am Target werden im Detail präsentiert.

Investigation of the dipole response of nickel isotopes in the presence of a high-frequency electromagnetic field

The electric dipole response of neutron-rich nickel isotopes has been investigated using the LAND setup at GSI in Darmstadt (Germany). Relativistic secondary beams of 56−57Ni and 67−72Ni at approximately 500 AMeV have been generated using projectile fragmentation of stable ions on a 4 g/cm2 Be target and subsequent separation in the magnetic dipole fields of the FRagment Separator (FRS). After reaching the LAND setup in Cave C, the radioactive ions were excited electromagnetically in the electric field of a Pb target. The decay products have been measured in inverse kinematics using various detectors. Neutron-rich 67−69Ni isotopes decay by the emission of neutrons, which are detected in the LAND detector. The present analysis concentrates on the (gamma,n) and (gamma,2n) channels in these nuclei, since the proton and three-neutron thresholds are unlikely to be reached considering the virtual photon spectrum for nickel ions at 500 AMeV. A measurement of the stable 58Ni isotope is used as a benchmark to check the accuracy of the present results with previously published data. The measured (gamma,n) and (gamma,np) channels are compared with an inclusive photoneutron measurement by Fultz and coworkers, which are consistent within the respective errors. The measured excitation energy distributions of 67−69Ni contain a large portion of the Giant Dipole Resonance (GDR) strength predicted by the Thomas-Reiche-Kuhn energy-weighted sum rule, as well as a significant amount of low-lying E1 strength, that cannot be attributed to the GDR alone. The GDR distribution parameters are calculated using well-established semi-empirical systematic models, providing the peak energies and widths. The GDR strength is extracted from the chi-square minimization of the model GDR to the measured data of the (gamma,2n) channel, thereby excluding any influence of eventual low-lying strength. The subtraction of the obtained GDR distribution from the total measured E1 strength provides the low-lying E1 strength distribution, which is attributed to the Pygmy Dipole Resonance (PDR). The extraction of the peak energy, width and strength is performed using a Gaussian function. The minimization of trial Gaussian distributions to the data does not converge towards a sharp minimum. Therefore, the results are presented by a chi-square distribution as a function of all three Gaussian parameters. Various predictions of PDR distributions exist, as well as a recent measurement of the 68Ni pygmy dipole-resonance obtained by virtual photon scattering, to which the present pygmy dipole-resonance distribution is also compared.

First doubly polarised photoproduction on 3 He at the photon beam of MAMI

Im Juli 2009 wurde am Mainzer Mikrotron (MAMI) erstmal ein Experiment durchgeführt, bei dem ein polarisiertes 3He Target mit Photonen im Energiebereich von 200 bis 800 MeV untersucht wurde. Das Ziel dieses Experiments war die Überprüfung der Gerasimov-Drell-Hearn Summenregel am Neutron. Die Verwendung der Messdaten welche mit dem polarisierten 3He Target gewonnen wurden, geben - im Vergleich mit den bereits existieren Daten vom Deuteron - aufgrund der Spin-Struktur des 3He einen komplementären und direkteren Zugang zum Neutron. Die Messung des totalen helizitätsabhängigen Photoabsorptions-Wirkungsquerschnitts wurde mittels eines energiemarkierten Strahls von zirkular polarisierten Photonen, welcher auf das longitudinal polarisierte 3He Target trifft, durchgeführt. Als Produktdetektoren kamen der Crystal Ball (4π Raumabdeckung), TAPS (als ”Vorwärtswand”) sowie ein Schwellen-Cherenkov-Detektor (online Veto zur Reduktion von elektromagnetischen Ereignissen) zum Einsatz. Planung und Aufbau der verschiedenen komponenten Teile des 3He Experimentaufbaus war ein entscheidender Teil dieser Dissertation und wird detailliert in der vorliegenden Arbeit beschrieben. Das Detektorsystem als auch die Analyse-Methoden wurden durch die Messung des unpolarisierten, totalen und inklusiven Photoabsoprtions-Wirkungsquerschnitts an flüssigem Wasserstoff getestet. Hierbei zeigten die Ergebnisse eine gute Übereinstimmung mit bereits zuvor publizierten Daten. Vorläufige Ergebnisse des unpolarisierten totalen Photoabsorptions-Wirkungsquerschnitts sowie der helizitätsabhängige Unterschied zwischen Photoabsorptions-Wirkungsquerschnitten an 3He im Vergleich zu verschiedenen theoretischen Modellen werden vorgestellt.

OPTIMAL SHAPE IN ELECTROMAGNETIC SCATTERING BY SMALL ASPHERICAL PARTICLES

We consider the question of optimal shapes, e.g., those causing minimal extinction among all shapes of equal volume. Guided by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (electrostatics) approximation, seeking to disentangle electric and geometric contributions. To that end, we survey the literature on shape functionals and focus on ellipsoids, giving a simple proof of spherical optimality for the coated ellipsoidal particle. Monotonic increase with asphericity in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections is also shown. Additional physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose connecting low and high frequency regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions of randomly oriented aspherical particles wash out the resonances for intermediate size parameters. This proposal is further supported by the sum rule for integrated extinction.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

A Measurement of the Proton Structure Function g2p at Low Q2

Experiments at Jefferson Lab have been conducted to extract the nucleon spin-dependent structure functions over a wide kinematic range. Higher moments of these quantities provide tests of QCD sum rules and predictions of chiral perturbation theory ($\chi$PT). While precise measurements of $g_{1}^n$, $g_{2}^n$, and $g_1^p$ have been extensively performed, the data of $g_2^p$ remain scarce. Discrepancies were found between existing data related to $g_2$ and theoretical predictions. Results on the proton at large $Q^2$ show a significant deviation from the Burkhardt-Cottingham sum rule, while results for the neutron generally follow this sum rule. The next-to-leading order $\chi$PT calculations exhibit discrepancy with data on the longitudinal-transverse polarizability $\delta_{LT}^n$. Further measurements of the proton spin structure function $g_2^p$ are desired to understand these discrepancies.

Experiment E08-027 (g2p) was conducted at Jefferson Lab in experimental Hall A in 2012. Inclusive measurements were performed with polarized electron beam and a polarized ammonia target to obtain the proton spin-dependent structure function $g_2^p$ at low Q$^2$ region (0.02$<$Q$^2$$<$0.2 GeV$^2$) for the first time. The results can be used to test the Burkhardt-Cottingham sum rule, and also allow us to extract the longitudinal-transverse spin polarizability of the proton, which will provide a benchmark test of $\chi$PT calculations. This thesis will present and discuss the very preliminary results of the transverse asymmetry and the spin-dependent structure functions $g_1^p$ and $g_2^p$ from the data analysis of the g2p experiment .

A Reliable Basis for Approximate Association Rules

For most of the work done in developing association rule mining, the primary focus has been on the efficiency of the approach and to a lesser extent the quality of the derived rules has been emphasized. Often for a dataset, a huge number of rules can be derived, but many of them can be redundant to other rules and thus are useless in practice. The extremely large number of rules makes it difficult for the end users to comprehend and therefore effectively use the discovered rules and thus significantly reduces the effectiveness of rule mining algorithms. If the extracted knowledge can’t be effectively used in solving real world problems, the effort of extracting the knowledge is worth little. This is a serious problem but not yet solved satisfactorily. In this paper, we propose a concise representation called Reliable Approximate basis for representing non-redundant approximate association rules. We prove that the redundancy elimination based on the proposed basis does not reduce the belief to the extracted rules. We also prove that all approximate association rules can be deduced from the Reliable Approximate basis. Therefore the basis is a lossless representation of approximate association rules.

Approximate multipole coefficients of RF ion traps as functions of aperture size

In this study we present approximate analytical expressions for estimating the variation in multipole expansion coefficients as a function of the size of the apertures in the electrodes in axially symmetric (3D) and two-dimensional (2D) ion trap ion traps. Following the approach adopted in our earlier studies which focused on the role of apertures to fields within the traps, here too, the analytical expression we develop is a sum of two terms, A(n,noAperiure), the multipole expansion coefficient for a trap with no apertures and A(n,dueToAperture), the multipole expansion coefficient contributed by the aperture. A(n,noAperture) has been obtained numerically and A(n,dueToAperture) is obtained from the n th derivative of the potential within the trap. The expressions derived have been tested on two 3D geometries and two 2D geometries. These include the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT) for 3D geometries and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for the 2D geometries. Multipole expansion coefficients A(2) to A(12), estimated by our analytical expressions, were compared with the values obtained numerically (using the boundary element method) for aperture sizes varying up to 50% of the trap dimension. In all the plots presented, it is observed that our analytical expression for the variation of multipole expansion coefficients versus aperture size closely follows the trend of the numerical evaluations for the range of aperture sizes considered. The maximum relative percentage errors, which provide an estimate of the deviation of our values from those obtained numerically for each multipole expansion coefficient, are seen to be largely in the range of 10-15%. The leading multipole expansion coefficient, A(2), however, is seen to be estimated very well by our expressions, with most values being within 1% of the numerically determined values, with larger deviations seen for the QIT and the LIT for large aperture sizes. (C) 2010 Elsevier B.V. All rights reserved.

A Modified Sum-Product Algorithm over Graphs with Isolated Short Cycles

We investigate into the limitations of the sum-product algorithm in the probability domain over graphs with isolated short cycles. By considering the statistical dependency of messages passed in a cycle of length 4, we modify the update equations for the beliefs at the variable and check nodes. We highlight an approximate log domain algebra for the modified variable node update to ensure numerical stability. At higher signal-to-noise ratios (SNR), the performance of decoding over graphs with isolated short cycles using the modified algorithm is improved compared to the original message passing algorithm (MPA).

Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ``energy-like measure'' in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics problems, variants of the trapezoidal rule that incorporate ``high-frequency'' dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid finite element framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacement-based and hybrid approaches against analytical solutions.

Studies of the representation of interatomic distances in molecules and crystal as sum of atomic radii

The electron diffraction investigation of the following compounds has been carried out: sulfur, sulfur nitride, realgar, arsenic trisulfide, spiropentane, dimethyltrisulfide, cis and trans lewisite, methylal, and ethylene glycol.

The crystal structures of the following salts have been determined by x-ray diffraction: silver molybdateand hydrazinium dichloride.

Suggested revisions of the covalent radii for B, Si, P, Ge, As, Sn, Sb, and Pb have been made, and values for the covalent radii of Al, Ga, In, Ti, and Bi have been proposed.

The Schomaker-Stevenson revision of the additivity rule for single covalent bond distances has been used in conjunction with the revised radii. Agreement with experiment is in general better with the revised radii than with the former radii and additivity.

The principle of ionic bond character in addition to that present in a normal covalent bond has been applied to the observed structures of numerous molecules. It leads to a method of interpretation which is at least as consistent as the theory of multiple bond formation.

The revision of the additivity rule has been extended to double bonds. An encouraging beginning along these lines has been made, but additional experimental data are needed for clarification.

Approximate credal network updating by linear programming with applications to decision making

Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to accurate inferences. A transformation is also derived to reduce decision making in credal networks based on the maximality criterion to updating. The decision task is proved to have the same complexity of standard inference, being NPPP-complete for general credal nets and NP-complete for polytrees. Similar results are derived for the E-admissibility criterion. Numerical experiments confirm a good performance of the method.