A measurement of the proton elastic form factors for 1 ≤ Q^2 ≤ 3 (GeV/c)^2

We report measurements of the proton form factors, G^p_E and G^p_M, extracted from elastic electron scattering in the range 1 ≤ Q^2 ≤ 3 (GeV/c)^2 with uncertainties of <15% in G^p_E and <3% in G^p_M. The results for G^p_E are somewhat larger than indicated by most theoretical parameterizations. The ratio of Pauli and Dirac form factors, Q^2(F^p_2/F^p_1), is lower in value and demonstrates less Q^2 dependence than these parameterizations have indicated. Comparisons are made to theoretical models, including those based on perturbative QCD, vector-meson dominance, QCD sum rules, and diquark constituents to the proton. A global extraction of the form factors, including previous elastic scattering measurements, is also presented.

Reactions of platinum(II) complexes with dioxygen: progress toward alkane functionalization

Whereas stoichiometric activation of C-H bonds by complexes of transition metals is becoming increasingly common, selective functionalization of alkanes remains a formidable challenge in organometallic chemistry. The recent advances in catalytic alkane functionalization by transition-metal complexes are summarized in Chapter I.

The studies of the displacement of pentafluoropyridine in [(tmeda)Pt(CH_3)(NC_5F_5)][BAr^f_4] (1) with γ- tetrafluoropicoline, a very poor nucleophile, are reported in Chapter II. The ligand substitution occurs by a dissociative interchange mechanism. This result implies that dissociative loss of pentafluoropyridine is the rate-limiting step in the C-H activation reactions of 1.

Oxidation of dimethylplatinum(II) complexes (N-N)Pt(CH_3)_2 (N-N = tmeda(1), α-diimines) by dioxygen is described in Chapter III. Mechanistic studies suggest a two-step mechanism. First, a hydroperoxoplatinum(IV) complex is formed in a reaction between (N-N)Pt(CH_3)_2 and dioxygen. Next, the hydroperoxy complex reacts with a second equivalent of (N-N)Pt(CH_3)_2 to afford the final product, (N-N)Pt(OH)(OCH_3)(CH_3)_2. The hydroperoxy intermediate, (tmeda)Pt(OOH)(OCH_3)(CH_3)_2 (2), was isolated and characterized. The reactivity of 2 with several dime thylplatinum(II) complexes is reported.

The studies described in Chapter IV are directed toward the development of a platinum(II)-catalyzed oxidative alkane dehydrogenation. Stoichiometric conversion of alkanes (cyclohexane, ethane) to olefins (cyclohexene, ethylene) is achieved by C-H activation with [(N-N)Pt(CH_3)(CF_3CH_2OH)]BF_4 (1, N-N is N,N'-bis(3,5-di-t- butylphenyl)-1,4-diazabutadiene) which results in the formation of olefin hydride complexes. The first step in the C-H activation reaction is formation of a platinum(II) alkyl which undergoes β-hydrogen elimination to afford the olefin hydride complex. The cationic ethylplatinum(II) intermediate can be generated in situ by treating diethylplatinum(II) compounds with acids. Treatment of (phen)PtEt_2 with [H(OEt_2)_2]Bar^f_4 at low temperatures resulted in the formation of a mixture of [(phen)PtEt(OEt_2)]Bar^f_4 (8) and [(phen)Pt(C_2H_4)H] Bar^f_4 (7). The cationic olefin complexes are unreactive toward dioxygen or hydrogen peroxide. Since the success of the overall catalytic cycle depends on our ability to oxidize the olefin hydride complexes, a series of neutral olefin complexes of platinum(II) with monoanionic ligands (derivatives of pyrrole-2-carboxyaldehyde N-aryl imines) was prepared. Unfortunately, these are also stable to oxidation.

A study of T = 2 states in ^(12)B, ^(12)C, ^(20)F and ^(28)Al

The lowest T = 2 states have been identified and studied in the nuclei ¹²C, ¹²B, ²⁰F and and ²⁸Al. The first two of these were produced in the reactions ¹⁴C(p,t)¹²C and ¹⁴C (p,³He)¹²B, at 50.5 and 63.4 MeV incident proton energy respectively, at the Oak Ridge National Laboratory. The T = 2 states in ²⁰F and ²⁸Al were observed in (³He,p) reactions at 12-MeV incident energy, with the Caltech Tandem accelerator.

The results for the four nuclei studied are summarized below:

(1) ¹²C: the lowest T = 2 state was located at an excitation energy of 27595 ± 20 keV, and has a width less than 35 keV.

(2) ¹²B: the lowest T = 2 state was found at an excitation energy of 12710 ± 20 keV. The width was determined to be less than 54 keV and the spin and parity were confirmed to be 0⁺. A second ¹²B state (or doublet) was observed at an excitation energy of 14860 ± 30 keV with a width (if the group corresponds to a single state) of 226 ± 30 keV.

(3) ²⁰F: the lowest T = 2 state was observed at an excitation of 6513 ± 5 keV; the spin and parity were confirmed to be 0⁺. A second state, tentatively identified as T = 2 from the level spacing, was located at 8210 ± 6 keV.

(4) ²⁸Al: the lowest T = 2 state was identified at an excitation of 5997 ± 6 keV; the spin and parity were confirmed to be 0⁺. A second state at an excitation energy of 7491 ± 11 keV is tentatively identified as T = 2, with a corresponding (tentative) spin and parity assignment J^π = 2⁺.

The results of the present work and the other known masses of T = 2 states and nuclei for 8 ≤ A ≤ 28 are summarized, and massequation coefficients have been extracted for these multiplets. These coefficients were compared with those from T = 1 multiplets, and then used to predict the mass and stability of each of the unobserved members of the T = 2 multiplets.

Crustal structure in Southern California from array data

Crustal structure in Southern California is investigated using travel times from over 200 stations and thousands of local earthquakes. The data are divided into two sets of first arrivals representing a two-layer crust. The Pg arrivals have paths that refract at depths near 10 km and the Pn arrivals refract along the Moho discontinuity. These data are used to find lateral and azimuthal refractor velocity variations and to determine refractor topography.

In Chapter 2 the Pn raypaths are modeled using linear inverse theory. This enables statistical verification that static delays, lateral slowness variations and anisotropy are all significant parameters. However, because of the inherent size limitations of inverse theory, the full array data set could not be processed and the possible resolution was limited. The tomographic backprojection algorithm developed for Chapters 3 and 4 avoids these size problems. This algorithm allows us to process the data sequentially and to iteratively refine the solution. The variance and resolution for tomography are determined empirically using synthetic structures.

The Pg results spectacularly image the San Andreas Fault, the Garlock Fault and the San Jacinto Fault. The Mojave has slower velocities near 6.0 km/s while the Peninsular Ranges have higher velocities of over 6.5 km/s. The San Jacinto block has velocities only slightly above the Mojave velocities. It may have overthrust Mojave rocks. Surprisingly, the Transverse Ranges are not apparent at Pg depths. The batholiths in these mountains are possibly only surficial.

Pn velocities are fast in the Mojave, slow in Southern California Peninsular Ranges and slow north of the Garlock Fault. Pn anisotropy of 2% with a NWW fast direction exists in Southern California. A region of thin crust (22 km) centers around the Colorado River where the crust bas undergone basin and range type extension. Station delays see the Ventura and Los Angeles Basins but not the Salton Trough, where high velocity rocks underlie the sediments. The Transverse Ranges have a root in their eastern half but not in their western half. The Southern Coast Ranges also have a thickened crust but the Peninsular Ranges have no major root.

Sputtering by multiply-charged ions, and preferential sputtering of isotopic mixtures

Collector-type experiments have been conducted to investigate two different aspects of sputtering induced by keV ions. The first study looked for possible ejection mechanisms related to the primary charge state of the projectile. Targets of CsI and LiNbO_3 were bombarded with 48 keV Ar^(q+), and a Au target was bombarded with 60 keV Ar^(q+), for q = 4, 8, and 11. The collectors were analyzed using heavy-ion Rutherford backscattering spectroscopy to determine the differential angular sputtering yields; these and the corresponding total yields were examined for variations as a function of projectile charge state. For the Au target, no significant changes were seen, but for the insulating targets slight (~10%) enhancements were observed in the total yields as the projectile charge state was increased from 4+ to 11+.

In the second investigation, artificial ^(92)Mo/^(100)Mo targets were bombarded with 5 and 10 keV beams of Ar^+ and Xe^+ to study the isotopic fractionation of sputtered neutrals as a function of emission angle and projectile fluence. Using secondary ion mass spectroscopy to measure the isotope ratio on the collectors, material ejected into normal directions at low bombarding fluences (~ 10^(15) ions cm^(-2)) was found to be enriched in the light isotope by as much as ~70‰ compared to steady state. Similar results were found for secondary Mo ions sputtered by 14.5 keV O^-. For low-fluence 5 keV Xe^+ bombardment, the light-isotope enrichment at oblique angles was ~20‰ less than the corresponding enrichment in the normal direction. No angular dependence could be resolved for 5 keV Ar^+ projectiles at the lowest fluence. The above fractionation decreased to steady-state values after bombarding fluences of a few times 10^(16) ions cm^(-2) , with the angular dependence becoming more pronounced. The fractionation and total sputtering yield were found to be strongly correlated, indicating that the above effects may have been related to the presence of a modified target surface layer. The observed effects are consistent with other secondary ion measurements and multiple-interaction computer simulations, and are considerably larger than predicted by existing analytic theory.

Some generalizations of commutativity for linear transformations on a finite dimensional vector space

Let L be the algebra of all linear transformations on an n-dimensional vector space V over a field F and let A, B, ƐL. Let A_i+1 = A_iB - BA_i, i = 0, 1, 2,…, with A = A_o. Let f_k (A, B; σ) = A_2K+1 - ^σ1^A2K-1 ^{+ σ}2^A2K-3 -… +(-1)^Kσ_KA₁ where σ = (σ₁, σ₂,…, σ_K), σ_i belong to F and K = k(k-1)/2. Taussky and Wielandt [Proc. Amer. Math. Soc., 13(1962), 732-735] showed that f_n(A, B; σ) = 0 if σ_i is the i^th elementary symmetric function of (β₄- β_s)², 1 ≤ r ˂ s ≤ n, i = 1, 2, …, N, with N = n(n-1)/2, where β₄ are the characteristic roots of B. In this thesis we discuss relations involving f_k(X, Y; σ) where X, Y Ɛ L and 1 ≤ k ˂ n. We show: 1. If F is infinite and if for each X Ɛ L there exists σ so that f_k(A, X; σ) = 0 where 1 ≤ k ˂ n, then A is a scalar transformation. 2. If F is algebraically closed, a necessary and sufficient condition that there exists a basis of V with respect to which the matrices of A and B are both in block upper triangular form, where the blocks on the diagonals are either one- or two-dimensional, is that certain products X₁, X₂…X_r belong to the radical of the algebra generated by A and B over F, where X_i has the form f₂(A, P(A,B); σ), for all polynomials P(x, y). We partially generalize this to the case where the blocks have dimensions ≤ k. 3. If A and B generate L, if the characteristic of F does not divide n and if there exists σ so that f_k(A, B; σ) = 0, for some k with 1 ≤ k ˂ n, then the characteristic roots of B belong to the splitting field of g_k(w; σ) = w^2K+1 - σ₁w^2K-1 + σ₂w^2K-3 - …. +(-1)^K σ_Kw over F. We use this result to prove a theorem involving a generalized form of property L [cf. Motzkin and Taussky, Trans. Amer. Math. Soc., 73(1952), 108-114]. 4. Also we give mild generalizations of results of McCoy [Amer. Math. Soc. Bull., 42(1936), 592-600] and Drazin [Proc. London Math. Soc., 1(1951), 222-231].