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.

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.

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.

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 …

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 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.