Physics
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Item Multiadatom effects in the chemisorption energy of ordered overlayers(American Physical Society, 1977) Einstein, Theodore L.The indirect interaction energy per adatom is evaluated for a c(2x2) overlayer in a model system, and is found to be very well approximated by (twice) the next-nearest-neighbor pair interaction energy, verifying the validity of earlier work. Three adatom (nonpairwise) interaction energies are also considered; while insignificant for total interaction energies, they are comparable to more-distant (viz., third-) neighbor pair interactions.Item Indirect Interaction between Adatoms on a Tight-Binding Solid(American Physical Society, 1973) Einstein, Theodore L.; Schrieffer, J. R.The indirect interaction between adatom pairs on the (100) surface of a simple-cubic tight-binding solid is investigated within a molecular-orbital approach. A general scheme for calculating the surface-density-of-states change and the interaction energy of one and two single-level adatoms is presented, and contact (and a correction) is made with Grimley's formulation. The method permits binding above surface atoms, at bridge sites, or at centered positions, and yields interaction energy as a function of band filling, adatom energy level, and a general hopping potential V between an adatom and the nearest surface atom(s).Item Statistical Mechanics of a Simple Model of a Displacive Ferroelectric(American Physical Society, 1973) Cohen, Michael; Einstein, Theodore L.Item Short-chain model of chemisorption: Exact and approximate results(American Physical Society, 1975) Einstein, Theodore L.The binding energy of an adatom to a chain consisting of three atoms is obtained exactly by computer as a function of adatom Coulomb repulsion, adatom-substrate hopping, and substrate bandwidth. Three simple approximations are also plotted: (i) weak-binding limit, in which the binding energy is given by the expectation value of the adatom-bulk hopping Hamiltonian calculated in second-order perturbation theory; (ii) rebonded surface complex, in which the adatom forms a diatomic molecule with its nearest neighbor in the chain, and the dimer rebonds perturbatively to the indented chain; and (iii) Hartree-Fock, both restricted and unrestricted. The first two schemes can be joined smoothly by hand, and the resulting curve is much better than Hartree-Fock. The physics of all three cases is carefully studied. An appendix treats the surface diatom case of just a single bulk atom. Here the exact solution and unrestricted Hartree-Fock can be performed analytically. Comparison is also given with Brenig and Schönhammer's solution based on Green's-function formalism with matrix self-energy corrections.Item Changes in density of states caused by chemisorption(American Physical Society, 1975) Einstein, Theodore L.The process of chemisorption is studied via the change in density of states when an adatom with a single level Ea bonds by a hopping parameter V to the (100) surface of an s-band simple cubic crystal. As V increases, the bond changes from a perturbative regime to the formation of a surface complex. Investigations of local and layer-summed show this dimerlike structure to be well localized near the bond. Steric effects (binding-site symmetry) are easily introduced. A damping parameter can be added to simulate decay effects of surface probes. Application of the model to photoemission angular-averaged and angular-resolved difference spectra for light gases on tungsten gives understanding of the bonding peak near the bottom of the band, of the depletion of states near the Fermi energy, and of the slight shifting of the energy-momentum-conserving peak.Item Partially Covariant Quantum Theory of Gravitation(1972) Moncrief, Vincent E.; Nutku, Yavuz; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, MD)In this thesis it is argued that a strict law of conservation of probability is necessary for the unambiguous interpretation of any proposed quantum theory of gravitation. After a brief review of the current canonicnl methods for quantizing the gravitational field we conclude that they do not guarantee conservation of probability owing to the difficulty of finding a suitable intrinsic time coordinate. In an attempt to circumvent this problem we have proposed an alternative method of quantization which has a conventional Schrodinger equation and therefore a law of probability conservation. This result is achieved by imposing a weaker form of the quantum constraint equations than that of the conventional theory. In order to justify this approach it is necessary to show that, in spite of the weak form of the constraint equations, the Einstein theory is recovered in the classical limit . A partial proof of the desired result is given. The proposed quantum theory is developed somewhat by considering the interaction of matter and gravitational fields. Quantum analogs of the covariant conservation laws are derived for the special case of a massive spin-zero field. Charge conservation is also considered and an invariant scheme for defining the number of particles and anti-particles is developed.Item Investigation of Vanishing of a Horizon for Bianchi Type IX (the Mixmaster) Universe(1972) Chitre, D.M.; Misner, Charles W.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)In this dissertation, the generic, non-rotating, homogeneous closed model universe ( the "Mixmaster Universe", Bianchi Type IX) is studied to gain some insight into how the broad-scale homogeneity of the universe may have been produced at very early times. We begin our discussion by sketching the development of relativistic cosmology until the last decade. In the second chapter we discuss particle horizons in the Robertson-Walker models. These standard models of the universe possess particle horizons. Thus, only a finite part of such a universe could have been causally connected; while the isotropy of 2.7°K microwave radiation implies the universe to be homogeneous on a much larger scale than the size of the horizon. The third chapter discusses in detail the evolution of the Mixmaster Universe near the singularity using the Hamiltonian techniques developed by Misner for these models . At a fixed time (or volume) epoch Ω0, a Mixmaster Universe is specified by initial conditions' β+, β- (shape anisotropy) and p+ , p- (expansion rate anisotropy). In the fourth chapter we derive the equations for rays of high-frequency sound waves and light waves. When these equations are applied in the Mixmaster Universe, we find that for certain subsets of initial conditions, some of these sound rays and light rays would circumnavigate the corresponding universes in certain directions. Our results for light rays parallel those of Doroshkevich and Novikov, however we use entirely different methods (Hamiltonian methods) for treating the Einstein equations. In the last chapter the evolution of the Mixmaster Universe is shown equivalent to a geodesic flow within a bounded region of the Lobatchewsky plane. The boundary shape makes this flow Ergodic. The ergodicity is proved by invoking a certain group of conformal transformations, G, which makes this flow of broken geodesics on the Lobatchewsky plane, D, into a continuous one on D/G. The Einstein equations in this problem lead to a natural measure on initial conditions related to β+, p+. The measure of the circumnavigation sets depends upon the epoch and it goes to zero as the volume of the universe shrinks to zero. Finally, we compute the probability for circumnavigation along any one axis of the universe, It turns out to be roughly 1% for an empty universe and it decreases to 0.02% for realistic models containing radiation and matter in them.Item A Direct Measurement of the Relativistic Effect of the Gravitational Potential on the Rats of Atomic Clocks Flown in an Aircraft(1976) Williams, Ralph Emerson; Alley, C . O.; Physics and Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)General relativity predicts that standard clocks placed at differing gravitational potentials will run at different rates. Although experiments confirming the gravitational redshift have been done, they involve frequency and not time, and need not appeal to general relativity for explanation. Therefore, considerable interest exists as to the result of an accurate experiment in which real macroscopic clocks are brought together for comparison before and after separation to differing potentials. This experiment consists of flying an ensemble of atomic clocks in a military aircraft and comparing them before and after flight to another clock ensemble remaining on the ground. The ground ensemble included several Hewlett-Packard Cesium Beam clocks, three Efratom optically pumped Rubidium clocks, and two hydrogen masers. The flying ensemble included at least three Hewlett-Packard Cesium clocks and three Efratom Rubidium clocks. Five of the Cesium clocks were new models delivered with a high beam current option resulting in higher stability than standard models. The clocks were maintained under stringent environmental controls to protect against vibration, magnetic fields, and changes in temperature, pressure, and power supply voltage. Five main flights were ma de, each at approximately 30,000 feet altitude for fifteen hours. The aircraft was continuously tracked by a theodolite calibrated radar which obtained position and velocity measurements for every second of flight. This allowed an accurate calculation of a theoretical prediction to compare to experiment. The flying clocks gained approximately 45 nanoseconds (45 x 10-9 s) with respect to the ground clocks. The normalized results (measured effect divided by predicted effect) and the experimental standard deviations of the mean for each of the five flights were as follows: .999 + .016 .977 + .026 .963 + .013 1.002 + .026 .991 + .037 The result for the entire experiment, with standard deviation of the mean, was .987 ±. .011. The statistically expected standard deviation of the mean based on knowledge of clock quality was approximately .015. Considering this result as well as systematic errors, a final result is established of Measured value/ Predicted value = 0.987 ± .016Item The Li6(a,2a)d Reaction at 50 to 80 MeV(1970) Watson, John W.; Pugh, Howel G.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)The Li6(a,2a)d reaction was studied at 50.4, 59.0, 60.5, 70.3 and 79.6 MeV bombarding energy. For each bombarding energy, several coincident energy spectra of the two emitted a-particles were measured. Special emphasis was placed on measuring spectra at pairs of angles where zero momentum (in the laboratory frame of reference) was possible for the residual deuteron. Using the constraints on three body kinematics, events corresponding to an a+ a+ d final state were selected from the coincident energy spectra. The cross section for these events was projected onto the E1 energy axis of the coincident spectra. The projected energy spectra were analyzed with the Plane Wave Impulse Approximation. From those points in the projected spectra which corresponded to zero deuteron recoil momentum, off-mass-shell a-a scattering cross sections were extracted. These were found to be in excellent agreement with free a-a scattering cross sections, if free cross sections for the final state center of mass energy of the two a's in the Li6 (a,2a)d reaction were chosen for the comparison. Off- mass-shell a-a cross sections were also extracted for data where the residual deuteron had a momentum of 30 MeV/c. These cross sections were also found to agree with free a-a scattering, but it was necessary to introduce an ad hoc shift in the a-a scattering angle to produce this agreement. Predictions of off-mass-shell a-a cross sections were made using a potential model. These indicate that the off-mass-shell cross section should indeed be very similar to the on-mass-shell cross section at the final state energy. Using the Plane Wave Impulse Approximation a momentum distribution for a's in Li6 was extracted from the experimental data. A cluster model for Li6 was devised to fit the binding energy and r.m.s. charge radius of Li6, as well as the 3s1 a-d scattering phase shift. For comparison with the experimental data, the momentum wave function of the a-particle in Li6 was calculated by taking the Fourier transform of the a-d relative motion. The theoretical and experimental momentum distributions were found to be in serious disagreement, both in magnitude and width at half maximum. By introducing a cut-off radius into the theoretical wave function, the discrepancies between theory and experiment were accounted for. It was also found, that if the cut-off radius is used as an adjustable parameter, then this Li6 wave function and reaction model explains the magnitudes and widths of the a-d relative momentum distributions determined from a wide variety of other reactions.Item A Field Theory of Extended Particles Based on Covariant Harmonic Oscillator Wavefunctions(1976) Karr, Thomas John; Kim, Young Suh; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)We attempt to combine the covariant harmonic oscillator (CHO) quark model with second quantized field theory. We review the CHO formalism for a system of two quarks (meson). We introduce a mesonic field Φ(x1 ,x2) that depends on the position of both quarks, and then derive the field equations from a covariant lagrangian L(x1, x2). The CHO equation allows a complete separation of the average meson coordinate X from the relative quark coordinate ξ. The CHO wavefunction in the field expresses the extended size and internal structure of the meson. Φ, describes mesons in the ground state and any excited state , with angular momentum ∞ mass^2. From Φ we construct conserved tensors like P^μ the meson momentum. We second quantize Φ in the X variable only and discuss the extended particle commutation relations. We investigate a Φ^3-type meson interaction where the vertex function is an overlap integral of the wavefunctions entering the interaction region. We derive a nonlinear integrodifferential equation for the U matrix , linearize and solve it by perturbation theory. The result is simple diagramatic rules for the S matrix. The S matrix is covariant and unitary. We do not find any contradiction between the principles of QFT and the CHO quark model. The Φ field theory includes scalar meson(point particle)theory as a special case, while its greater generality illuminates the difference between point and extended particles.