<p>This thesis discusses the process of extracting the longitudinal asymmetry, $A_L</p><p>{W\pm}$, describing $W\rightarrow\mu$ production in forward kinematic regimes. This asymmetry is used to constrain our understanding of the polarized parton distribution functions characterizing $\bar{u}$ and $\bar{d}$ sea quarks in the proton. This asymmetry will be used to constrain the overall contribution of the sea-quarks to the total proton spin. The asymmetry is evaluated over the pseudorapidity range of the PHENIX Muon Arms, $2.1 < |\eta|2.6$, for longitudinally polarized proton-proton collisions at 510 GeV $\sqrt{s}$. In particular, I will discuss the statistical methods used to characterize real muonic $W$ decays and the various background processes is presented, including a discussion of likelihood event selection and the Extended Unbinned Maximum Likelihood fit. These statistical methods serve estimate the yields of $W$ muonic decays, which are used to calculate the longitudinal asymmetry.

The sudden loss of the plasma magnetic confinement, known as disruption, is one of the major issue in a nuclear fusion machine as JET (Joint European Torus), Disruptions pose very serious problems to the safety of the machine. The energy stored in the plasma is released to the machine structure in few milliseconds resulting in forces that at JET reach several Mega Newtons. The problem is even more severe in the nuclear fusion power station where the forces are in the order of one hundred Mega Newtons. The events that occur during a disruption are still not well understood even if some mechanisms that can lead to a disruption have been identified and can be used to predict them. Unfortunately it is always a combination of these events that generates a disruption and therefore it is not possible to use simple algorithms to predict it. This thesis analyses the possibility of using neural network algorithms to predict plasma disruptions in real time. This involves the determination of plasma parameters every few milliseconds. A plasma boundary reconstruction algorithm, XLOC, has been developed in collaboration with Dr. D. Ollrien and Dr. J. Ellis capable of determining the plasma wall/distance every 2 milliseconds. The XLOC output has been used to develop a multilayer perceptron network to determine plasma parameters as ?i and q? with which a machine operational space has been experimentally defined. If the limits of this operational space are breached the disruption probability increases considerably. Another approach for prediction disruptions is to use neural network classification methods to define the JET operational space. Two methods have been studied. The first method uses a multilayer perceptron network with softmax activation function for the output layer. This method can be used for classifying the input patterns in various classes. In this case the plasma input patterns have been divided between disrupting and safe patterns, giving the possibility of assigning a disruption probability to every plasma input pattern. The second method determines the novelty of an input pattern by calculating the probability density distribution of successful plasma patterns that have been run at JET. The density distribution is represented as a mixture distribution, and its parameters arc determined using the Expectation-Maximisation method. If the dataset, used to determine the distribution parameters, covers sufficiently well the machine operational space. Then, the patterns flagged as novel can be regarded as patterns belonging to a disrupting plasma. Together with these methods, a network has been designed to predict the vertical forces, that a disruption can cause, in order to avoid that too dangerous plasma configurations are run. This network can be run before the pulse using the pre-programmed plasma configuration or on line becoming a tool that allows to stop dangerous plasma configuration. All these methods have been implemented in real time on a dual Pentium Pro based machine. The Disruption Prediction and Prevention System has shown that internal plasma parameters can be determined on-line with a good accuracy. Also the disruption detection algorithms showed promising results considering the fact that JET is an experimental machine where always new plasma configurations are tested trying to improve its performances.

I report the results of three investigations in the fermion Dyson-Schwinger Equations (DSE's) of four-dimensional quantum electrodynamics (QED$\sb4$) and quantum chromodynamics (QCD), using different Ansatze for the boson propagator and the fermion-boson vertex. / The first study compared the effects of four vertex forms (bare $\gamma\sp{\nu}$, renormalized $\gamma\sp{\nu}$, minimal Ball-Chiu (1) and Curtis-Pennington (2)) in the quark propagator DSE, with an infrared-singular gluon propagator, with several forms for the nonperturbative IR behavior of the effective gluon coupling. It was found that, generally, the more naive the vertex Ansatz was, the smaller was the degree of dynamical chiral symmetry breaking (DCSB). Although no vertex appeared to lead to a completely satisfactory relationship between the scale parameter $\Lambda\sb{\sc QCD}$, pion decay constant $f\sb{\pi}$, and quark condensate, all quantities could be found within two standard deviations of their accepted values. / The second study considers an IR-vanishing gluon propagator of the form / In the course of this study, techniques were developed to analyze the chiral phase transition, and to test a Euclidean propagator for confinement. These are applicable to propagators developed under any models, and are arguably of greater importance than the results for the particular models studied. / Finally I give results from an ongoing study of subtractive renormalization in massive strong-coupling quenched QED$\sb4$. The procedure is straightforward to implement and numerically stable. This is the first study in which this technique is used; it will be useful in future DSE studies, whenever renormalization is required in numerical work. / Source: Dissertation Abstracts International, Volume: 55-09, Section: B, page: 3950. / Co-Major Professors: Anthony G. Williams; Donald Robson. / Thesis (Ph.D.)--The Florida State University, 1994.

We performed Monte Carlo simulations of pure SU(3) lattice gauge theory using a Hamiltonian having a known vacuum state. A vacuum fixing term which vanishes in the classical continuum limit was added to the Kogut-Susskind Hamiltonian. We variationally estimate glueball mass spectra over a gauge invariant basis and extract the string tension from the area law behavior of these states. We show that in the continuum limit, the vacuum expectation value of the vacuum fixing term does not vanish. In (2+1) dimensions, we calculated string tension and the $J\sp{\rm PC} = 0\sp{++}$ spectrum using a basis consisting of square loops having up to 7 links to a side. Asymptotic scaling is seen in both the string tension and the two lowest-lying 0$\sp{++}$ glueball states consistent with published analytic results. String tension in (3+1) dimensions was calculated using square loops up to 7 x 7 links and yields an exponential scaling window having a different decay constant than the perturbative QCD prediction. Using a basis of square, rectangular, twisted, and bent loops up to 1 x 2 in size, we find a 0$\sp{++}$ state with the same asymptotic scaling behavior as the string tension over a large range of the lattice coupling. A second basis consisting of square, planar loops up to 7 x 7 links, yields ratio scaling for the lowest 0$\sp{++}$ and 2$\sp{++}$ eigenstates but not asymptotic scaling. We conclude that the complicated loops are required to accurately represent (3+1)-d glueballs. Mass ratios are in agreement with the alternative Lagrangian approach. / Source: Dissertation Abstracts International, Volume: 54-07, Section: B, page: 3676. / Major Professor: Donald Robson. / Thesis (Ph.D.)--The Florida State University, 1993.

A model has been constructed of the interaction between protons and applied to the calculation of spin-dependent elastic scattering parameters over a range of beam momenta from 3 to 24 GeV/c. The interaction uses a one boson exchange potential, augmented by a zero-range core, and a zero-range imaginary potential to account for inelastic channels. The quark structure of the proton is taken into account by means of transition form factors modifying the meson exchange potentials. These form factors were derived from the assumption that massless quarks are bound into protons by a linear confining potential which incorporates chiral symmetry. The scattering equation was a new continuum form of the instantaneous Bethe-Salpeter Equation, which contains some of the effects of negative energy intermediate states. / The model provides excellent agreement with experimental measurements of the unpolarized differential cross-section, and reproduces the qualitative features of the transverse asymmetry and spin correlation. The absorptive potential is found to dominate the real potential by two orders of magnitude at 24 GeV/c. The lowest partial waves were found to be almost completely absorbed. This suggests that perturbative quantum chromodynamics does not apply to elastic scattering at the length scales examined here, since absorptive effects prevent the quarks from approaching to appropriately small separations. / Source: Dissertation Abstracts International, Volume: 50-12, Section: B, page: 5700. / Major Professor: Donald Robson. / Thesis (Ph.D.)--The Florida State University, 1989.

We have determined the branching ratio for single charge exchange using stopped negative pions on $\sp{115}$In, $\sp{45}$Sc, $\sp{32}$S, $\sp{31}$P, $\sp{27}$Al, $CH\sb2$. The experiment was done at the LEP channel at LAMPF. Negative pions at $50MeV$ were slowed down in a graphite degrader and brought to rest in the target nuclei. The neutral pions that comes from single charge exchange, decays into two gamma rays, which are then detected using the LAMPF $\pi\sp0$ spectrometer. The measured branching ratios are discussed within the framework of the simple shell model. The discussion of the observed branching ratios require consideration of angular momentum, parity, and energy. These results will allow theorists to determine the strength of the isovector pion-nucleon interaction in nuclei. This information can possibly be used to determine the origin of the large repulsion of the s-wave isoscalar pion-nucleon interaction in nuclei. / Source: Dissertation Abstracts International, Volume: 51-02, Section: B, page: 0811. / Major Professor: Hans S. Plendl. / Thesis (Ph.D.)--The Florida State University, 1989.

<p> Fusion in neutron-rich environments is presently a topic of considerable interest. For example, the optical emission spectrum from the neutron star merger GRB170817A clearly establishes this neutron-rich environment as an important nucleosynthetic site. Fusion of neutron-rich light nuclei in the outer crust of an accreting neutron star has also been proposed as responsible for triggering X-ray super-bursts. The underlying hypothesis in this proposition is that the fusion of neutron-rich nuclei is enhanced as compared to stable nuclei. A good approach to understand how fusion proceeds in neutron-rich nuclei is to measure the fusion excitation function for an isotopic chain of nuclei. Modern radioactive beam facilities provide the opportunity to systematically address this question. An experimental program has been established to measure the fusion excitation function for light and mid-mass neutron-rich nuclei using low-intensity radioactive beams. The technique was initially demonstrated by measuring the fusion excitation functions for <i>18</i>O and ¹⁹O nuclei incident on a ¹²C target. The beam of ¹⁹O ions was produced by the <i>18</i>O(d,p) reaction with an intensity of 2-4 x 10⁴ p/s at Florida State University. Evaporation residues resulting from the de-excitation of the fusion product were distinguished by measuring their energy and time-of-flight. To explore mid-mass neutron-rich nuclei much further from stability, the fusion excitation functions for ^39,47K + ²⁸Si were measured using the ReA3 reaccelerator facility at the National Superconducting Cyclotron Laboratory at Michigan State University. Incident ions were identified on a particle-by-particle basis by &Delta;E-TOF just upstream of the target. Fusion products were directly measured and identified by the E-TOF technique with an efficiency of ~70%. The measured fusion excitation functions for both the light and mid-mass systems have been compared to various theoretical models to elucidate how structure and dynamics impact the fusion of neutron-rich nuclei.</p><p>

The Lie groups SU(3) &sub; U(3) play an important role in nuclear physics. All their representations are highest weight representations. When the representation space is symmetry adapted to the rotation group SO(3) their representations can be used to describe collective rotational motion of the nucleus. Elliott's SU(3) model and the interacting boson model exhibit a rotational spectrum if the Hamiltonian can be approximately written in terms of Casimir invariants. The electromagnetic transition rates can be approximated by the reduced matrix elements of the quadrupole tensor operator Q, which are the output of part 1 of the program. Part 2 generates the Clebsch-Gordan coefficients as well as the isoscalar factors by coupling two irreducible representations of U(3). All results are analytic, that is exact as opposed to numerical This program uses that the highest weight representations of U(3) can be realized on certain polynomial spaces, which can be endowed with a simple differentiation inner product. In order to generate the polynomial basis and to reduce the representations in the desired subgroup chain U(3) &sup; SO(3) &sup; SO(2), the elegant Cartan-Weyl theory is used. This means that the irreducible representations are generated by continued application of the lowering operators to the highest weight vector. This theory is very suitable for implementation on a computer algebra program like Macsyma. The method of combining the Cartan-Weyl theory with polynomial spaces is not particular to U(3) and can be used for representations of U(n) in any subgroup chain. However, what is possible in reality depends on the available computer power / acase@tulane.edu

Given a many-fermion system and a set of relevant physical observables that close under commutation to form a Lie algebra g* , a mean field theory is determined naturally on the algebra's dual space g* . The dual space consists of generalized density matrices, defined as the expectation of each element (or observable) in the Lie algebra. An algebraic mean field theory is a Hamiltonian dynamical system on a coadjoint orbit of the Lie group. Coadjoint orbits are even-dimensional surfaces in g* with a non-degenerate Poisson bracket defined on them. The energy function on a coadjoint orbit is determined from physical considerations. In essence, a generalized mean field theory for a Lie algebra g optimizes the predictions for the expectations of the algebra's generators. No prediction is made for observables that are not elements of the algebra. The advantages of the algebraic mean field theory, in comparison to the corresponding models based on irreducible representations, are generally lower dimensions and simplicity of analysis This generalized mean field construction is defined and applied to two paradigm cases: the dynamical symmetry models ROT(3) and SU(3) of collective rotational motion in nuclei. The eight-dimensional algebra rot(3) is generated by the angular momentum and the microscopic mass quadrupole operator. It is shown that its mean field theory describes rigid rotation. The eight-dimensional algebra su (3) is spanned by the angular momentum and the Elliott quadrupole operator. Its mean field theory is related to the cranked anisotropic oscillator. Both rotational mean field theories share many properties with the corresponding irreducible representations / acase@tulane.edu

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