"The projection operator technique is used to generate electronic wave functions which are eigenfunctions of both spin and orbital angular momentum. All the functions which arise in the L-S coupling of any allowed system of electrons in a single s, p, d, or f shell are computed as well as some functions for a few electrons in the g-shell. In addition, functions arising in the coupling of electrons in different shells are obtained, and these eigenfunctions are of particular interest in configuration interaction studies of atomic structure. A few representative eigenfunctions are listed."

"The canonical theory of motion of a charged particle in a slowly varying, static electromagnetic field is formulated. The Hamiltonian is written down explicitly in terms of the coordinates of the gyration and the drift. The method of approach is analogous to that of the canonical formalism with subsidiary condition as used in theories of collective motion in many-body systems, such as the motion of the center of gravity. In the lowest order of the perturbation, it is shown that the Hamiltonian for the drift motion averaged over the gyration phase is given by adding to the original Hamiltonian a potential term equal to the product of the magnetic moment and the magnetic field strength."

"It is shown that in a class of models of quantum field theory, the perturbation expansion of the resolvent operator, (H - z)-1, converges for all complex z. The class of models consists of all theories with Yukawa coupling in which the vacuum polarization is neglected. The method used is that of comparison with the exactly solvable neutral solar model."

"A generalized discontinuous solution was found for the adiabatic two- fluid equations in the steady state: it covers the case of strong shocks and enables a complete account to be made of the steady state solutions of these equations. By considering a piston problem using numerical methods, time dependent solutions of the equations were also found; these rapidly steepened and converged to the discontinuous steady state solutions whenever these existed."

"The limitation of the speed and memory of calculating machines places an upper bound on the number of meshpoints that may be used in a finite difference calculation. This means that in problems involving many independent variables (and for present-day machines, three is many) the mesh employed is necessarily coarse. Therefore in order to get reasonably accurate final results one must employ highly accurate difference approximations. The purpose of this paper is to set up and analyze such difference schemes for solving the initial value problem for first order symmetric hyperbolic systems of partial differential equations in two space variable."

"The one-dimensional propagation of disturbances in an inviscid conducting fluid of finite magnetic Reynolds number is investigated. The basic equations are not hyperbolic but nevertheless the slow wave has a domain of dependence determined by the sound velocity."

"Electron emission during the adsorption of a monolayer of oxygen on a clean'' tungsten surface is reported. This emission is attributed to the excitation of conduction band electrons during adsorption, probably as the result of Auger transitions to the chemisorbed state. Calculations based on this model of chemisorption agree qualitatively with the experimental yield."

"A specific feature of the finite difference scheme proposed is that in it the boundary condition and the differential equation are treated simultaneously. The scheme results from a variational principle of the original differential equation problem, simply by using the Ritz method employing piecewise linear approximation functions. Thus a rather uniform treatment of boundary condition and differential equation will result. The coefficients of the substitute boundary condition will be given as the areas of sections of triangles cut out by the boundary; they are therefore not sensitive to variations of the direction of the boundary. An advantage of the approach is that the mean convergence of the solutions of the difference equations (including first difference quotients) to that of the differential equation is implied by the general theory and requires no special proof. Whether or not the scheme is useful in actual computation is still to be seen. The scheme for the Neumann problem of Laplace's equation is first described; then its extension to systems of second order is discussed. A lower estimate is given for the eigenvalues of the matrix involved. The method for extending the scheme to the Dirichlet problem is indicated."

"A kinetic study is made of a system of neutral particles which interact under gravitational forces. The Jeans instability is recaptured in the limit of long wavelengths where the growth rate assumes a characteristic maximum value. As the wavelength diminishes to a certain critical distance, the instability vanishes. This distance is consistent with thermal-gravitational estimates for the diameter of a star. Plasma oscillations are found in the central region of a one-component charged gas cloud."

"The full size seal (5 1/2" shaft diameter) was redesigned to incorporate the latest seal geometry which was developed as a result of the model seal test program. A number of compatible seal face material combinations, which performed satisfactorily during the model seal test program, was also selected for evaluation in the full size seal. All the detail drawings of the seal and test stand were completed. A test program for the full size seal was prepared and approved."

"The model seal test program was continued throughout the period covered by this report. Of notable mention, a test, 507 hours in duration, was conducted at 2000 psig and 2.75 GPH leakage. Examination of the seal faces after the test showed that there was no measurable wear within the limits of an optical inspection. The full size seal (5-1/2" shaft diameter) and the related test strand are in the manufacturing phase. The instrumentation and associated equipment for the full size seal test are on order."

"The model seal test program was concluded during this Quarterly Report. The final test, 1014 hours in duration, was conducted at a sea1ing pressure of between 2100 to 2300 psig and at a leakage rate of 2.14 gph. The seal face materials evaluated were an aluminum oxide rotor running against a stator face made of tungsten carbide for the high pressure seal and Graphitiar 39 for the low pressure element. Optical examination of the faces after the test showed no measurable wear. Nine unscheduled shutdowns were made during the test without damaging the seal faces or affecting the performance of the seal after each startup. The shutdowns were automatically accomplished in a predetermined sequence through a control system which was calibrated to monitor the test and stop it in the advent of equipment failure. The manufacture of the full size seal (51/2-inch shaft diameter) is 50% complete. All of the test equipment and instrumentation for the full size test rig has been received and assembled. The full size seal is scheduled for assembly by mid August 1963."

"The hyperon-nucleon scattering is calculated for LAMBDA laboratory energies to 315 Mev. The potentials used were those linear combinations of the nucleon-nucleon potentials as prescribed by global symmetry. The mass difference between the LAMBDA - and SIGMA -hyperon was taken into account in the kinematics. The mass differences between the SIGMA -hyperons and between the nucleons are neglected. Angular distributions and total cross sections are given for all the possible hyperon-nucleon scattering reactions."

"The properties of solutions of KI, AgNO/sub 3/, CoCl/sub 2/, and CoBr/ sub 2/ in anhydrous acetonitrile were studied by means of measurements of electric conductance, density, viscosity, and spectrophotometry. The data are examined in the light of theoretical concepts of electrolytes. The properties of acetonitrile as an ionizing solvent are discussed briefly, and a summary of existing information for inorganic salts in this solvent is presented."

"The interactions of 141 plus/minus 8 Nev n minus mesons with deuterium were studied using a 15 cm deuterium bubble chamber. The elastic differential cross section was measured by examining the angular correlation, range of positive recoil, and coplanarity of those scatterings which resulted in two outgoing charged particles. The accuracy of the measurement sin the backward hemisphere was on the order of 10-15 percent. This elastic differential cross section was compared to the results of impulse approximation calculations and they were found not to agree for backward scattering."

A matrix of twenty 2 x 12 mm squared surface barrier counters has been constructed for use in the image plane of a magnetic spectrometer. The outputs of individual crystals are displayed in predetermined channels of a 100-channel pulse height analyzer. This is done by connecting separate crystals to succession sections of a delay line and converting the time difference between signals arriving at the ends of the line into pulse heights. Simple procedures for producing reliable Ge-Au surface barriers and contacts and certain properties of such counters are discussed. A sample of information decoded by this unit is presented.

"Norm estimates are derived for the rate of convergence of the basic alternating direction methods for solving elliptic difference equations. The equations treated have variable coefficients and are defined in arbitrary regions."

"The natural exponential decay of a radioisotope used as a heat source for a thermoelectric generator makes the use of a power flattening'' device highly desirable, especially when the duration of the mission is large compared to the half-life of the radioisotope. Power-flattening devices are considered which either dump excess heat outside the thermoelectric generator or use the characteristics of the generator to absorb the excess heat and thereby regulate the hot junction temperature. A number of power-flattening devices were studied both analytically and experimentally with a view toward operability in space. The most promising concepts are (a) to utilize a secondary radiator of variable area; (b) to provide thermal shunts that are sequentially removed during the mission; (c) to use a secondary radiator coupled to the heat source through a slowly evaporating thermal connection."

"Work accomplished in incorporating plutonium oxide in glass and glass fibers between July 1960 and March 1961 is summarized. The purpose of producing plutonium bearing glass and glass fibers was to eliminate or reduce the radiological and toxicological hazards associated with plutonium. Initial results using "wipe" tests showed no removable alpha contaminant in freshly prepared samples. Leaching studies were made using water, dilute HCl, and HNO/ sub 3/. The amount of PuO/sub 2/ leached from the glass can be greatly reduced by substituting Al/sub 2/O/sub 3/, CaO, and K/sub 2/O for much of the Na/sub 2/O component in the glass composition."

"Results of molecular studies showed that, depending on the chemical composition, polyphosphates are either linear or branched flexible chain molecules. The branch points were easily destroyed by hydrolysis. Hydrolytic stability studies showed that the rate constants are much smaller for the splitting of internal bonds than for the hydrolysis near the chain ends, where both monomeric and trimeric rings are formed. The kinetic study of the degradation of sodium pentaphosphate was continued. Preliminary results indicated that, in the absence of calcium, the formation of each trimeric ring is accompanied by the formation of two orthophosphate rather than one pyrophosphate molecule. The influence of different univalent cations on the behavior of polyphosphates was studied by electrophoresis, conductivity, membrane equilibrium, and viscosity measurements. The effects of divalent ions were also studied."

"Mathematical methods are being developed for calculations in fluid dynamics. The work to date on the Mach reflection calculation is summarized. In the flow, there are two curved shocks, a slip surface, a plane shock, and rigid walls. The desired solution of the fluid-dynamics equations is stationary in similarity variables; approximate initial data are therefore assumed, with the expectation that the flow will settle down to the desired one asymptotically. The Eulerian equations for the smooth parts of the flow are coupled to the jump and boundary conditions on the various surfaces. Two-dimensional fitting procedures were devised to apply the jump and boundary conditions. All parts of the code now appear to operate satisfactorily except for the treatment of the slip surface, which showed instabilities after about 50-70 cycles. The main problem was temporarily discontinued, in order to concentrate on the slip surface. A simplified problem of a nearly plane slip surface between parallel walls and with periodicity conditions along the surface is described. This problem uses all the machinery of the main code except for the parts having to do with the shocks, and it has additional subroutines for computing an analytic solution based on the linearized theory of …

"The long wavelength modes of excitation of a two component plasma in a steady magnetic field are examined. Two linearized Boltzmann equations are given with collision terms which are coupled through the difference in temperatures and difference in velocities of the two gases. A formal means of classification of phenomena is described in terms of the nature of the roots about k = 0. Two types of behavior are uncovered: MHD, magnetohydrodynamics, which include finite phase speed phenomena near k = 0; and PEM, plasma electromagnetics, which includes infinite phase speed phenomena near k = 0. The dissipative effects of collisions are included. In the limit of vanishing collision frequency, roots previously obtained are recaptured. The relevance of the pertinent domains are discussed and the complex interplay between the fast and Alfven modes of MHD and the plasma- magnetic modes of PEM is demonstrated. Equations macroscopic in appearance are derived which include the effects of the initial configuration. In the limit of large collision frequency the equations reduce to standard forms. The dispersion of the Nth order Larmor resonance is given which includes the effect of the mass ratio. A discussion of the transfer equations of a plasma is included."

"The study of the single channel scattering problem was extended to include the multi-channel case. The scattering problem was formulated in a mathematically rigorous way which reflects the time-independent point of view but is not limited by any dependence on a configuration space representation. Wave operators were defined by an integral representation. When the conditions necessary for the time-dependent formulation are valid these wave operators will be identical to those defined by the asymptotic limits and will provide a solution of the scattering problem. But these conditions are stronger than those which are sufficient for a solution, so there should exist a class of Hamiltonian operators for which a solution of the scattering problem exists but for which the asymptotic conditions are not valid."

"A new 350 KV power supply was installed, and major modifications of the accelerator were completed. The changes include the installation of new focusing and extractor supplies, an extension of the accelerator column, and the replacement of the isolation transformer by a motor generator set. Improved performance at voltages up to 200 KV was obtained, but a modification of the electrostatic lens system will be required for operation at 350 KV. The results of an investigation of the C/sup 12/(n, alpha )Be/sup 9/ reaction and a search for an excited state in He/sup 5/ are discussed. Work in progress includes: N/sup 14/ and O/sup 16/ (n, alpha ) angular distribution measurements with counters; studies of I/sup 127/ (n,d)Te/sup 126/ using counters and I/sup 127/(n,p)Te/sup 127/ using emulsions; and the development of an E x dE/dx pulse height multiplier."