Origin of the E.S.R. hyperfine anisotropy and the cos2 θ rule of the β-fluorine couplings

The origin of the hyperfine couplings of β-fluorine nuclei in free radicals has been studied using the hyperfine tensors determined for and in single crystals. The direction of the maximum principal element of the β-fluorine coupling tensor in was found to be very close to the direction of the maximum overlap of the fluorine 2p π orbital with the half-filled carbon 2p π orbital. This means that the spin density in the fluorine 2p π orbital is mainly due to the direct overlap with the carbon 2p π orbital and the contributions from the hyperconjugation and the spin polarization mechanisms are less important. The cos²θ rule, B ₀ + B cos²θ, for the β-fluorine coupling tensor was also derived from the conformational dependence of the overlap integral. Using the ratio of B/B ₀ calculated from the overlap integral together with the observed hyperfine tensor for , the absolute values of B ₂ and B were determined and results were applied to the β-fluorine coupling tensor of the rotating CF₃ group in . The calculated tensor is in very good agreement with the one observed.     

E.S.R. spectra of the radicals produced in γ-irradiated diborane in the solid state

The hopping and Coulomb repulsion integrals of the Hubbard model, as applied to the NMP-TCNQ charge-transfer crystal, are found by an INDO calculation of the neutral and charged monomer and dimer of TCNQ. The ratio of these integrals is in satisfactory agreement with experiment, although the calculated integrals themselves are very different from the effective ones for electronic transport, due to renormalization, caused largely by counter-ion polarizability.     

N.M.R. spectra of the XnAA′ Xn′ type

The method described previously for the calculation of the X spectrum for spin systems of of the X_nAA′X_n′ type is extended by means of magnetic equivalence factoring to cases in which the long-range coupling constant J_x is non-zero. This coupling is treated as a first-order perturbation to the energy levels obtained when J_x =0, and it is found that J_x may be measured directly from the separations between easily identified lines in the spectrum. A detailed account of the X ₃ AA′X ₃′ system is given, and the N.M.R. spectrum of fluoro-N,N′-dimethyl-1,3,2,4-diazadiphosphetidine is analysed. The spectral parameters obtained are discussed. A computer programme which calculates the spectra of systems involving magnetic equivalence is used to examine the validity of the approximations in the method.     

Nobel Prizes in the “light” of Vavilov–Cherenkov radiation. To the 125th anniversary of the birth of S.I. Vavilov

The objective of this paper is not a detailed review or an analysis of the studies in the field of high-energy physics initiated by the discovery of Vavilov–Cherenkov radiation, occurred more than 80 years ago at the Lebedev Physical Institute, and awarded Nobel Prizes. The paper is written to emphasize the historical significance of the discovery of the effect and its key role in further studies in high-energy physics, commended by the high award of the Nobel committee. In 1958, 24 years after the first publication about the new phenomenon, i.e., emission of electrons moving in matter with the superlight speed, discovered by P.A. Cherenkov under the supervision by S.I. Vavilov, the Nobel Prize was awarded to a group of scientists of the Lebedev Physical Institute, P.A. Cherenkov, I.M. Frank, and I.E. Tamm “for the discovery and explanation of the Cherenkov effect”. Since then, practical application of Vavilov–Cherenkov radiation is widely spread.     

Reply to the Comment by A.W. Thomas et al. on “The role of the orbital angular momentum in the proton spin”

The orbital angular momenta L^u and L^d of up- and down-quarks in the proton are estimated as functions of the energy scale as model independently as possible on the basis of Ji's angular-momentum sum rule. This analysis indicates that L ^u - L ^d is large and negative even at the low energy scale of nonperturbative QCD, in contrast to Thomas' similar analysis based on the refined cloudy bag model. We pursuit the origin of this apparent discrepancy and suggest that it may have a connection with the fundamental question of how to define quark orbital angular momenta in QCD.     

On the occurrence of b.c.c.–h.c.p. structural phase transition in Mo under pressure

Abstract

To resolve the controversy on the occurrence of a b.c.c.–h.c.p. transition in shock as well as static measurements in Mo, we have done more accurate total energy electronic structure calculations. Our results show that this phasetransition should occur at much higher pressures than suggested by earlier calculations.     

On the relation of the Methagalaxy mass to the gravitation constant. 1. from Einstein’s theory to the Einstein–Cartan theory

The notion of the dimensionless gravitational charge defined through the Planck mass and the fundamental constants specifying this mass itself is introduced. The Big Bang is related to the unified physical interaction decay and the drop of Newton’s gravitational constant by 40.67 orders of magnitude in comparison with the electromagnetic constant taken as unity. This causes an increase in theMetagalaxy curvature radius by the same value and a decrease in the average density of space–time curvature sources by 122 orders of magnitude: from the maximum allowable Planck density to the observed critical density. The microphysics appears naturally related to cosmology.     

From extensive air showers to the characteristics of primary cosmic rays. To the 120th Anniversary of the Birth of D. V. Skobel’tsyn

The works by D.V. Skobel’tsyn that laid the foundation of the contemporary physics of cosmic rays and the physics of high energies are considered. Skobel’tsyn demonstrated that cosmic rays contain particles whose energy substantially surpasses the energies that are typical of radioactive decay, discovered the existence of air showers, i.e., when several particles hit an array simultaneously, and performed a series of investigations into extensive air showers that resulted in the discovery of a nuclear-cascade process in the atmosphere. The results that Skobel’tsyn obtained were of primary importance for the further development of cosmic-ray physics.     

‘Factors of ignorance’ and the rationalized M.K.S.A. system of units

An attempt is made, by means of an allusive (rather than a systematic) historical account of the development of the subject, to exhibit the essentially unique character of the rationalized M.K.S.A. system of units. The establishment of this system involved one arbitrary decision—the determination to retain unaltered the size of the previously accepted unit of current. Thereafter, any choice of derived units, other than the choice actually made, would have destroyed the basic symmetry of the formulation.     

Regarding the publication by G. B. Malykin and V. I. Pozdnyakova “On the Velocity of a Light Spot Moving over a Cylindrical Screen”

It has been shown that, in the article by G. B. Malykin and V. I. Pozdnyakova “On the Velocity of a Light Spot Moving over a Cylindrical Screen” [Tech. Phys. 52, 133 (2007)], errors were made in the calculation of the velocity of a light spot moving over a cylindrical screen. As a result, incorrect formulas were obtained to calculate the velocity of the light spot as applied to classical mechanics and the Tangherlini transformation. Correct formulas for calculating the velocity of a light spot moving over a cylindrical in classical mechanics and in the Tangherlini transformation are proposed.     

Large field renormalization. I. The basic step of the ℝ operation

We construct the renormalization operation of the expressions connected with the large field regions. This operation, denoted by , removes the main obstacle to prove the ultraviolet stability of four-dimensional gauge field theories. The proof will be completed in the second part of this paper.Research supported in part by the National Science Foundation under Grant DMS-86 02207     

The infra-red L.M.R. spectrum of SeH in the X 2Π state

Magnetic dipole transitions between the ²Π_1/2 and ²Π_3/2 components of the ground state of SeH have been observed at about 1780 cm^-1 in a L.M.R. experiment using a CO laser. Transitions have been detected for the four most abundant natural isotopes of Se. The transition frequencies depend primarily on the magnitude of the spin-orbit coupling constant and have been analysed in conjunction with data from the E.P.R. spectrum to yield

The admixture of other electronic states by spin-orbit coupling has been investigated to third order in perturbation theory and found to produce significant effects.     

Direct gauging of the poincaré group. III. Interactions with internal symmetries

The problem of gauging matter fields with a Poincaré invariant action functional that admits anr parameter, semisimple groupG(r) of internal symmetries is considered. A minimal replacement operator for the total groupP ₁₀×G(r) is obtained, together with the requisite compensating 1-forms for both the Poincaré and theG(r) sectors. A basis forP ₁₀×G(r)-invariant Lagrangian densities for the free fields is obtained. Restriction to Lagrangian densities that are at most quadratic in the associated curvature and torsion fields eliminates active coupling between theP ₁₀ free field Lagrangian and theG(r) free field Lagrangian, although there is passive coupling that arises through the requirement of tensorial covariance under general coordinate transformations generated by the local action of the translation group. A superposition principle, modulo passive coupling, thus holds for quadratic free field Lagrangian for the total group:L _TOT=L _P +L _G(r) . Field equations for the matter fields and the compensating fields of theG(r) sector are obtained. Both share the passive coupling toP ₁₀ that is required in order to achieve tensorial covariance, but only the matter fields couple directly to the Poincaré fields and only to the Lorentz sector. For weak Poincaré fields, the field equations for the matter fields and the compensating fields of the internal symmetries go over into the standard field equations of gauge theory for an internal symmetry group.     

Spin pumping at the Co2FeAlo.sSio.5/Pt interface

Spin pumping at the Co2FeAlo.sSio.5/Pt and Pt/Co2FeAIo.sSio.5 interfaces has been studied by ferromagnetic res- onance technology （FMR）. The spin mixing conductance of the Co, FeA~o.sSio.s/Pt and Pt/Co2FeAlo.sSio.5 interfaces was determined to be 3.7~ lO19 m-2 and 2.1 ~ lO19 m 2 by comparing the Gilbert damping in a Co2FeAIo.sSio.5 sin- gle film, Co2FeAlo.sSio.s/Pt bilayer film and a Pt/Co2FeAIo.sSio.s/Pt trilayer film. Spin pumping is more efficient in the Co2FeAlosSios/Pt bilayer film than in permalloy/Pt bilayer film.     

Direct gauging of the Poincaré group. II

This paper continues the study of direct gauge theory of the Poincaré groupP ₁₀. The meanings and implications of transformations induced by the local action ofP ₁₀ are studied, and transformation rules for all field quantities are derived for the local action ofP ₁₀ in a sufficiently small neighborhood of the identity. These results lead directly to a system of fundamental partial differential equations that are both necessary and sufficient for invariance of the free field Lagrangian density. Homogeneity arguments and the classical theory of invariants are used to obtain the most general free field Lagrangian density. Gauge conditions are shown to imply coordinate conditions, and an algebraic system of antiexact gauge conditions is implemented. The underlying Minkowski space,M ₄, and the resulting Riemann-Cartan space,U ₄, become attached at their centers, as do their respective frame and coframe bundles. Weak constraints of vanishing torsion are studied. All field quantities are shown to be determined in terms of the compensating l-forms for the Lorentz sector alone provided an explicit system of integrability conditions is satisfied. Field equations of the Einstein type are shown to result.     

Large Deviations, Guerra’s and A.S.S. Schemes, and the Parisi Hypothesis

We investigate the problem of computing $$\lim_{N \to \infty}\frac{1}{aN}\log EZ_N^a$$ for any value of a, where Z _N is the partition function of the celebrated Sherrington-Kirkpatrick (SK) model, or of some of its natural generalizations. This is a natural “large deviation” problem. Its study helps to get a fresh look at some of the recent ideas introduced in the area, and raises a number of natural questions. We provide a complete solution for a ≥ 0.     

The 1/N F expansion of the γ and β functions in Q.E.D.

The Callan-Symanzik- and-functions are calculated analytically for Q.E.D. in the limit of a large number of leptons (N _F) up to terms of order 1/N _F inclusive. We give closed analytic expressions for the coefficients of these terms in their series expansion in powers ofK N _F/. We have been able to sum these series and to obtain some striking results.