A pair of nonidentical two-level atoms, separated by a fixed distance R, interact through photon exchange. The system is described by a state vector which is assumed to be a superposition of four "essential states": (1) the first atom is excited, the second one is in the ground state, and no photon is present, (2) the first atom is in its ground state, the second one is excited, and no photon is present, (3) both atoms are in their ground states and a photon is present, and (4) both atoms are excited and a photon is also present. The system is initially in state (1). The probabilities of each atom being excited are calculated for both the minimally-coupled interaction and the multipolar interaction in the electric dipole approximation. For the minimally-coupled interaction Hamiltonian, the second atom has a probability of being instantaneously excited, so the interaction is not retarded. For the multipolar interaction Hamiltonian, the second atom is not excited before the retardation time, which agrees with special relativity. For the minimally-coupled interaction the nonphysical result occurs because the unperturbed Hamiltonian is not the energy operator in the Coulomb gauge. For the multipolar Hamiltonian in the electric dipole approximation the …

The problem with which this investigation is concerned is that of measuring the rate coefficients for termolecular charge transfer reactions of He2+ in atmospheric pressure afterglows with the minority reacting species. Of particular interest was the discovery that the presence of a third body can change an improbable charge transfer reaction involving He+2 into a very probable one, as in the case of the reaction with argon. For example, in Tables II and II it was shown that less than a 300 torr pressure of helium was required to double the effective rate of reaction of argon with He2+ while over 3000 torr was required for CH4. The sensitivity of the method has been sufficient to detect termolecular components as small as 2 x 10-30 cm /sec and values were found to range widely from 2 x 10 for Ne to 67 x 10-30 cm6/sec for CO2. The size of these termolecular rates not only served to explain specific anomalous efficiencies of the charge transfer process observed in atmospheric pressure lasers but also suggested the general importance of three-body ion-molecule reactions in higher pressure plasmas.

A variation of the excite-and-probe technique is used to measure the picosecond evolution of laser-induced transient gratings that are produced in germanium by the direct absorption of 40 psec optical pulses at 1.06-μm. Grating lifetimes are determined for free carrier densities between 10¹⁸ cm⁻³ and 10²¹ cm⁻³ . For carrier densities less than 10¹⁹ cm⁻³ , a linear diffusion-recombination model for the grating provides a good fit to the experimental data and allows the extraction of the diffusion coefficient and an estimation of the linear recombination lifetime. Above carrier densities of approximately 10²⁰ cm⁻³ , the density dependence of the diffusion coefficient and nonlinear recombination processes must be considered. Numerical solutions to the resulting nonlinear partial differential equation are obtained that allow extraction of information concerning the high density diffusion coefficient and the nonlinear recombination rates.

Protons with energies ranging from 0.4 to 2.0 MeV were used to measure K-shell vacancy production cross sections (oVK) for N_2, CH_4, C_2H_4, C_2H_6, and CO_2 gas targets under single collision conditions. An electron-ion time-of-flight coincidence technique was used to determind the ration of the K-K electron capture cross section, OECK, to the K-vacancy production cross section, oVK. These ratios were then combined with the measured values of oVK to extract the K-K electron capture cross sections. Measurements were also made for protons of the same energy range but with regard to L-shell vacancy production and L-K electron capture for Ar targets. In addition, K-K electron capture cross sections were measured for 1.0 to 2.0 Mev 42He^_ ions on CH_4.

The picosecond optical response of germanium is investigated by performing excitation-probe experiments on a thin, intrinsic-germanium wafer maintained at 135 K. The results of three distinct experiments are reported: (1) the transmission of a single pulse is measured as a function of irradiance, (2) the probe transmission is measured at a fixed time after excitation as a function of the excitation energy, and (3) the transmission of a probe pulse is monitored as a function of time after excitation. These experiments employ 10-picosecond laser pulses at 1.06 um and Stokes-shifted pulses at 1.55-um.

Bulk laser-induced breakdown and self-focusing in single samples of fused quartz and NaCl were examined using picosecond optical pulses at 1.0 ym and 0.5 ym. The results of three separate but related experiments are reported. First the nonlinear index of refraction, n2, of each of the test materials is measured near the respective damage thresholds of the samples. The values of 1*2 were determined by detecting beam distortions in the far field, transmitted laser beam profile caused by the irradiance dependent index of refraction. The experimental traces were compared to theoretical beam profiles generated by a nonlinear propagation code and n2 was extracted from the resulting fits.

A system of nonrelativistic charged particles and radiation is canonically quantized in the Coulomb gauge and Maxwell's equations in quantum electrodynamics are derived. By requiring form invariance of the Schrodinger equation under a space and time dependent unitary transformation, operator gauge transformations on the quantized electromagnetic potentials and state vectors are introduced. These gauge transformed potentials have the same form as gauge transformations in non-Abelian gauge field theories. A gauge-invariant method for solving the time-dependent Schrodinger equation in quantum electrodynamics is given. Maxwell's equations are written in a form which holds in all gauges and which has formal similarity to the equations of motion of non-Abelian gauge fields. A gauge-invariant derivation of conservation of energy in quantum electrodynamics is given. An operator gauge transformation is made to the multipolar gauge in which the potentials are expressed in terms of the electromagnetic fields. The multipolar Hamiltonian is shown to be the minimally coupled Hamiltonian with the electromagnetic potentials in the multipolar gauge. The model of a charged harmonic oscillator in a single-mode electromagnetic field is considered as an example. The gauge-invariant procedure for solving the time-dependent Schrodinger equation is used to obtain the gauge-invariant probabilities that the oscillator is in an …

Incident ¹H⁺ and ⁴He⁺ ions at 0.3-2.6 MeV and ¹⁹F^q⁺ ions at 25, 27 and 35 MeV were used to study the M-shell x-ray production cross sections of Au, Pb, Bi and U. For the incident fluorine ions, projectile charge state dependence of the cross sections were extracted from measurements made with varying target thicknesses ( ~1 to ~300 μg/cm²). The efficiency of the Si(Li) detector was determined by measuring the K-shell x-ray production of various low Z elements and comparing these values to the prediction of the CPSS theory. The experimental results are compared to the prediction of first Born approximation for direct ionization to the continuum and to the OBK of Nikolaev for the electron capture to the K-, L-, M-...shells of the incident ion. Comparison is also made with the ECPSSR theory that accounts for the energy loss, Coulomb deflection, and relativistic effects in the perturbed stationary state theory.

An experiment has been completed which demonstrated quantum mechanical tunneling of electrons between two gold electrodes separated in vacuum. The tunneling current between the gold electrodes has been measured, for fixed voltages of 0.1 and 0.01 volts, as the electrode spacing was varied from a distance of approximately 2.0 nm down to a point where the electrodes touched. Current-voltage characteristics for fixed electrode spacing in the direct tunneling region have also been measured. Numerical calculations of the tunneling current based on the free-electron model of the electrodes and the barrier, an image-potential reduced barrier, and a WKB approximation for the tunneling probability have been performed and compared with Simmons' theory and with the experimental results. Within experimental error the results indicate that an image potential reduced barrier with the modifications suggested by Lang and Kohn gives a close approximation to the true barrier for metal-vacuum-metal tunneling. For the first time, the work function of the electrodes in a tunneling experiment has been deduced from experimental parameters independent of the tunneling device.

The Bogoliubov theory of excitations in superfluid helium is used to study collective modes at zero temperature. A repulsive delta function shell potential is used in the quasiparticle excitation energy spectrum to fit the observed elementary excitation spectrum, except in the plateau region. The linearized equation of motion method is used to obtain the secular equation for a collective mode consisting of a linear combination of one and two free quasiparticles of zero total momentum. It is shown that in this case for high-lying collective modes, vertices involving three quasiparticles cancel, and only vertices involving four quasiparticles are important. A decomposition into various angular momentum states is then made. Bound roton pairs in the angular momentum D-state observed in light-scattering experiments exist only for an attractive coupling between helium atoms in this oversimplified model. Thus, the interaction between particles can be reinterpreted as a phenomenological attractive coupling between quasiparticles, in order to explain the Raman scattering from bound roton pairs in superfluid helium.

The K-shell x-ray and ionization cross sections are measured for protons on Ag, Cd, Sn, Sb, Te, Ba, and La over the ion energy range of 0.6 to 2.0 MeV. The data are compared to the predictions of the PWBA, the PWBA with corrections for binding energy and/or Coulomb deflection, the BEA, and the constrained BEA predictions. In general, the non-relativistic PWBA with binding energy correction gives the best overall agreement with the measurements of proton-induced x-ray processes for the K-shell of the elements studied in this work. The data further suggest the need for relativistic PWBA treatment of the interactions in the K-shell for the range of binding energies represented by the elements investigated in this work.

The density amplitude of an isolated quantum vortex line in superfluid 4He is calculated using a generalized Gross-Pitaevskii (G-P) equation. The generalized G-P equation for the order parameter extends the usual mean-field approach by replacing the interatomic potential in the ordinary G-P equation by a local, static T matrix, which takes correlations between the particles into account. The T matrix is a sum of ladder diagrams appearing in a diagrammatic expansion of the mean field term in an exact equation for the order parameter. It is an effective interaction which is much softer than the realistic interatomic Morse dipole-dipole potential from which it is calculated. A numerical solution of the generalized G-P equation is required since it is a nonlinear integro-differential equation with infinite limits. For the energy denominator in the T matrix equation, a free-particle spectrum and the observed phonon-roton spectrum are each used. For the fraction of particles in the zero-momentum state (Bose-Einstein dondensate) which enters the equation, both a theoretical value of 0.1 and an experimental value of 0.024 are used. The chemical potential is adjusted so that the density as a function of distance from the vortex core approaches the bulk density asymptotically. Solutions of the …

This investigation is a theoretical study of the influence of defects of finite volume on the electrical conductivity in the quantum size effect regime. Correction terms to existing equations are derived, and a physical explanation of the results is given. Many macroscopic properties of films exhibit an oscillatory dependence on thickness when the thickness is comparable to the de Broglie wavelength of an electron at the Fermi surface. This behavior is called the quantum size effect. In very thin films, scattering from surfaces, phonons, and crystal defects plays an increasingly important role. In this investigation the influence of scattering centers (defects) in semimetal films on the electrical conductivity is explored by extending existing work to include scattering centers of finite range. The purpose of this study is to determine the overall change in the conductivity and the alteration of the amplitude of the oscillations. The Boltzmann transport equation is the starting point for the calculation. An equation for the vector mean free path is derived, and a solution is obtained by the iterative process. The relaxation approximation need not be made since the vector mean free path is determined. The sample is a thin slab that is infinite in two …

The purpose of this study is to determine the characteristics of the solar cosmic ray flux. This report describes the design and construction of a cosmic ray detector system used in this study and describes the analysis of the data obtained from these systems.

The Hartree-Fock-Bogoliubov theory of homogeneous boson systems at finite temperatures is rederived using, a free energy variational principle. It is shown that a t-matrix naturally emerges in the theory. Phenomenological modifications are made (1) to remove the energy gap at zero momentum, and (2) to eliminate the Hartree-Fock-like terms, which dress the kinetic energy of the particle. A numerical calculation of the energy spectrum is made over a temperature range of 0.00 to 3.14 K using the Morse dipole-dipole-2 potential and the Frost-Musulin potential. The energy spectrum of the elementary excitations is calculated self-consistently. It has a phonon behavior at low momentum and a roton behavior at higher momentum, so it is in qualitative agreement with the observed energy spectrum of liquid He II. However, the temperature dependence of the spectrum is incorrectly given. At the observed density of 0.0219 atoms A-3, the depletion of the zero-momentum state at zero temperature is 40.5% for the Morse dipole-dipole-2potential, and 43.2% for the Frost- Musulin potential. The depletion increases gradually until at 3.14 K the zero momentum density becomes zero discontinuously, which indicates a transition to the ideal Bose gas.

The gauge-invariant formulation of quantum mechanics is compared to the conventional approach for the case of a one-dimensional charged harmonic oscillator in an electromagnetic field in the electric dipole approximation. The probability of finding the oscillator in the ground state or excited states as a function of time is calculated, and the two approaches give different results. On the basis of gauge invariance, the gauge-invariant formulation of quantum mechanics gives the correct probability, while the conventional approach is incorrect for this problem. Therefore, expansion coefficients or a wave function cannot always be interpreted as probability amplitudes. For a physical interpretation as probability amplitudes the expansion coefficients must be gauge invariant.

In the course of experiments using uniaxial double alignment channeling to investigate radiation damage in single crystals, an anomalously large ion-scattering yield from the near surface of disordered or simulated disordered solid targets was observed. The chronology of the discovery of this new ion-solid effect and its explanation are presented along with experiments detailing the dependence of the new effect upon ion type and energy, as well as target atomic number and density. Targets included a spectrum of polycrystalline elemental targets in a range Z = 29 to Z = 82. Also, the influence of the effect upon scattering yields from an aligned Au(110) single crystal is demonstrated.

The usual virial theorem, relating kinetic and potential energy, is extended to a molecule by the use of the true wave function. The virial theorem is also obtained for a molecule from a trial wave function which is scaled separately for electronic and nuclear coordinates.