I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Experiments in Neutrino Mass and Mixing: Part I - New Limits on Heavy Neutrino Emission in Nuclear Beta Decay. Part II - Fast Neutron Backgrounds for the San Onofre Neutrino Detector

In Part I of this thesis, a new magnetic spectrometer experiment which measured the β spectrum of ^(35)S is described. New limits on heavy neutrino emission in nuclear β decay were set, for a heavy neutrino mass range between 12 and 22 keV. In particular, this measurement rejects the hypothesis that a 17 keV neutrino is emitted, with sin^2 θ = 0.0085, at the 6δ statistical level. In addition, an auxiliary experiment was performed, in which an artificial kink was induced in the β spectrum by means of an absorber foil which masked a fraction of the source area. In this measurement, the sensitivity of the magnetic spectrometer to the spectral features of heavy neutrino emission was demonstrated.

In Part II, a measurement of the neutron spallation yield and multiplicity by the Cosmic-ray Underground Background Experiment is described. The production of fast neutrons by muons was investigated at an underground depth of 20 meters water equivalent, with a 200 liter detector filled with 0.09% Gd-loaded liquid scintillator. We measured a neutron production yield of (3.4 ± 0.7) x 10^(-5) neutrons per muon-g/cm^2, in agreement with other experiments. A single-to-double neutron multiplicity ratio of 4:1 was observed. In addition, stopped π^+ decays to µ^+ and then e^+ were observed as was the associated production of pions and neutrons, by the muon spallation interaction. It was seen that practically all of the π^+ produced by muons were also accompanied by at least one neutron. These measurements serve as the basis for neutron background estimates for the San Onofre neutrino detector.

A high pressure xenon time projection chamber for double beta decay

This thesis describes the design, construction and performance of a high-pressure, xenon, gas time projection chamber (TPC) for the study of double beta decay in ^(136) Xe. The TPC when operating at 5 atm can accommodate 28 moles of 60% enriched ^(136) Xe. The TPC has operated as a detector at Caltech since 1986. It is capable of reconstructing a charged particle trajectory and can easily distinguish between different kinds of charged particles. A gas purification and xenon gas recovery system were developed. The electronics for the 338 channels of readout was developed along with a data acquistion system. Currently, the detector is being prepared at the University of Neuchatel for installation in the low background laboratory situated in the St. Gotthard tunnel, Switzerland. In one year of runtime the detector should be sensitive to a 0ν lifetime of the order of 10^(24) y, which corresponds to a neutrino mass in the range 0.3 to 3.3 eV.

The decay properties of the ψ(3770)

The decays of the ψ(3770) resonance to final states that do not contain charmed D mesons are measured for the first time. Using a sample of 9.3pb ^(-1) of e^+e^- annihilations at √s = 3.77 GeV, collected with the Mark III detector at SPEAR, we have measured the branching ratio for the decays ψ(3770) → J/ψπ^(+)π^(-) and γχ_j. These branching ratios together with the electronic widths of the ψ(3685) and ψ(3770) are used to determine the mixing angle between the 2^(3)S_1 and 1^(3)D_1 Charmonium states and are compared with a number of predictions. In addition, evidence is found for other non-DD hadronic final states, such as 3π, 4π, and 5π, as well as η2π, η4π, pp2π and pp3π.

Investigations of charge-carrier dynamics at semiconductor/liquid interfaces

Theoretical and experimental investigations of charge-carrier dynamics at semiconductor/liquid interfaces, specifically with respect to interfacial electron transfer and surface recombination, are presented.

Fermi's golden rule has been used to formulate rate expressions for charge transfer of delocalized carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. The treatment allows comparison between charge-transfer kinetic data at metallic, semimetallic, and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been determined from experimental data for charge transfer at metallic electrodes. The maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10^-17-10^-16 cm⁴ s^-1, which is in excellent agreement with prior theoretical models and experimental results for charge-transfer kinetics at semiconductor/liquid interfaces.

Double-layer corrections have been evaluated for semiconductor electrodes in both depletion and accumulation conditions. In conjuction with the Gouy-Chapman-Stern model, a finite difference approach has been used to calculate potential drops at a representative solid/liquid interface. Under all conditions that were simulated, the correction to the driving force used to evaluate the interfacial rate constant was determined to be less than 2% of the uncorrected interfacial rate constant.

Photoconductivity decay lifetimes have been obtained for Si(111) in contact with solutions of CH₃OH or tetrahydrofuran containing one-electron oxidants. Silicon surfaces in contact with electrolyte solutions having Nernstian redox potentials > 0 V vs. SCE exhibited low effective surface recombination velocities regardless of the different surface chemistries. The formation of an inversion layer, and not a reduced density of electrical trap sites on the surface, is shown to be responsible for the long charge-carrier lifetimes observed for these systems. In addition, a method for preparing an air-stable, low surface recombination velocity Si surface through a two-step, chlorination/alkylation reaction is described.

The theory of long distance electron transfer reactions

The rate of electron transport between distant sites was studied. The rate depends crucially on the chemical details of the donor, acceptor, and surrounding medium. These reactions involve electron tunneling through the intervening medium and are, therefore, profoundly influenced by the geometry and energetics of the intervening molecules. The dependence of rate on distance was considered for several rigid donor-acceptor "linkers" of experimental importance. Interpretation of existing experiments and predictions for new experiments were made.

The electronic and nuclear motion in molecules is correlated. A Born-Oppenheimer separation is usually employed in quantum chemistry to separate this motion. Long distance electron transfer rate calculations require the total donor wave function when the electron is very far from its binding nuclei. The Born-Oppenheimer wave functions at large electronic distance are shown to be qualitatively wrong. A model which correctly treats the coupling was proposed. The distance and energy dependence of the electron transfer rate was determined for such a model.

Measurement of the neutron beta decay asymmetry using ultracold neutrons

The free neutron beta decay correlation A₀ between neutron polarization and electron emission direction provides the strongest constraint on the ratio λ = g_A/g_V of the Axial-vector to Vector coupling constants in Weak decay. In conjunction with the CKM Matrix element V_ud and the neutron lifetime τ_n, λ provides a test of Standard Model assumptions for the Weak interaction. Leading high-precision measurements of A₀ and τ_n in the 1995-2005 time period showed discrepancies with prior measurements and Standard Model predictions for the relationship between λ, τ_n, and V_ud. The UCNA experiment was developed to measure A₀ from decay of polarized ultracold neutrons (UCN), providing a complementary determination of λ with different systematic uncertainties from prior cold neutron beam experiments. This dissertation describes analysis of the dataset collected by UCNA in 2010, with emphasis on detector response calibrations and systematics. The UCNA measurement is placed in the context of the most recent τ_n results and cold neutron A₀ experiments.

Electron tunneling in proteins and water

The subject of this thesis is electronic coupling in donor-bridge-acceptor systems. In Chapter 2, ET properties of cyanide-bridged dinuclear ruthenium complexes were investigated. The strong interaction between the mixed-valent ruthenium centers leads to intense metal-to-metal charge transfer bands (MMCT). Hush analysis of the MMCT absorption bands yields the electronic-coupling strength between the metal centers (H_(AB)) and the total reorganization energy (λ). Comparison of ET kinetics to calculated rates shows that classical ET models fail to account for the observed kinetics and nuclear tunneling must be considered.

In Chapter 3, ET rates were measured in four ruthenium-modified highpotential iron-sulfur proteins (HiPIP), which were modified at position His50, His81, His42 and His18, respectively. ET kinetics for the His50 and His81 mutants are a factor of 300 different, while the donor-acceptor separation is nearly identical. PATHWAY calculations corroborate these measurements and highlight the importance of structural detail of the intervening protein matrix.

In Chapter 4, the distance dependence of ET through water bridges was measured. Photoinduced ET measurements in aqueous glasses at 77 K show that water is a poor medium for ET. Luminescence decay and quantum yield data were analyzed in the context of a quenching model that accounts for the exponential distance dependence of ET, the distance distribution of donors and acceptors embedded in the glass and the excluded volumes generated by the finite sizes of the donors and acceptors.

In Chapter 5, the pH-dependent excited state dynamics of ruthenium-modified amino acids were measured. The [Ru(bpy)_(3)] ^(2+) chromophore was linked to amino acids via an amide linkage. Protonation of the amide oxygen effectively quenches the excited state. In addition. time-resolved and steady-state luminescence data reveal that nonradiative rates are very sensitive to the protonation state and the structure of the amino acid moiety.

Radiative tau production and decay

A study of the muon decay channel of the τ lepton with the presence of a photon has been carried out to verify theoretical predictions for the production rate of e⁺e^- → τ⁺τ^-γ and for the branching ratio of τ^- → ν_τ µ^-ν_µγ. Included in this study is the first direct measurement of radiative tau decay. Using e⁺e^- annihilation data taken at 29 GeV center-of-mass energy with the Mark II detector, we find the ratio of the measured τ^- → ν_τ µ^-ν_µγ branching fraction to the expected value from QED to be 1.03 ± 0.42. The ratio of measured-to-predicted number of events from radiative T production, e⁺e^- → τ⁺τ^-γ, where one of the τ's decay to μνν is found to be 0.91 ± 0.20. We have not seen an indication of anomalous behavior in radiative tau events.

Excitation energies and decay properties of T = 3/2 states in ^(17)O, ^(17)F and ^(21)Na

The two lowest T = 3/2 levels in ²¹Na have been studied in the ¹⁹F(³He, n), ²⁰Ne (p,p) and ²⁰Ne (p,p’) reactions, and their excitation energies, spins, parities and widths have been determined. In a separate investigation, branching ratios were measured for the isospin-nonconserving particle decays of the lowest T = 3/2 levels in ¹⁷O and ¹⁷F to the ground state and first two excited states of ¹⁶O, by studying the ¹⁵N(³He,n) ¹⁷F*(p) ¹⁶O and ¹⁸O(³He, α)¹⁷O*(n) ¹⁶O reactions.

The ¹⁹F(³He,n) ²¹Na reaction was studied at incident energies between 4.2 and 5.9 MeV using a pulsed-beam neutron-time-of-flight spectrometer. Two T = 3/2 levels were identified at excitation energies of 8.99 ± 0.05 MeV (J > ½) and 9.22 ± 0.015 MeV (J ^π = ½⁺, Γ ˂ 40 keV). The spins and parities were determined by a comparison of the measured angular distributions with the results of DWBA calculations.

These two levels were also obsesrved as isospin-forbidden resonances in the ²⁰Ne(p,p) and ²⁰Ne(p,p’) reactions. Excitation energies were measured and spins, parities, and widths were determined from a single level dispersion theory analysis. The following results were obtained:

E_x = 8.973 ± 0.007 MeV, J ^π = 5/2 ⁺ or 3/2⁺, Γ ≤ 1.2 keV,

^Γp_o = 0.1 ± 0.05 keV; E_x = 9.217 ± 0.007 MeV, J^π = ½ ⁺,

Γ = 2.3 ± 0.5 keV, ^Γp_o = 1.1 ± 0.3 keV.

Isospin assignments were made on the basis of excitation energies, spins, parities, and widths.

Branching ratios for the isospin-nonconserving proton decays of the 11.20 MeV, T = 3/2 level in ¹⁷F were measured by the ¹⁵N(³He,n) ¹⁷ F*(p) ¹⁶O reaction to be 0.088 ± 0.016 to the ground state of ¹⁶O and 0.22 ± 0.04 to the unresolved 6.05 and 6.13 MeV levels of ¹⁶O. Branching ratios for the neutron decays of the analogous T = 3/2 level, at 11.08 MeV in ¹⁷O, were measured by the ¹⁶O(³He, α)¹⁷O*(n)¹⁶O reaction to be 0.91 ± 0.15 to the ground state of ¹⁶O and 0.05 ± 0.02 to the unresolved 6.05 and 6.13 MeV states. By comparing the ratios of reduced widths for the mirror decays, the form of the isospin impurity in the T = 3/2 levels is shown to depend on T_z.

Electromagnetic decay of the 1.7- and 2.43-MeV levels in ^9Be

The 1.7- and 2.43-MeV levels in ⁹Be were populated with the reaction ¹¹B(d, α)⁹Be* by bombarding thin boron on carbon foils with 1.7-MeV deuterons. The alpha particles were analyzed in energy with a surface-barrier counter set at the unique kinematically determined angle and the recoiling ⁹Be nuclei at 90^o were analyzed in rigidity with a magnetic spectrometer, in energy by a surface-barrier counter at the spectrometer focus, and in velocity by the time delay between an alpha and a ⁹Be count. When a pulse from the spectrometer counter was in the appropriate delayed coincidence with a pulse from the alpha counter, the two pulses were recorded in a two-dimensional pulse height analyzer. Most of the ⁹Be* decay by particle breakup. Only those that gamma decay are detected by the spectrometer counter. Thus the experiment provides a direct measurement of Γ_rad/Γ. Analysis of 384 observed events gives Γ_rad/Γ = (1.16 ± 0.14) X 10^-4 for the 2.43-MeV level. Combining this ratio with the value of Γ_rad = 0.122 ± 0.015 eV found from inelastic electron scattering gives Γ = (1.05 ± 0.18) keV. For the 1.7-MeV level, an upper limit, Γ_rad/Γ ≤ 2.4 = 10^-5, was determined.

Photochemical electron transfer at fixed distance : a synthetic model of the photosynthetic primary process

A series of meso-phenyloctamethylporphyrins covalently bonded at the 4'phenyl position to quinones via rigid bicyclo[2.2.2]octane spacers were synthesized for the study of the dependence of electron transfer reaction rate on solvent, distance, temperature, and energy gap. A general and convergent synthesis was developed based on the condensation of ac-biladienes with masked quinonespacer-benzaldehydes. From picosecond fluorescence spectroscopy emission lifetimes were measured in seven solvents of varying polarity. Rate constants were determined to vary from 5.0x10⁹sec^-1 in N,N-dimethylformamide to 1.15x10¹⁰ Sec^-1 in benzene, and were observed to rise at most by about a factor of three with decreasing solvent polarity. Experiments at low temperature in 2-MTHF glass (77K) revealed fast, nearly temperature-independent electron transfer characterized by non-exponential fluorescence decays, in contrast to monophasic behavior in fluid solution at 298K. This example evidently represents the first photosynthetic model system not based on proteins to display nearly temperature-independent electron transfer at high temperatures (nuclear tunneling). Low temperatures appear to freeze out the rotational motion of the chromophores, and the observed nonexponential fluorescence decays may be explained as a result of electron transfer from an ensemble of rotational conformations. The nonexponentiality demonstrates the sensitivity of the electron transfer rate to the precise magnitude of the electronic matrix element, which supports the expectation that electron transfer is nonadiabatic in this system. The addition of a second bicyclooctane moiety (15 Å vs. 18 Å edge-to-edge between porphyrin and quinone) reduces the transfer rate by at least a factor of 500-1500. Porphyrinquinones with variously substituted quinones allowed an examination of the dependence of the electron transfer rate constant κ_ET on reaction driving force. The classical trend of increasing rate versus increasing exothermicity occurs from 0.7 eV≤ |ΔG^0'(R)| ≤ 1.0 eV until a maximum is reached (κ_ET = 3 x 10⁸ sec^-1 rising to 1.15 x 10¹⁰ sec^-1 in acetonitrile). The rate remains insensitive to ΔG⁰ for ~ 300 mV from 1.0 eV≤ |ΔG^0’(R)| ≤ 1.3 eV, and then slightly decreases in the most exothermic case studied (cyanoquinone, κ_ET = 5 x 10⁹ sec^-1).

CP and the three pion decay of the K°

The time distribution of the decays of an initially pure K° beam into π+π-π° has been analyzed to determine the complex parameter W (also known as Ƞ^+-° and (x + iy)). The K° beam was produced in a brass target by the interactions of a 2.85 GeV/c π- beam which was generated on an internal target in the Lawrence Radiation Laboratory (LRL) Bevatron. The counters and hodoscopes in the apparatus selected for events with a neutral (K°) produced in the brass target, two charged secondaries passing through a magnet spectrometer and a ɣ-ray shower in a shower hodoscope.

From the 275K apparatus triggers, 148 K → π+π-π° events were isolated. The presence of a ɣ-ray shower in the optical shower chambers and a two-prong vee in the optical spark chambers were devices used to isolate the events. The backgrounds were further reduced by reconstructing the momenta of the two charged secondaries and applying kinematic constraints.

The best fit to the final sample of 148 events distributed between .3 and 7.0 K_S lifetimes gives:

ReW = -.05 ±.17

ImW = +.39 +.35/-.37

This result is consistent with both CPT invariance (ReW = 0) and CP invariance (W = 0). Backgrounds are estimated to be less than 10% and systematic effects have also been estimated to be negligible.

An analysis of the present data on CP violation in this decay mode and other K° decay modes has estimated the phase of ɛ to be 45.3 ± 2.3 degrees. This result is consistent with the super weak theories of CP violation which predicts the phase of ɛ to be 43°. This estimate is in turn used to predict the phase of Ƞ°° to be 48.0 ± 7.9 degrees. This is a substantial improvement on presently available measurements. The largest error in this analysis comes from the present limits on W from the world average of recent experiments. The K → πuʋ mode produces the next largest error. Therefore further experimentation in these modes would be useful.