Formate anion: The physical force field

Unequivocal assignments for all of the vibrational modes of the formate ion have been made from isotopic shifts measured in the Fourier transform infrared and Raman spectra of polycrystalline samples of the sodium salts of HCO₂^?, H¹³CO₂^?, DCO₂^?, and D¹³CO₂^?. Literature frequencies for DCO¹⁸O^? and DC¹⁸O₂^? have been added to the above results for the unique determination of the 10 force constants in the general harmonic force field. Product rule relations among the harmonic frequencies are shown to interfere seriously with the determination of the physical force field by the standard normal coordinate computation. The least-squares refinement is found to be particularly sensitive to identified types of anharmonic error in the frequencies. Refinements characterized as Φ^aH and Φ^aD improve reliability by elimination of the deuterium isotopic shift for νCH. The physical force field is interpreted in terms of the geometric and electronic structure.     

Nonlocal theory of single pion photoproduction

A nonlocal interaction theory is formulated for photoproduction processes by introducing a form function. An effective nonlocal, Lorentz invariant and gauge invariant Lagrangian density for the four-field interaction that gives rise to a production amplitude is constructed. The general structure of the form function is investigated by using some restrictions of the form function. For low energy ⁰ photoproduction an explicit form of the Fourier component of the form function is obtained. The physical model of the present formalism is to assume, similar to the strong absorption model, that the system in intermediate states is confined in a finite domain of space. For ⁰ production the linear dimension of this domain is obtained to be ₀ = 3·88F. It is important to observe that the extent of electromagnetic distribution in a nucleon is also nearly the size of ₀. This is believed to be the reason that in low energy pion photoproduction the effects of electromagnetic structure of a nucleon are irrelevant. The unpolarized differential and total cross sections are calculated for ⁰ production in helicity representation and the predictions are found to be in good agreement with experiments.     

A unified theory of matter. II. Derivation of the fundamental physical law

The equation for the fundamental field quantity ? is obtained. It is Div \(\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } \) ,where h is an arbitrary function oft andr, and [,]_? is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ?.(2) Relativistic covariance of the equations governing ?.(3) Principle of continguous action.(4) Conservation of total amount of ?. The equation appears to be unique. It is suggested that the physical world corresponds to ? being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential A^μ is identified with ε ρ^μ dΩ. Conservation laws on various measures of ? are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ? to the metric is made via Einstein's gravitational equation G_μυ =_KT_μυ.     

Nonlocal integral conservation laws and tetradic currents in the Einstein-Cartan theory I. Nonlocal conservation laws

Nonlocal integral conservation laws in the Einstein-Cartan theory for the energy-momentum tensor of general-form sources, in essence being an integral equivalent of convoluted Bianchi identities, are obtained.     

The physical interpretation of wave mechanics. II

Continuing the considerations given in the first part of this series (I), we use the analysis of the Aharonov-Bohm effect to show that the hydrodynamical variables by which the quantum mechanical one-body problem can be represented are of direct physical significance. It is shown in a particular case that the final state of a system can be obtained from its initial state in a unique manner if both states are characterized by hydrodynamical variables.     

Nonlocal integral conservation laws and tetradic currents in the Einstein-Cartan theory. II. Problem of the gravitational energy and tetradic currents

Einstein-Cartan gravitational field equations are formed as Maxwell equations: the codifferential of the tetrad differential is equal to the conserved tetradic current. This yields local integral conservation laws for any tetrad field and, in particular, allows solving the old problem of the gravitational energy in the general relativity and Einstein-Cartan theories.     

Perturbation theory for projected states in the pairing force model: (II). The problem of convergence

In a previous paper second-order calculations were carried out on the two-level pairing force model using perturbation theory for projected states and the results were compared with those of BCS or ordinary perturbation theory. In the present paper criteria for convergence are applied to two different forms of the perturbation series for both the projected and ordinary perturbation theories. It is found that the superior results obtained for the convergence rates in the projected theory tally neatly with the results of the second-order calculations, and give further support to the use of the projected perturbation theory.     

Superspace unmasked: The physical interpretation of supergravity theory

Supergravity admits a geometric formulation in terms of an expanded algebra of functions on ordinary spacetime. This formulation, called graded manifold theory, is equivalent to the usual superspace supergravity constructions but avoids the anticommuting coordinates of superspace. The geometry suggests an operational interpretation of supergravity theory in terms of measurements made by local observers in spacetime.     

The physical optics of phase-conjugate mirrors: Scalar theory

A scalar theory of physical optics is developed for the scattered waves by finite or infinite phase-conjugate mirrors. The method is applied to the scattering problem of waves by a semi-infinite phase-conjugate mirror. The results are examined numerically and compared with the scattered waves by a conducting half-plane. The effect of the phase-conjugation to the location of the transition region is outlined.     

The adsorption and decomposition of methanol on tungsten. II

A clean tungsten filament adsorbs methanol rapidly at room temperature, the initial sticking probability being 0.8. At saturation, the composition of the adsorbed layer is roughly CO:H = 1:1 and it is suggested that the hydrogen may be in the form of a surface complex. The continuous decomposition of methanol by the hot filament under steady-state conditions, or when the filament had been previously oxygenated, followed a different course from that previously reported for the newly-cleaned filament. Rather than a rapid rise in the rate of decomposition (to CO + H₂) for 600 < T_fil < 1300 K to a high plateau above 1300 K, decompositon to formaldehyde, carbon monoxide and methane was observed. The rates at which these products appeared passed through low maxima between 900 and 1100 K. The change in the relative importance of formaldehyde and carbon monoxide production with filament temperature within this range is attributed to a temperature-dependent life-time of formaldehyde molecules on the oxygenated surface. At the highest temperature (> 1500 K) the reactivity increased rapidly to join that of the clean surface, probably due to the desorption of surface oxygen.     

The physical theory of rock magnetism

Magnetite and hematite are representative of the ferrimagnetic and weakly ferromagnetic minerals which are responsible for the magnetic properties of rocks reviewed in this paper. Magnetite grains are multi-domains in the size range of interest (0.1 μ–1000 μ), whereas hematite grains in the same size range are almost certainly single domains. Properties discussed are coercivity, susceptibility, magnetic viscosity, thermo- and isothermal remanence, alternating field demagnetization, anhysteretic, chemical and detrital magnetization, anisotropy, piezomagnetic effects and self-reversals. Problems requiring more experimental data are emphasized, especially the basal plane anisotropy of hematite, the Barkhausen discreteness of domains in magnetite and the possibility that grains of cubic minerals may have some uniaxial character arising from grain shape or internal strains.     

On the derivation of quantum kinetic equations. II. Nonlocal Uehling-Uhlenbeck equation

The binary and triple collision terms of the quantum kinetic equation derived previously are analyzed in the weak coupling approximation. In this approximation the equation appears to be a nonlocal Markovian extension of the kinetic equation due to Uehling and Uhlenbeck. After linearization, its relationship with non-Markovian formulations found in the literature is studied.This investigation is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (ZWO).     

The adsorption of water vapor on clean cleaved germanium: II. Electrical properties

Clean germanium surfaces obtained by cleavage in ultrahigh vacuum were exposed to water vapor in the range from 10^?9 up to 1 Torr min. Surface state properties have been derived from measurements of surface conductivity and field effect mobility. At coverages close to a monolayer a steplike change in surface state density indicates a change of the adsorption state similar to a phase transition. The results are described quantitatively by assuming that each structure has its characteristic surface state distribution.     

The adsorption of cyclic hydrocarbons on Ru(001): II. Cyclohexane

The adsorption of cyclohexane on Ru(001) at 90 K has been investigated by thermal desorption mass spectrometry, EELS, UV photoemission and LEED. Thermal desorption indicates the adsorption of the undissociated molecule first in a chemisorbed monolayer (T_d = 200 K) with subsequent formation of multilayers (T_d = 165 K) at higher exposures. The vibrational spectrum obtained by EELS is characterized by a frequency shift of the C-H stretching mode from 2920 cm^?1 (multilayer) to 2560 cm^?1 for the chemisorbed monolayer. Off-specular EELS data indicate two different electron scattering mechanisms for the C-H stretching mode. Whereas for the C-H stretching mode of the multilayer, large angle electron impact scattering is observed, the C-H soft-mode of the monolayer is largely due to small angle dipolar scattering. The He I photoelectron spectra of cyclohexane multilayers are characteristic of the undissociated molecule. A new assignment of C(2s) and the lowest C(2p) level, based on a comparison with benzene, shows that the chemisorbed monolayer is characterized by the absence of emission or broadening of the 2a_1u level. This is attributed to C_3v symmetry of the chemisorbed layer and to a possible interaction of the 2a_Iu orbital with the metal surface.     

The determination of atomic force constants in cubic solid solutions: II. Experimental

The microscopic elastic theory of Matsubara-Kanzaki-Krivolglaz has been applied to the determination of the atomic force constants in disordered Cu₃Au from the diffuse scattering pattern due to local atomic order and static atomic displacements. The analysis of the effect of experimental errors and the assumptions underlying this method of analysis indicate, however, that these results may be considerably in error. A discussion of the source of these errors and their influence on the determination of the atomic force constants in solid solution alloys is presented. It will be shown that it is not possible to determine these constants from X-ray diffraction data from clustering alloys, but in some cases for ordering alloys, this may be possible.