I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Imaging the earth with ambient noise and earthquakes

In this thesis, I develop the velocity and structure models for the Los Angeles Basin and Southern Peru. The ultimate goal is to better understand the geological processes involved in the basin and subduction zone dynamics. The results are obtained from seismic interferometry using ambient noise and receiver functions using earthquake- generated waves. Some unusual signals specific to the local structures are also studied. The main findings are summarized as follows:

(1) Los Angeles Basin

The shear wave velocities range from 0.5 to 3.0 km/s in the sediments, with lateral gradients at the Newport-Inglewood, Compton-Los Alamitos, and Whittier Faults. The basin is a maximum of 8 km deep along the profile, and the Moho rises to a depth of 17 km under the basin. The basin has a stretch factor of 2.6 in the center decreasing to 1.3 at the edges, and is in approximate isostatic equilibrium. This "high-density" (~1 km spacing) "short-duration" (~1.5 month) experiment may serve as a prototype experiment that will allow basins to be covered by this type of low-cost survey.

(2) Peruvian subduction zone

Two prominent mid-crust structures are revealed in the 70 km thick crust under the Central Andes: a low-velocity zone interpreted as partially molten rocks beneath the Western Cordillera – Altiplano Plateau, and the underthrusting Brazilian Shield beneath the Eastern Cordillera. The low-velocity zone is oblique to the present trench, and possibly indicates the location of the volcanic arcs formed during the steepening of the Oligocene flat slab beneath the Altiplano Plateau.

The Nazca slab changes from normal dipping (~25 degrees) subduction in the southeast to flat subduction in the northwest of the study area. In the flat subduction regime, the slab subducts to ~100 km depth and then remains flat for ~300 km distance before it resumes a normal dipping geometry. The flat part closely follows the topography of the continental Moho above, indicating a strong suction force between the slab and the overriding plate. A high-velocity mantle wedge exists above the western half of the flat slab, which indicates the lack of melting and thus explains the cessation of the volcanism above. The velocity turns to normal values before the slab steepens again, indicating possible resumption of dehydration and ecologitization.

(3) Some unusual signals

Strong higher-mode Rayleigh waves due to the basin structure are observed in the periods less than 5 s. The particle motions provide a good test for distinguishing between the fundamental and higher mode. The precursor and coda waves relative to the interstation Rayleigh waves are observed, and modeled with a strong scatterer located in the active volcanic area in Southern Peru. In contrast with the usual receiver function analysis, multiples are extensively involved in this thesis. In the LA Basin, a good image is only from PpPs multiples, while in Peru, PpPp multiples contribute significantly to the final results.

Solubility and Diffusivity of Water in Lunar Basalt, and Chemical Zonation in Olivine-Hosted Melt Inclusions

I report the solubility and diffusivity of water in lunar basalt and an iron-free basaltic analogue at 1 atm and 1350 °C. Such parameters are critical for understanding the degassing histories of lunar pyroclastic glasses. Solubility experiments have been conducted over a range of fO₂ conditions from three log units below to five log units above the iron-wüstite buffer (IW) and over a range of pH₂/pH₂O from 0.03 to 24. Quenched experimental glasses were analyzed by Fourier transform infrared spectroscopy (FTIR) and secondary ionization mass spectrometry (SIMS) and were found to contain up to ~420 ppm water. Results demonstrate that, under the conditions of our experiments: (1) hydroxyl is the only H-bearing species detected by FTIR; (2) the solubility of water is proportional to the square root of pH₂O in the furnace atmosphere and is independent of fO₂ and pH₂/pH₂O; (3) the solubility of water is very similar in both melt compositions; (4) the concentration of H₂ in our iron-free experiments is <3 ppm, even at oxygen fugacities as low as IW-2.3 and pH₂/pH₂O as high as 24; and (5) SIMS analyses of water in iron-rich glasses equilibrated under variable fO₂ conditions can be strongly influenced by matrix effects, even when the concentrations of water in the glasses are low. Our results can be used to constrain the entrapment pressure of the lunar melt inclusions of Hauri et al. (2011).

Diffusion experiments were conducted over a range of fO₂ conditions from IW-2.2 to IW+6.7 and over a range of pH₂/pH₂O from nominally zero to ~10. The water concentrations measured in our quenched experimental glasses by SIMS and FTIR vary from a few ppm to ~430 ppm. Water concentration gradients are well described by models in which the diffusivity of water (D^*_water) is assumed to be constant. The relationship between D^*_water and water concentration is well described by a modified speciation model (Ni et al. 2012) in which both molecular water and hydroxyl are allowed to diffuse. The success of this modified speciation model for describing our results suggests that we have resolved the diffusivity of hydroxyl in basaltic melt for the first time. Best-fit values of D^*_water for our experiments on lunar basalt vary within a factor of ~2 over a range of pH₂/pH₂O from 0.007 to 9.7, a range of fO₂ from IW-2.2 to IW+4.9, and a water concentration range from ~80 ppm to ~280 ppm. The relative insensitivity of our best-fit values of D^*_water to variations in pH₂ suggests that H₂ diffusion was not significant during degassing of the lunar glasses of Saal et al. (2008). D^*_water during dehydration and hydration in H₂/CO₂ gas mixtures are approximately the same, which supports an equilibrium boundary condition for these experiments. However, dehydration experiments into CO₂ and CO/CO₂ gas mixtures leave some scope for the importance of kinetics during dehydration into H-free environments. The value of D^*_water chosen by Saal et al. (2008) for modeling the diffusive degassing of the lunar volcanic glasses is within a factor of three of our measured value in our lunar basaltic melt at 1350 °C.

In Chapter 4 of this thesis, I document significant zonation in major, minor, trace, and volatile elements in naturally glassy olivine-hosted melt inclusions from the Siqueiros Fracture Zone and the Galapagos Islands. Components with a higher concentration in the host olivine than in the melt (MgO, FeO, Cr₂O₃, and MnO) are depleted at the edges of the zoned melt inclusions relative to their centers, whereas except for CaO, H₂O, and F, components with a lower concentration in the host olivine than in the melt (Al₂O₃, SiO₂, Na₂O, K₂O, TiO₂, S, and Cl) are enriched near the melt inclusion edges. This zonation is due to formation of an olivine-depleted boundary layer in the adjacent melt in response to cooling and crystallization of olivine on the walls of the melt inclusions concurrent with diffusive propagation of the boundary layer toward the inclusion center.

Concentration profiles of some components in the melt inclusions exhibit multicomponent diffusion effects such as uphill diffusion (CaO, FeO) or slowing of the diffusion of typically rapidly diffusing components (Na₂O, K₂O) by coupling to slow diffusing components such as SiO₂ and Al₂O₃. Concentrations of H2O and F decrease towards the edges of some of the Siqueiros melt inclusions, suggesting either that these components have been lost from the inclusions into the host olivine late in their cooling histories and/or that these components are exhibiting multicomponent diffusion effects.

A model has been developed of the time-dependent evolution of MgO concentration profiles in melt inclusions due to simultaneous depletion of MgO at the inclusion walls due to olivine growth and diffusion of MgO in the melt inclusions in response to this depletion. Observed concentration profiles were fit to this model to constrain their thermal histories. Cooling rates determined by a single-stage linear cooling model are 150–13,000 °C hr^-1 from the liquidus down to ~1000 °C, consistent with previously determined cooling rates for basaltic glasses; compositional trends with melt inclusion size observed in the Siqueiros melt inclusions are described well by this simple single-stage linear cooling model. Despite the overall success of the modeling of MgO concentration profiles using a single-stage cooling history, MgO concentration profiles in some melt inclusions are better fit by a two-stage cooling history with a slower-cooling first stage followed by a faster-cooling second stage; the inferred total duration of cooling from the liquidus down to ~1000 °C is 40 s to just over one hour.

Based on our observations and models, compositions of zoned melt inclusions (even if measured at the centers of the inclusions) will typically have been diffusively fractionated relative to the initially trapped melt; for such inclusions, the initial composition cannot be simply reconstructed based on olivine-addition calculations, so caution should be exercised in application of such reconstructions to correct for post-entrapment crystallization of olivine on inclusion walls. Off-center analyses of a melt inclusion can also give results significantly fractionated relative to simple olivine crystallization.

All melt inclusions from the Siqueiros and Galapagos sample suites exhibit zoning profiles, and this feature may be nearly universal in glassy, olivine-hosted inclusions. If so, zoning profiles in melt inclusions could be widely useful to constrain late-stage syneruptive processes and as natural diffusion experiments.

Photoproduction of ETA mesons from hydrogen at photon energies between 0.8 and 1.45 GeV

We measured the differential cross section of the process γp → pƞ at the 1.5 GeV Caltech electron synchrotron, at photon energies from 0.8 to 1.45 GeV, at various angles between 45° and 100° in the center of mass. A counter-spark chamber array was used to determine the kinematics of all particles in the final state of the partial mode γp → pƞ (ƞ → 2γ). Analysis of 40,000 pictures yielded 6,000 events above a background which varied with energy from 5% to 30% of foreground. The cross section shows an energy dependence confirming earlier results up to 1000 MeV, but with improved statistics; it then remains roughly constant (at 50° C.M.), to 1.45 GeV. The data show a small angular variation, within the limited range covered, at energies between 1000 and 1100 MeV.

Design, Synthesis, and Study of Novel Platforms for Iron-N2 Chemistry and Photoinduced, Copper-mediated C-N Bond Formation

Several new ligand platforms designed to support iron dinitrogen chemistry have been developed. First, we report Fe complexes of a tris(phosphino)alkyl (CP^iPr₃) ligand featuring an axial carbon donor intended to conceptually model the interstitial carbide atom of the nitrogenase iron-molybdenum cofactor (FeMoco). It is established that in this scaffold, the iron center binds dinitrogen trans to the C_alkyl anchor in three structurally characterized oxidation states. Fe-C_alkyl lengthening is observed upon reduction, reflective of significant ionic character in the Fe-C_alkyl interaction. The anionic (CP^iPr₃)FeN₂^- species can be functionalized by a silyl electrophile to generate (CP^iPr₃)Fe-N₂SiR₃. This species also functions as a modest catalyst for the reduction of N₂ to NH₃. Next, we introduce a new binucleating ligand scaffold that supports an Fe(μ-SAr)Fe diiron subunit that coordinates dinitrogen (N₂-Fe(μ-SAr)Fe-N₂) across at least three oxidation states (Fe^IIFe^II, Fe^IIFe^I, and Fe^IFe^I). Despite the sulfur-rich coordination environment of iron in FeMoco, synthetic examples of transition metal model complexes that bind N₂ and also feature sulfur donor ligands remain scarce; these complexes thus represent an unusual series of low-valent diiron complexes featuring thiolate and dinitrogen ligands. The (N₂-Fe(μ-SAr)Fe-N₂) system undergoes reduction of the bound N₂ to produce NH₃ (~50% yield) and can efficiently catalyze the disproportionation of N₂H₄ to NH₃ and N₂. The present scaffold also supports dinitrogen binding concomitant with hydride as a co-ligand. Next, inspired by the importance of secondary-sphere interactions in many metalloenzymes, we present complexes of iron in two new ligand scaffolds ([SiP^NMe₃] and [SiP^iPr₂P^NMe]) that incorporate hydrogen-bond acceptors (tertiary amines) which engage in interactions with nitrogenous substrates bound to the iron center (NH₃ and N₂H₄). Cation binding is also facilitated in anionic Fe(0)-N₂ complexes. While Fe-N₂ complexes of a related ligand ([SiP^iPr₃]) lacking hydrogen-bond acceptors produce a substantial amount of ammonia when treated with acid and reductant, the presence of the pendant amines instead facilitates the formation of metal hydride species.

Additionally, we present the development and mechanistic study of copper-mediated and copper-catalyzed photoinduced C-N bond forming reactions. Irradiation of a copper-amido complex, ((m-tol)₃P)₂Cu(carbazolide), in the presence of aryl halides furnishes N-phenylcarbazole under mild conditions. The mechanism likely proceeds via single-electron transfer from an excited state of the copper complex to the aryl halide, generating an aryl radical. An array of experimental data are consistent with a radical intermediate, including a cyclization/stereochemical investigation and a reactivity study, providing the first substantial experimental support for the viability of a radical pathway for Ullmann C-N bond formation. The copper complex can also be used as a precatalyst for Ullmann C-N couplings. We also disclose further study of catalytic C_alkyl-N couplings using a CuI precatalyst, and discuss the likely role of [Cu(carbazolide)₂]^- and [Cu(carbazolide)₃]^- species as intermediates in these reactions.

Finally, we report a series of four-coordinate, pseudotetrahedral P₃Fe^II-X complexes supported by tris(phosphine)borate ([PhBP₃Fe^R]^-) and phosphiniminato X-type ligands (-N=PR'₃) that in combination tune the spin-crossover behavior of the system. Low-coordinate transition metal complexes such as these that undergo reversible spin-crossover remain rare, and the spin equilibria of these systems have been studied in detail by a suite of spectroscopic techniques.

I. Site effects and exciton structure in molecular crystals - Benzene. II. The first and second triplet states of solid benzene

The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C₆H₆, C₆H₅D, m-C₆H₄D₂, p-C₆H₄D₂, sym-C₆H₃D₃, C₆D₅H, and C₆D₆ in either a C₆H₆ or C₆D₆ host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C₆H₆, C₆D₆, and sym-C₆H₃D₃; c) the orientational effect for the isotopes without a trigonal axis in both the ¹B_2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be^-Cr - A/r⁶ ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (³B_1u and ³E_1u) is given.

Invertible dark-center diffraction of the metal film induced by femtosecond laser

We found reversible dark-center diffraction of the transmitted probe beam passing through the chromium film. which is induced by the pump femtosecond laser. The dark-center diffraction of I he transmitted probe beam appears and disappears with and without the pump beam. A view of diffractive optics with binary phase plate is put forward, which explains the reversible dark-center diffractive optical phenomenon. The pre-ablated hole on the metal film can be regarded as a uniform light filed without phase modulation, the Surrounding Circular part around the pre-ablated hole can be regarded as "phase modulated". Therefore, this diffraction optic view might be helpful for us to understand the phase change of the metal film introduced by the femtosecond laser pulse. (C) 2008 Elsevier B.V, All rights reserved.

Study of near-infrared nonvolatile two-center holographic recording in LiNbO3:Fe:Rh crystal

The near-infrared nonvolatile holographic recording has been realized in a doubly doped LiNbO3:Fe:Rh crystal by the traditional two-center holographic recording scheme, for the first time. The recording performance of this crystal has been investigated by recording with 633 nm red light, 752 nm red light and 799 nm near-infrared light and sensitizing with 405 nm purple light. The experimental results show that, co-doped with Fe and Rh, the near-infrared absorption and the photovoltaic coefficient of shallow trap Fe are enhanced in this LiNbO3:Fe:Rh crystal, compared with other doubly doped LiNbO3 crystals Such as LiNbO3:Fe:Mn. It is also found that the sensitizing light intensity affects the near-infrared recording sensitivity in a different way than two-center holographic recording with shorter wavelength, and the origin of experimental results is analyzed. (C) 2007 Elsevier GrnbH. All rights reserved.

Photodisintegration of helium-3 at energies between 200 and 600 MEV

We have measured differential cross-sections for the two-body photodisintegration of Helium-3, ɣ + He³ → p + d, between incident photon energies of 200 and 600 MeV, and for center of mass frame angles between 30° and 150°. Both final state particles were detected in arrays of wire spark chambers and scintillation counters; the high momentum particle was analyzed in a magnet spectrometer. The results are interpreted in terms of amplitudes to produce the ∆(1236) resonance in an intermediate state, as well as non-resonant amplitudes. This experiment, together with an (unfinished) experiment on the inverse reaction, p + d → He³ + ɣ, will provide a reciprocity test of time reversal invariance.

Hypoxic and low pH water in the nearshore marine environments of Monterey Bay, California: characterizing a decade of oxygen and pH, and drivers of variability.

A decade-long time series recorded in southern Monterey Bay, California demonstrates that the shallow, near-shore environment (17 m depth) is regularly inundated with pulses of cold, hypoxic and low pH water. During these episodes, oxygen can drop to biologically threatening levels, and pH levels were lower than expected. Weekly water chemistry monitoring revealed that the saturation state of aragonite (the more soluble form of calcium carbonate) was often below saturation and had a moderate positive relationship with pH, however, analytical and human error could be high. Pulses of hypoxia and low pH water with the greatest intensity arise at the onset of the spring upwelling season, and fluctuations are strongly semidurnal (tidal) and diurnal. Arrival of cold, hypoxic water on the inner shelf typically occurs 3 days after the arrival of a strong upwelling event and appears to be driven by upwelling modulated by internal tidal fluctuations. I found no relationship between the timing of low-oxygen events and the diel solar cycle nor with terrestrial nutrient input. These observations are consistent with advection of hypoxic water from the deep, offshore environment where water masses experience a general decline of temperature, oxygen and pH with depth, and inconsistent with biochemical forcing. Comparisons with concurrent temperature and oxygen time series taken ~20 km away at the head of the Monterey Canyon show similar patterns but even more intense hypoxic events due to stronger semidiurnal forcing there. Analysis of the durations of exposure to low oxygen levels establishes a framework for assessing the ecological relevance of these events. Increasing oceanic hypoxia and acidification of both surface and deep waters may increase the number, intensity, duration and spatial extent of future intrusions along the Pacific coast. Evaluation of the resiliency of nearshore ecosystems such as kelp forests, rocky reefs and sandy habitats, will require consideration of these events.

Social structure and underwater behavior of harbor seals in southern Monterey Bay, California

To understand harbor seal social and mating strategies, I examined site fidelity, seasonal abundance and distribution, herd integrity, and underwater behavior of individual harbor seals in southern Monterey Bay. Individual harbor seals (n = 444) were identified by natural markings and represented greater than 80% of an estimated 520 seals within this community. Year to year fidelity of individual harbor seals to southern Monterey Bay coastline was 84% (n = 388), and long-term associations (>2 yrs) among individuals were common (>40%). Consistent with these long-term associations, harbor seals were highly social underwater throughout the year. Underwater social behavior included three primary types: (1) visual and acoustic displays, such as vocalizing, surface splashing, and bubble-blowing; (2) playful or agonistic social behavior such as rolling, mounting, attending, and biting; and (3) signal gestures such as head-thrusting, fore-flipper scratch~ng, and growling. Frequency of these types of behavior was related to seal age, gender, season, and resource availability. Underwater behavior had a variety of functions, including promotion of learning and social development, reduction of aggression and preservation of social bonds by maintaining social hierarchy, and facilitation of mate selection during breeding season. Social behavior among adult males was significantly correlated with vocalization characteristics (r = 0.99, X2 = 37.7, p = 0.00087), indicating that seals may assess their competition based on underwater vocalization displays and adopt individual strategies for attracting females during breeding season based on social status. Individual mating strategies may include defending underwater territories, using scramble tactics, and developing social alliances. (PDF contains 105 pages)

Remote Sensing and Field Assessment of Tsunami Effects on Coastal Pond Aquaculture in Northern Sumatra

An attempt was made to conduct spatial assessment of the pattern and extent of damage to coastal aquaculture ponds along the east coast of Aceh province in Sumatra, Indonesia, resulting from the tsunami event of 26 December 2004. High-resolution satellite imagery, i.e., SPOT-5 multispectral scenes covering the 700 km stretch of the coast, acquired before and after the tsunami, were digitally enhanced and visually interpreted to delineate pockets of aquaculture ponds that were discerned to be damaged and relatively intact. Field checks were conducted at 87 sites in the four eastern coastal districts. The results indicate that SPOT-5 multispectral imagery was minimally sufficient to detect areas of damaged and relatively intact aquaculture ponds, but the 10-m spatial resolution poses limitations to evaluating the extent of pond damage. Nevertheless, the 60 km swath of the imagery makes it reasonably affordable for large-area assessment to identify pockets of severe damage for targeting more detailed assessments. The image maps produced from a mosaic of the SPOT-5 scenes can also serve as base maps for spatial planning in the challenging task of reconstruction and rehabilitation of the disrupted livelihoods of the coastal communities.

First-principles calculations of electronic structures and absorption spectra of YAlO3 crystals with F center

National Nature Science Foundation of China (Grant No. 60607015)