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Item Crenshaw transcripts 2023(0023-08-24) Crenshaw, Kenyatta; Elby, AndrewItem Vapor Pressures of Saturated Aqueous Salt Solutions of Selected Inorganic Salts(1965) Acheson, Donald Theodore; Mason, Edward A.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)The vapor pressure of saturated aqueous salt solutions as functions of temperature have been measured for lithium bromide, lithium iodide, sodium bromide, potassium hydroxide, cesium fluoride, and zinc bromide. The temperature range is about plus s 0 c. to 70°c., with this range extended from minus 10°c. to plus 105°c. for lithium bromide and restricted to plus s 0 c. to 35°c. for sodium bromide. Vapor pressures, water 0 activities, and heats of vaporization and solution are tabulated at 5 C. intervals except in the vicinities of changes of hydration of the solid phase, where pressures and activities are plotted with sufficient frequency to show details. The experimental uncertainty in pressure is + 10 x 10-3 millibars and that in the heat of solution is+ 2 percent.Item Infinite Red-Shifts in General Relativity(Cornell University Press, 1967) Misner, Charles W; Beckedorff, David LThe Oppenheimer-Snyder description of continued gravitational collapse is reformulated as a matching together of two familiar solutions of the Einstein gravitational equations. From one solution, the Friedmann cosmology with zero-pressure matter, one selects the interior of a sphere whose points move on timelike geodesics. From the other solution one selects the exterior of such a sphere in the vacuum Schwarzschild solution. For the expected choice of parameters (sphere circumference, interior density, exterior mass) these can be fit together smoothly enough to satisfy the Einstein equations. The matching conditions are that the first and second fundamental forms at the joining 3-surface agree. The description of this collapsing ball of matter survives its passage through Finkelstein's (1958) smooth unidirectional membrane€ at r=2M and is most conveniently presented using the Kruskal coordinates for the Schwarzschild solution. This project was proposed and designed by Misner (choice of solutions and matching requirements), but the execution and first written presentation were carried out by Beckedorff and provided his Princeton senior thesis in April 1962. ( http://www.physics.umd.edu/grt/cwm/Beckedorff1962.pdf ) In this 1963 presentation Misner emphasizes that the properties of matter at high densities are irrelevant to the question of whether such a collapse can occur for sufficiently massive objects. The detailed computations by Beckedorff are here linked in an appended file.Item Almost Symmetric Spaces and Gravitational Radiation(1967) Matzner, Richard Alfred; Misner, Charles W.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Item Gravitational Radiation in the Limit of High Frequency(1967) Isaacson, Richard Allen; Misner, Charles W.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)This dissertation deals with a technique for obtaining approximate radiative solutions to the Einstein equations of general relativity in situations where the gravitational fields of interest are quite strong. In the first chapter, we review the history of the problem and discuss previous work along related lines. In the second chapter, we assume the radiation to be of high frequency and expand the field equations in powers of the small wavelength this supplies. This assumption provides an approximation scheme valid for all orders of 1/r, for arbitrary velocities up to that of light, and for arbitrary intensities of the gravitational field. To lowest order we obtain a gauge invariant linear wave equation for gravitational radiation, which is a covariant generalization of that for massless spin-two fields in flat space, This wave equation is then solved by the W.K.B. approximation to show that gravitational waves travel on null geodesics with amplitude and frequency modified by gravitational fields in exactly the same way as are those of light waves, and with their polarization parallel transported along the geodesics, again as is the case for light. The metric containing high frequency gravitational waves is shown to be type N to lowest order, and some limits to the methods used are discussed. In the third chapter we go beyond the linear terms in the high frequency expansion, and consider the lowest order non-linear terms. They are shown to provide a natural, gauge invariant, averaged effective stress tensor for the energy localized in the high frequency radiation. By assuming the W.K.B. form for the field, this tensor is found to have the same structure as that for an electromagnetic null field. A Poynting vector is used to investigate the flow of energy and momentum in the gravitational wave field, and it is seen that high frequency waves propagate along null hypersurfaces and are not backscattered off by the curvature of space. Expressions for the total energy and momentum carried by the field to flat null infinity are given in terms of coordinate independent integrals valid within regions of strong field strength. The formalism is applied to the case of spherical gravitational waves where a news function is obtained, and where the source is found to lose exactly the energy and momentum contained in the radiation field.Item The Stability of the Schwarzschild Metric(1968) Vishveshwara, C. V.; Misner, Charles W.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)The stability of the Schwarzschild exterior metric against small perturbations is investigated. The exterior extending from the Schwarzschild radius r =2m to spatial infinity is visualized as having been produced by a spherically symmetric mass distribution that collapsed into the Schwarzschild horizon in the remote past. As a preamble to the stability analysis, the phenomenon of spherically symmetric gravitational collapse is discussed under the conditions of zero pressure, absence of rotation and adiabatic flow. This is followed by a brief study of the Kruskal coordinates in which the apparent singularity at r = 2m is no longer present; the process of spherical collapse and the consequent production of the Schwarzschild empty space geometry down to the Schwarzschild horizon are depicted on the Kruskal diagram. The perturbations superposed on the Schwarzschild background metric are the same as those given by Regge and Wheeler consisting of odd and even parity classes, and with the time dependence exp(-ikt), where k is the frequency. An analysis of the Einstein field equations computed to first order in the perturbations away from the Schwarzschild background metric shows that when the frequency is made purely imaginary, the solutions that vanish at large values of r, conforming to the requirement of asymptotic flatness, will diverge near the Schwarzschild surface in the Kruskal coordinates even at the initial instant t = 0. Since the background metric itself is finite at this surface, the above behaviour of the perturbation clearly contradicts the basic assumption that the perturbations are small compared to .the background metric. Thus perturbations with imaginary frequencies that grow exponentially with time are physically unacceptable and hence the metric is stable. In the case of the odd perturbations, the above proof of stability is made rigorous by showing that the radial functions for real values of k form a complete set, by superposition of which any well behaved initial perturbation can be represented so that the time development of such a perturbation is non-divergent, since each of the component modes is purely oscillatory in time. A similar rigorous extension of the proof of stability has not been possible in the case of the even perturbations because the frequency (or k2) does not appear linearly in the differential equation. A study of stationary perturbations (k = 0) shows that the only nontrivial stationary perturbation that can exist is that due to the rotation of the source which is given by the odd perturbation with the angular momentum £ = 1. Finally, complex frequencies are introduced under the boundary conditions of only outgoing waves at infinity and purely incoming waves at the Schwarzschild surface. The physical significance of this situation is discussed and its connection with phenomena such as radiation damping and resonance scattering, and with the idea of causality is pointed out.Item 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 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 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 Electrons and Spin Waves in Itinerant Ferromagnets(1976) Murray, Joanne; Korenman, Victor; Physics and Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Though it is accepted that the 3-d magnetic electrons of transition metals such as nickel are itinerant, at high temperature these itinerant ferromagnets act as if the electrons were localized at lattice sites. In particular, three experimental results conflict with the Stoner itinerant model: 1) The spin band gap does not decrease with temperature as the average magnetization, but much more slowly. 2) Spin waves of short wavelength propagate above the Curie temperature. 3) Magnetic degrees of freedom play a role in determining thermodynamic properties n ear and above TC. The source of these discrepancies is the failure of Stoner theory to take into account magnetization fluctuations. In this paper, I do calculations of single particle and spin wave properties in a generalization of Stoner theory devised by R. E. Prange and V. Korenman to take account of fluctuations. In Stoner theory, electrons interact with an effective magnetic field proportional to the average magnetization, which becomes zero at the phase transition. The basic idea of the generalization of Stoner theory is that electrons are sensitive to their local environment and therefore that electronic and spin wave properties should be calculated in the presence of a local slowly fluctuating magnetization configuration. Only after calculating these properties should the fluctuations be thermally averaged. As a result, electrons interact with an effective magnetic field which is basically proportional to the magnitude of the local magnetization vector and which need not become zero at TC. Single particle properties are calculated by making a transformation to the spatially varying frame of reference of the local magnetization and doing perturbation theory with the magnetization gradients as the small perturbation parameter. We find that the spin eigenstates are approximately in or opposite to the direction of the local magnetization. Even when there is no longer a macroscopic magnetization, an energy gap is maintained between spin-split bands, the bands now being defined in terms of the local magnetization direction. The change in the energy gap from its zero temperature value is proportional only to the average square o f a magnetization gradient, a quantity which may be small even above TC. Thus we can understand that the gap changes only slowly with temperature and that the spin wave does not decay into Stoner single particle excitations even at high temperature. A free energy is found which is very similar in form to the free energy used to compute thermodynamic properties in localized models; thus we find that magnetic degrees of freedom are still important in computing thermodynamic properties above TC. It is the existence of a population difference and energy gap, rather than a macroscopic average magnetization that permits the existence of a spin flip collective excitation. We find a secular equation for the spin wave frequency in the presence of fluctuations which is very similar to the usua1 RPA secular equation, except for small perturbations proportional to the square of magnetization gradients. The corrections to the spin wave frequency and lifetime include the effect of the perturbation of single electron energies by the background, and also of the scattering of the spin wave from single particle spin-conserving excitations and from other spin waves. These corrections are quite small and allow for propagation even above TC. Thus it is a prediction of our theory that one see spin waves even above the critical temperature, so long as an appropriate Population difference maintains a locally ordered magnetization.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 Gravitational Radiation Detection(1976) Rydbeck, Gustaf H. B.; Weber, Joseph; Physics and Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)This dissertation studies resonant gravitational wave detectors and related data analysis. Different forms (strain amplitude) of the equation of motion for a medium responding to a gravitational wave are discussed in relation to the detection of such waves. Utilizing "Bayesian techniques" an optimal method for data analysis is developed. Noise and filter theory is reviewed. It is seen that the “Bayesian techniques" integrates filter theory and data analysis, providing both filter properties and optimal methods for integrating the data.(In particular the method leads to a non threshold type of analysis, and "looks for" correlation between two detectors without the use of time delay). Expressions for optimal sensitivity (and filters) of detector systems are given, including the limit of perfect sensors and electronics. The signal to noise ratio in terms of the spectral power of the gravitational radiation is derived. Long baseline interferometry is discussed. A computer program simulating a pair of Weber type detectors is developed to study different approaches to data analysis.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.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 Effect of the central atom potential on the extended fine structure above appearance potential thresholds(American Physical Society, 1980) Laramore, G.E.; Einstein, Theodore L.; Roelofs, L. D.; Park, Robert L.The formalism previously given for describing the extended fine structure above appearance-potential-spectroscopy (APS) thresholds is extended by incorporating the effects of the excited "central" atom potential in an exact manner. The excitation-matrix elements are expressed in terms of the exact wave functions of the central atom potential. This introduces a "phase renormalization" into the excitation-matrix elements and eliminates a previously noted "phase difference" between single- and multiple-scattering calculations employing a plane-wave basis set. A series of approximations is then made which leads to an expression for the APS extended fine structure in terms of sinusoidal functions and hence provides a rationale for a Fourier-transform analysis. Simple model calculations assuming a constant "bare" excitation-matrix element, a spherically symmetric electronic density of states, and only S-wave scattering from the atomic cores are performed for a cluster of atoms having the atomic geometry of bulk vanadium. These calculations display the major predictions of the formalism and indicate that for a given system there may be some optimal energy range for data analysis. The problem of electron characteristic losses is considered, and it is pointed out that in the small-momentum-transfer limit the simple dipole selection rules appropriate to a photon-excitation process again apply. This may obviate many of the problems introduced by multiple angular momentum final states in the APS process.Item Extended Appearance-Potential Fine-Structure Analysis: Oxygen on Al(100)(American Physical Society, 1980) Laramore, G.E.; Einstein, Theodore L.; Roelofs, L. D.; Park, Robert L.To measure O-Al separation at Al(100) surfaces disordered (low-energy electron-diffraction beams extinguished) by reaction with oxygen, the extended appearance-potential fine structure was analyzed above the threshold for electron-bombardment excitation of the O 1s core. Calculation shows that the outgoing electron has angular momentum l=0, allowing simple Fourier inversion of the fine structure. The separation, 1.9+-0.05 A, suggests that oxygen lies under the top layer, a result undetectable in extended-x-ray-absorption fine-structure measurements on thicker films.