Two-body photodisintegration of the deuteron at intermediate energy

We have measured the differential cross section for two-body deuteron photodisintegration at center-of-mass angles of 90°, 53° and 37° with photon energies from 1.6 Ge V to 2.8 Ge V. Additional data were taken at θ* = 37° and E_γ = 4.2 GeV. Invariant cross sections at θ* =90° and 53° appear to follow a simple scaling law predicted by constituent counting rules of perturbative QCD, while the cross section at θ* = 37° shows a slower fall-off with photon energy. Angular distributions show increasing forward peaking at higher energies. Agreement with various theoretical predictions based on pQCD and meson-exchange models is discussed.

Relativistic quark models and the current algebra

In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axial-vector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.

We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)-independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any two-quark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).

In the free-quark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m³. However, it may be possible to solve the factorized SU(2) problem with this model.

The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4-momentum, which seem unphysical.

Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.

One-dimensional models for organic magnetic materials

In the preparation of small organic paramagnets, these structures may conceptually be divided into spin-containing units (SCs) and ferromagnetic coupling units (FCs). The synthesis and direct observation of a series of hydrocarbon tetraradicals designed to test the ferromagnetic coupling ability of m-phenylene, 1,3-cyclobutane, 1,3- cyclopentane, and 2,4-adamantane (a chair 1,3-cyclohexane) using Berson TMMs and cyclobutanediyls as SCs are described. While 1,3-cyclobutane and m-phenylene are good ferromagnetic coupling units under these conditions, the ferromagnetic coupling ability of 1,3-cyclopentane is poor, and 1,3-cyclohexane is apparently an antiferromagnetic coupling unit. In addition, this is the first report of ferromagnetic coupling between the spins of localized biradical SCs.

The poor coupling of 1,3-cyclopentane has enabled a study of the variable temperature behavior of a 1,3-cyclopentane FC-based tetraradical in its triplet state. Through fitting the observed data to the usual Boltzman statistics, we have been able to determine the separation of the ground quintet and excited triplet states. From this data, we have inferred the singlet-triplet gap in 1,3-cyclopentanediyl to be 900 cal/mol, in remarkable agreement with theoretical predictions of this number.

The ability to simulate EPR spectra has been crucial to the assignments made here. A powder EPR simulation package is described that uses the Zeeman and dipolar terms to calculate powder EPR spectra for triplet and quintet states.

Methods for characterizing paramagnetic samples by SQUID magnetometry have been developed, including robust routines for data fitting and analysis. A precursor to a potentially magnetic polymer was prepared by ring-opening metathesis polymerization (ROMP), and doped samples of this polymer were studied by magnetometry. While the present results are not positive, calculations have suggested modifications in this structure which should lead to the desired behavior.

Source listings for all computer programs are given in the appendix.

Transition metal clusters supported by multinucleating ligand frameworks as models of biological active sites

This dissertation describes efforts to model biological active sites with small molecule clusters. The approach used took advantage of a multinucleating ligand to control the structure and nuclearity of the product complexes, allowing the study of many different homo- and heterometallic clusters. Chapter 2 describes the synthesis of the multinucleating hexapyridyl trialkoxy ligand used throughout this thesis and the synthesis of trinuclear first row transition metal complexes supported by this framework, with an emphasis on tricopper systems as models of biological multicopper oxidases. The magnetic susceptibility of these complexes were studied, and a linear relation was found between the Cu-O(alkoxide)-Cu angles and the antiferromagnetic coupling between copper centers. The triiron(II) and trizinc(II) complexes of the ligand were also isolated and structurally characterized.

Chapter 3 describes the synthesis of a series of heterometallic tetranuclear manganese dioxido complexes with various incorporated apical redox-inactive metal cations (M = Na⁺, Ca²⁺, Sr²⁺, Zn²⁺, Y³⁺). Chapter 4 presents the synthesis of heterometallic trimanganese(IV) tetraoxido complexes structurally related to the CaMn₃ subsite of the oxygen-evolving complex (OEC) of Photosystem II. The reduction potentials of these complexes were studied, and it was found that each isostructural series displays a linear correlation between the reduction potentials and the Lewis acidities of the incorporated redox-inactive metals. The slopes of the plotted lines for both the dioxido and tetraoxido clusters are the same, suggesting a more general relationship between the electrochemical potentials of heterometallic manganese oxido clusters and their “spectator” cations. Additionally, these studies suggest that Ca²⁺ plays a role in modulating the redox potential of the OEC for water oxidation.

Chapter 5 presents studies of the effects of the redox-inactive metals on the reactivities of the heterometallic manganese complexes discussed in Chapters 3 and 4. Oxygen atom transfer from the clusters to phosphines is studied; although the reactivity is kinetically controlled in the tetraoxido clusters, the dioxido clusters with more Lewis acidic metal ions (Y³⁺ vs. Ca²⁺) appear to be more reactive. Investigations of hydrogen atom transfer and electron transfer rates are also discussed.

Appendix A describes the synthesis, and metallation reactions of a new dinucleating bis(N-heterocyclic carbene)ligand framework. Dicopper(I) and dicobalt(II) complexes of this ligand were prepared and structurally characterized. A dinickel(I) dichloride complex was synthesized, reduced, and found to activate carbon dioxide. Appendix B describes preliminary efforts to desymmetrize the manganese oxido clusters via functionalization of the basal multinucleating ligand used in the preceding sections of this dissertation. Finally, Appendix C presents some partially characterized side products and unexpected structures that were isolated throughout the course of these studies.

Two topics in elementary particle physics. I. Crossing as a group and elimination of exotic channels. II. Real parts of meson-nucleon forward scattering amplitudes.

I. Crossing transformations constitute a group of permutations under which the scattering amplitude is invariant. Using Mandelstem's analyticity, we decompose the amplitude into irreducible representations of this group. The usual quantum numbers, such as isospin or SU(3), are "crossing-invariant". Thus no higher symmetry is generated by crossing itself. However, elimination of certain quantum numbers in intermediate states is not crossing-invariant, and higher symmetries have to be introduced to make it possible. The current literature on exchange degeneracy is a manifestation of this statement. To exemplify application of our analysis, we show how, starting with SU(3) invariance, one can use crossing and the absence of exotic channels to derive the quark-model picture of the tensor nonet. No detailed dynamical input is used.

II. A dispersion relation calculation of the real parts of forward π^±p and K^±p scattering amplitudes is carried out under the assumption of constant total cross sections in the Serpukhov energy range. Comparison with existing experimental results as well as predictions for future high energy experiments are presented and discussed. Electromagnetic effects are found to be too small to account for the expected difference between the π^-p and π⁺p total cross sections at higher energies.

Heterometallic Complexes as Models of Enzymatic Active Sites

This dissertation describes studies on two multinucleating ligand architectures: the first scaffold was designed to support tricopper complexes, while the second platform was developed to support tri- and tetrametallic clusters.

In Chapter 2, the synthesis of yttrium (and lanthanide) complexes supported by a tripodal ligand framework designed to bind three copper centers in close proximity is described. Tricopper complexes were shown to react with dioxygen in a 1:1 [Cu₃]/O₂ stoichiometry to form intermediates in which the O–O bond was fully cleaved, as characterized via UV-Vis spectroscopy and determination of the reaction stoichiometry. Pre-arrangement of the three Cu centers was pivotal to cooperative O₂ activation, as mono-copper complexes reacted differently with dioxgyen. The reactivity of the observed intermediates was studied with various substrates (reductants, O-atom acceptors, H-atom donors, Brønsted acids) to determine their properties. In Chapter 3, the reactivity of the same yttrium-tricopper complex with nitric oxide was explored. Reductive coupling to form a trans-hyponitrite complex (characterized by X-ray crystallography) was observed via cooperative reactivity by an yttrium and a copper center on two distinct tetrametallic units. The hyponitrite complex was observed to release nitrous oxide upon treatment with a Brønsted acid, supporting its viability as an intermediate in nitric oxide reduction to nitrous oxide.

In Chapter 4, a different multinucleating ligand scaffold was employed to synthesize heterometallic triiron clusters containing one oxide and one hydroxide bridges. The effects of the redox-inactive, Lewis acidic heterometals on redox potential was studied by cyclic voltammetry, unveiling a linear correlation between redox potential and heterometal Lewis acidity. Further studies on these complexes showed that the Lewis acidity of the redox-inactive metals also affected the oxygen-atom transfer reactivity of these clusters. Comparisons of this reactivity with manganese systems, collaborative efforts to reassign the structures of related manganese oxo-hydroxo clusters, and synthetic attempts to access related dioxo clusters are also described.

In Appendix A, ongoing efforts to synthesize new clusters supported by the same multinucleating ligand platform are described. Studies of novel approaches towards ligand exchange in tetrametallic clusters and incorporation of new supporting and bridging ligand motifs in trinuclear complexes are presented.

New Physics Models in the Diphoton Final State at CMS

Since the discovery of the Higgs boson at the LHC, its use as a probe to search for beyond the standard model physics, such as supersymmetry, has become important, as seen in a recent search by the CMS experiment using razor variables in the diphoton final state. Motivated by this search, this thesis examines the LHC discovery potential of a SUSY scenario involving bottom squark pair production with a Higgs boson in the final state. We design and implement a software-based trigger using the razor variables for the CMS experiment to record events with a bottom quark-antiquark pair from a Higgs boson. We characterize the full range of signatures at the LHC from this Higgs-aware SUSY scenario and demonstrate the sensitivity of the CMS data to this model.