Photoproduction of charged pion pairs from hydrogen at energies up to 1500 MeV

Charged pion pair photoproduction has been investigated up to a gamma energy of 1500 MeV, using the Caltech 12-inch heavy liquid bubble chamber with a small diameter, high intensity photon beam passing through a central beam tube gaseous hydrogen target surrounded by the sensitive Freon. Scanning, analysis, and data reduction techniques have been developed to deal with the problems of two-vie stereo, hidden event origins, absence of magnetic field, and the range-energy and multiple scattering relationships that occur in the heavy materials. Roughly 5700 pictures have been scanned and analyzed, yielding 754 acceptable events. Cross section and parameter distributions are generally consistent with the results of previous experiments. A statistically insignificant “bump” was observed in the dipion mass spectrum in the region of 500 MeV, the disputed σ meson mass. This region was investigated as carefully as the limited statistics would allow; dipion angular distributions are consistent with isotropy, and there is indication that some of the events in this region might come from decay of an intermediate N*₁₁ (1425) into a proton and dipion.

Photographic materials on pp. 18, 20, 22, and 24 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

Analyses of planetary atmospheres across the spectrum : from Titan to exoplanets

Planetary atmospheres exist in a seemingly endless variety of physical and chemical environments. There are an equally diverse number of methods by which we can study and characterize atmospheric composition. In order to better understand the fundamental chemistry and physical processes underlying all planetary atmospheres, my research of the past four years has focused on two distinct topics. First, I focused on the data analysis and spectral retrieval of observations obtained by the Ultraviolet Imaging Spectrograph (UVIS) instrument onboard the Cassini spacecraft while in orbit around Saturn. These observations consisted of stellar occultation measurements of Titan's upper atmosphere, probing the chemical composition in the region 300 to 1500 km above Titan's surface. I examined the relative abundances of Titan's two most prevalent chemical species, nitrogen and methane. I also focused on the aerosols that are formed through chemistry involving these two major species, and determined the vertical profiles of aerosol particles as a function of time and latitude. Moving beyond our own solar system, my second topic of investigation involved analysis of infra-red light curves from the Spitzer space telescope, obtained as it measured the light from stars hosting planets of their own. I focused on both transit and eclipse modeling during Spitzer data reduction and analysis. In my initial work, I utilized the data to search for transits of planets a few Earth masses in size. In more recent research, I analyzed secondary eclipses of three exoplanets and constrained the range of possible temperatures and compositions of their atmospheres.

Charged pion contribution to the anomalous magnetic moment of the muon

The model dependence inherent in hadronic calculations is one of the dominant sources of uncertainty in the theoretical prediction of the anomalous magnetic moment of the muon. In this thesis, we focus on the charged pion contribution and turn a critical eye on the models employed in the few previous calculations of $a_\mu^{\pi^+\pi^-}$. Chiral perturbation theory provides a check on these models at low energies, and we therefore calculate the charged pion contribution to light-by-light (LBL) scattering to $\mathcal{O}(p^6)$. We show that the dominant corrections to the leading order (LO) result come from two low energy constants which show up in the form factors for the $\gamma\pi\pi$ and $\gamma\gamma\pi\pi$ vertices. Comparison with the existing models reveal a potentially significant omission - none include the pion polarizability corrections associated with the $\gamma\gamma\pi\pi$ vertex. We next consider alternative models where the pion polarizability is produced through exchange of the $a_1$ axial vector meson. These have poor UV behavior, however, making them unsuited for the $a_\mu^{\pi^+\pi^-}$ calculation. We turn to a simpler form factor modeling approach, generating two distinct models which reproduce the pion polarizability corrections at low energies, have the correct QCD scaling at high energies, and generate finite contributions to $a_\mu^{\pi^+\pi^-}$. With these two models, we calculate the charged pion contribution to the anomalous magnetic moment of the muon, finding values larger than those previously reported: $a_\mu^\mathrm{I} = -1.779(4)\times10^{-10}\,,\,a_\mu^\mathrm{II} = -4.892(3)\times10^{-10}$.

Dating and characterizing late holocene earthquakes using paleomagnetics

In this thesis I apply paleomagnetic techniques to paleoseismological problems. I investigate the use of secular-variation magnetostratigraphy to date prehistoric earthquakes; I identify liquefaction remanent magnetization (LRM), and I quantify coseismic deformation within a fault zone by measuring the rotation of paleomagnetic vectors.

In Chapter 2 I construct a secular-variation reference curve for southern California. For this curve I measure three new well-constrained paleomagnetic directions: two from the Pallett Creek paleoseismological site at A.D. 1397-1480 and A.D. 1465-1495, and one from Panum Crater at A.D. 1325-1365. To these three directions I add the best nine data points from the Sternberg secular-variation curve, five data points from Champion, and one point from the A.D. 1480 eruption of Mt. St. Helens. I derive the error due to the non-dipole field that is added to these data by the geographical correction to southern California. Combining these yields a secular variation curve for southern California covering the period A.D. 670 to 1910, with the best coverage in the range A.D. 1064 to 1505.

In Chapter 3 I apply this curve to a problem in southern California. Two paleoseismological sites in the Salton trough of southern California have sediments deposited by prehistoric Lake Cahuilla. At the Salt Creek site I sampled sediments from three different lakes, and at the Indio site I sampled sediments from four different lakes. Based upon the coinciding paleomagnetic directions I correlate the oldest lake sampled at Salt Creek with the oldest lake sampled at Indio. Furthermore, the penultimate lake at Indio does not appear to be present at Salt Creek. Using the secular variation curve I can assign the lakes at Salt Creek to broad age ranges of A.D. 800 to 1100, A.D. 1100 to 1300, and A.D. 1300 to 1500. This example demonstrates the large uncertainties in the secular variation curve and the need to construct curves from a limited geographical area.

Chapter 4 demonstrates that seismically induced liquefaction can cause resetting of detrital remanent magnetization and acquisition of a liquefaction remanent magnetization (LRM). I sampled three different liquefaction features, a sandbody formed in the Elsinore fault zone, diapirs from sediments of Mono Lake, and a sandblow in these same sediments. In every case the liquefaction features showed stable magnetization despite substantial physical disruption. In addition, in the case of the sandblow and the sandbody, the intensity of the natural remanent magnetization increased by up to an order of magnitude.

In Chapter 5 I apply paleomagnetics to measuring the tectonic rotations in a 52 meter long transect across the San Andreas fault zone at the Pallett Creek paleoseismological site. This site has presented a significant problem because the brittle long-term average slip-rate across the fault is significantly less than the slip-rate from other nearby sites. I find sections adjacent to the fault with tectonic rotations of up to 30°. If interpreted as block rotations, the non-brittle offset was 14.0+2.8, -2.1 meters in the last three earthquakes and 8.5+1.0, -0.9 meters in the last two. Combined with the brittle offset in these events, the last three events all had about 6 meters of total fault offset, even though the intervals between them were markedly different.

In Appendix 1 I present a detailed description of my standard sampling and demagnetization procedure.

In Appendix 2 I present a detailed discussion of the study at Panum Crater that yielded the well-constrained paleomagnetic direction for use in developing secular variation curve in Chapter 2. In addition, from sampling two distinctly different clast types in a block-and-ash flow deposit from Panum Crater, I find that this flow had a complex emplacement and cooling history. Angular, glassy "lithic" blocks were emplaced at temperatures above 600° C. Some of these had cooled nearly completely, whereas others had cooled only to 450° C, when settling in the flow rotated the blocks slightly. The partially cooled blocks then finished cooling without further settling. Highly vesicular, breadcrusted pumiceous clasts had not yet cooled to 600° C at the time of these rotations, because they show a stable, well clustered, unidirectional magnetic vector.

Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.

I. Anisotropy and crystal structure of ferromagnetic thin films. II. Investigations into magnetic microstructure by Lorentz microscopy

The induced magnetic uniaxial anisotropy of Ni-Fe alloy films has been shown to be related to the crystal structure of the film. By use of electron diffraction, the crystal structure or vacuum-deposited films was determined over the composition range 5% to 85% Ni, with substrate temperature during deposition at various temperatures in the range 25° to 500° C. The phase diagram determined in this way has boundaries which are in fair agreement with the equilibrium boundaries for bulk material above 400°C. The (α+ ɤ) mixture phase disappears below 100°C.

The measurement of uniaxial anisotropy field for 25% Ni-Fe alloy films deposited at temperatures in the range -80°C to 375°C has been carried out. Comparison of the crystal structure phase diagram with the present data and those published by Wilts indicates that the anisotropy is strongly sensitive to crystal structure. Others have proposed pair ordering as an important source of anisotropy because of an apparent peak in the anisotropy energy at about 50% Ni composition. The present work shows no such peak, and leads to the conclusion that pair ordering cannot be a dominant contributor.

Width of the 180° domain wall in 76% Ni-Fe alloy films as a function of film thickness up to 1800 Å was measured using the defocused mode of Lorentz microscopy. For the thinner films, the measured wall widths are in good agreement with earlier data obtained by Fuchs. For films thicker than 800 Å, the wall width increases with film thickness to about 9000 Å at 1800 Å film thickness. Similar measurements for polycrystalline Co films with thickness from 200 to 1500 Å have been made. The wall width increases from 3000 Å at 400 Å film thickness to about 6000 Å at 1500 Å film thickness. The wall widths for Ni-Fe and Co films are much greater than predicted by present theories. The validity of the classical determination of wall width is discussed, and the comparison of the present data with theoretical results is given.

Finally, an experimental study of ripple by Lorentz microscopy in Ni-Fe alloy films has been carried out. The following should be noted: (1) the only practical way to determine experimentally a meaningful wavelength is to find a well-defined ripple periodicity by visual inspection of a photomicrograph. (2) The average wavelength is of the order of 1µ. This value is in reasonable agreement with the main wavelength predicted by the theories developed by others. The dependence of wavelength on substrate deposition temperature, alloy composition and the external magnetic field has been also studied and the results are compared with theoretical predictions. (3) The experimental fact that the ripple structure could not be observed in completely epitaxial films gives confirmation that the ripple results from the randomness of crystallite orientation. Furthermore, the experimental observation that the ripple disappeared in the range 71 and 75% Ni supports the theory that the ripple amplitude is directly dependent on the crystalline anisotropy. An attempt to experimentally determine the order of magnitude of the ripple angle was carried out. The measured angle was about 0.02 rad. The discrepancy between the experimental data and the theoretical prediction is serious. The accurate experimental determination of ripple angle is an unsolved problem.

Decoding cosets of first-order Reed-Muller code

Proper encoding of transmitted information can improve the performance of a communication system. To recover the information at the receiver it is necessary to decode the received signal. For many codes the complexity and slowness of the decoder is so severe that the code is not feasible for practical use. This thesis considers the decoding problem for one such class of codes, the comma-free codes related to the first-order Reed-Muller codes.

A factorization of the code matrix is found which leads to a simple, fast, minimum memory, decoder. The decoder is modular and only n modules are needed to decode a code of length 2ⁿ. The relevant factorization is extended to any code defined by a sequence of Kronecker products.

The problem of monitoring the correct synchronization position is also considered. A general answer seems to depend upon more detailed knowledge of the structure of comma-free codes. However, a technique is presented which gives useful results in many specific cases.

Studies of the equation of state and elasticity of mantle minerals

Because the Earth’s upper mantle is inaccessible to us, in order to understand the chemical and physical processes that occur in the Earth’s interior we must rely on both experimental work and computational modeling. This thesis addresses both of these geochemical methods. In the first chapter, I develop an internally consistent comprehensive molar volume model for spinels in the oxide system FeO-MgO-Fe₂O₃-Cr₂O₃-Al₂O₃-TiO₂. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure. In the second chapter, I calibrate a molar volume model for cubic garnets in the system SiO₂-Al₂O₃-TiO₂-Fe₂O₃-Cr₂O₃-FeO-MnO-MgO-CaO-Na₂O. I use the method of singular value analysis to calibrate excess volume of mixing parameters for the garnet model. The implications the model has for the density of the lithospheric mantle are explored. In the third chapter, I discuss the nuclear inelastic X-ray scattering (NRIXS) method, and present analysis of three orthopyroxene samples with different Fe contents. Longitudinal and shear wave velocities, elastic parameters, and other thermodynamic information are extracted from the raw NRIXS data.

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

I. Singular perturbation problems involving singular points and turning points. II. On the averaged Lagrangian technique for nonlinear dispersive waves

In Part I a class of linear boundary value problems is considered which is a simple model of boundary layer theory. The effect of zeros and singularities of the coefficients of the equations at the point where the boundary layer occurs is considered. The usual boundary layer techniques are still applicable in some cases and are used to derive uniform asymptotic expansions. In other cases it is shown that the inner and outer expansions do not overlap due to the presence of a turning point outside the boundary layer. The region near the turning point is described by a two-variable expansion. In these cases a related initial value problem is solved and then used to show formally that for the boundary value problem either a solution exists, except for a discrete set of eigenvalues, whose asymptotic behaviour is found, or the solution is non-unique. A proof is given of the validity of the two-variable expansion; in a special case this proof also demonstrates the validity of the inner and outer expansions.

Nonlinear dispersive wave equations which are governed by variational principles are considered in Part II. It is shown that the averaged Lagrangian variational principle is in fact exact. This result is used to construct perturbation schemes to enable higher order terms in the equations for the slowly varying quantities to be calculated. A simple scheme applicable to linear or near-linear equations is first derived. The specific form of the first order correction terms is derived for several examples. The stability of constant solutions to these equations is considered and it is shown that the correction terms lead to the instability cut-off found by Benjamin. A general stability criterion is given which explicitly demonstrates the conditions under which this cut-off occurs. The corrected set of equations are nonlinear dispersive equations and their stationary solutions are investigated. A more sophisticated scheme is developed for fully nonlinear equations by using an extension of the Hamiltonian formalism recently introduced by Whitham. Finally the averaged Lagrangian technique is extended to treat slowly varying multiply-periodic solutions. The adiabatic invariants for a separable mechanical system are derived by this method.

The hydro-kinetic theory of liquid helium II

In Part I the kinetic theory of excitations in flowing liquid He II is developed to a higher order than that carried out previously, by Landau and Khalatnikov, in order to demonstrate the existence of non-equilibrium terms of a new nature in the hydrodynamic equations. It is then shown that these terms can lead to spontaneous destabilization in counter currents when the relative velocity of the normal and super fluids exceeds a critical value that depends on the temperature, but not on geometry. There are no adjustable parameters in the theory. The critical velocities are estimated to be in the 14-20 m/sec range for T ≤ 2.0° K, but tend to zero as T → T_λ. The possibility that these critical velocities may be related to the experimentally observed "intrinsic" critical velocities is discussed.

Part II consists of a semi-classical investigation of rotonquantized vortex line interactions. An essentially classical model is used for the collision and the behavior of the roton in the vortex field is investigated in detail. From this model it is possible to derive the HVBK mutual friction terms that appear in the phenomenalogical equations of motion for rotating liquid He II. Estimates of the Hall and Vinen B and B' coefficients are in good agreement with experiments. The claim is made that the theory does not contain any arbitrary adjustable parameters.

Methods of multiparameter inversion of seismic data using the acoustic and elastic born approximations

This thesis presents two different forms of the Born approximations for acoustic and elastic wavefields and discusses their application to the inversion of seismic data. The Born approximation is valid for small amplitude heterogeneities superimposed over a slowly varying background. The first method is related to frequency-wavenumber migration methods. It is shown to properly recover two independent acoustic parameters within the bandpass of the source time function of the experiment for contrasts of about 5 percent from data generated using an exact theory for flat interfaces. The independent determination of two parameters is shown to depend on the angle coverage of the medium. For surface data, the impedance profile is well recovered.

The second method explored is mathematically similar to iterative tomographic methods recently introduced in the geophysical literature. Its basis is an integral relation between the scattered wavefield and the medium parameters obtained after applying a far-field approximation to the first-order Born approximation. The Davidon-Fletcher-Powell algorithm is used since it converges faster than the steepest descent method. It consists essentially of successive backprojections of the recorded wavefield, with angular and propagation weighing coefficients for density and bulk modulus. After each backprojection, the forward problem is computed and the residual evaluated. Each backprojection is similar to a before-stack Kirchhoff migration and is therefore readily applicable to seismic data. Several examples of reconstruction for simple point scatterer models are performed. Recovery of the amplitudes of the anomalies are improved with successive iterations. Iterations also improve the sharpness of the images.

The elastic Born approximation, with the addition of a far-field approximation is shown to correspond physically to a sum of WKBJ-asymptotic scattered rays. Four types of scattered rays enter in the sum, corresponding to P-P, P-S, S-P and S-S pairs of incident-scattered rays. Incident rays propagate in the background medium, interacting only once with the scatterers. Scattered rays propagate as if in the background medium, with no interaction with the scatterers. An example of P-wave impedance inversion is performed on a VSP data set consisting of three offsets recorded in two wells.

Fundamental Studies of Carbon Oxygen Bond Activation in Nickel Diphosphine Ether Complexes. And, Metallomacrocycles as Ligands: Synthesis and Characterization of Aluminum-Bridged Bisglyoximato Complexes of Iron and Cobalt

In order to develop better catalysts for the cleavage of aryl-X bonds fundamental studies of the mechanism and individual steps of the mechanism have been investigated in detail. As the described studies are difficult at best in catalytic systems, model systems are frequently used. To study aryl-oxygen bond activation, a terphenyl diphosphine scaffold containing an ether moiety in the central arene was designed. The first three chapters of this dissertation focus on the studies of the nickel complexes supported by this diphosphine backbone and the research efforts in regards to aryl-oxygen bond activation.

Chapter 2 outlines the synthesis of a variety of diphosphine terphenyl ether ligand scaffolds. The metallation of these scaffolds with nickel is described. The reactivity of these nickel(0) systems is also outlined. The systems were found to typically undergo a reductive cleavage of the aryl oxygen bond. The mechanism was found to be a subsequent oxidative addition, β-H elimination, reductive elimination and (or) decarbonylation.

Chapter 3 presents kinetic studies of the aryl oxygen bond in the systems outlined in Chapter 2. Using a series of nickel(0) diphosphine terphenyl ether complexes the kinetics of aryl oxygen bond activation was studied. The activation parameters of oxidative addition for the model systems were determined. Little variation was observed in the rate and activation parameters of oxidative addition with varying electronics in the model system. The cause of the lack of variation is due to the ground state and oxidative addition transition state being affected similarly. Attempts were made to extend this study to catalytic systems.

Chapter 4 investigates aryl oxygen bond activation in the presence of additives. It was found that the addition of certain metal alkyls to the nickel(0) model system lead to an increase in the rate of aryl oxygen bond activation. The addition of excess Grignard reagent led to an order of magnitude increase in the rate of aryl oxygen bond activation. Similarly the addition of AlMe3 led to a three order of magnitude rate increase. Addition of AlMe₃ at -80 °C led to the formation of an intermediate which was identified by NOESY correlations as a system in which the AlMe3 is coordinated to the ether moiety of the backbone. The rates and activation parameters of aryl oxygen bond activation in the presence of AlMe3 were investigated.

The last two chapters involve the study of metalla-macrocycles as ligands. Chapter 5 details the synthesis of a variety of glyoxime backbones and diphenol precursors and their metallation with aluminum. The coordination chemistry of iron on the aluminum scaffolds was investigated. Varying the electronics of the aluminum macrocycle was found to affect the observed electrochemistry of the iron center.

Chapter 6 extends the studies of chapter 5 to cobalt complexes. The synthesis of cobalt dialuminum glyoxime metal complexes is described. The electrochemistry of the cobalt complexes was investigated. The electrochemistry was compared to the observed electrochemistry of a zinc analog to identify the redox activity of the ligand. In the presence of acid the cobalt complexes were found to electrochemically reduce protons to dihydrogen. The electronics of the ancillary aluminum ligands were found to affect the potential of proton reduction in the cobalt complexes. These potentials were compared to other diglyoximate complexes.

Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

I. Spectroscopic observation of discrete sites in simple liquids. II. Infrared intensity perturbations of hydrogen halide fundamentals in liquid xenon. III. Rotation of HCl in solid rare gases.

Part I

The spectrum of dissolved mercury atoms in simple liquids has been shown to be capable of revealing information concerning local structures in these liquids.

Part II

Infrared intensity perturbations in simple solutions have been shown to involve more detailed interaction than just dielectric polarization. No correlation has been found between frequency shifts and intensity enhancements.

Part III

Evidence for perturbed rotation of HCl in rare gas matrices has been found. The magnitude of the barrier to rotation is concluded to be of order of 30 cm^(-1).