Extension to velocity dependent gauge transformations

In previous papers it was shown that in phase space a generator of gauge transformations for a singular Lagrangian \(L(q,\dot q)\) is given byG[ε^α]=ε _k ^α φ _α ^k (q,p,t) where φ _α ^k are first class constraints andG is subjected to a stationarity condition. A non-trivial extension from velocity (or momentum) independent gauge transformations to velocity dependent ones is realized, by replacing gauge functions ε^α(t) with momentum dependent functions ε^α(q,p,t), as long asG satisfies the stationarity condition. Inversely, it is proved in a classical framework that, within velocity dependent gauge transformations, all generators of gauge transformations can be expressed in terms of the linear combinations of φ _α ^k .     

Atomic-vacancy ordering in the lowest tungsten carbide W2C

Atomic-vacancy ordering in the lowest tungsten carbide W₂C with an L′3-type basic hexagonal structure has been studied by neutron diffraction and X-ray diffraction. In the temperature range 2700–1370 K, the only ordered phase of the lowest tungsten carbide is shown to be the trigonal ?-W₂C phase (space group P $\overline 3 $ 1m). This trigonal ?-W₂C phase is found to form via a disorder-order phase transition channel, which includes three superstructure vectors (k ₁₅ ⁽¹⁾ , k ₁₅ ⁽²⁾ , k ₁₇ ⁽¹⁾ ) of two Lifshitz stars ({k ₁₅}, {k ₁₇}, and to be described by two long-range order parameters (η₁₅, η₁₇). The distribution function of carbon atoms in the trigonal ?-W₂C superstructure is calculated, and the corresponding region of the allowable values of the long-range order parameters η₁₅ and η₁₇ is found. Symmetry analysis of other possible superstructures of the lowest tungsten carbide W₂C is performed, and the physically acceptable sequence of phase transformations in W₂C is determined.     

Electroweak one-loop corrections to the decay of the charged vector boson

The electroweak radiative corrections to the decay widths of theW-boson, Γ \((W \to l\bar v,\bar ud,\bar cs)\) , have been calculated in the standard theory. The results are presented in terms of an electroweak form factorρ ^W and their dependence onm _t , andM _H (masses oft-quark and higgs boson) is studied. Typically,ρ ^W ?1 is of an order of one percent. The differenceρ _lv ^W ?ρ _qq′ ^W is negligible, 0.046%. The calculational scheme used is described in detail.     

On the signatures of the canonical and the metrical energy densities of vector fields

The energy-density components Θ ₀ ⁰ andT ₀ ⁰ of the canonical and of the metrical energy-momentum tensors Θ _k ⁱ andT _k ⁱ for a statical field of vector mesons have opposite signatures: Θ ₀ ⁰ =H=?T ₀ ⁰ =?L. From this property some relativistic and field-theoretical theorems can be deduced in an elementary way.     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

Investigation of N 2 + (C 2Σ u + → X 2Σ g + fluorescence excited through auger decay of the 1s −1π* resonance

A theoretical investigation of N ₂ ⁺ (C ²Σ _u ⁺ → X ²Σ _g ⁺ molecular fluorescence excited through the Auger decay of the 1s ^?1π* resonance is carried out. The fluorescence cross sections are calculated with due regard for the dependence of the matrix element of the C → X dipole transition on the internuclear distance, the interference between channels of excitation via different vibrational levels v _r of the 1s ^?1π* resonance, the rotational structure of the fluorescence band, and the predissociation of the N ₂ ⁺ C ²Σ _u ⁺ v′ ≥3) states. The calculated cross sections are in good agreement with the experimental results of recent measurements. The results of the calculations have demonstrated that the observed dependence of the cross section of the (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″) fluorescence on the excitation energy and the fluorescence wavelength for a group of bands with equal values of the difference Δv = v′ ? v″ is associated with transitions between the vibrational levels of the electronic states involved in the excitation and subsequent cascade decay of the 1s ^?1π* resonance: N₂ (v ₀ = 0) → N*₂(1s ^?1π*(v _r)) ? N ₂ ⁺ : (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″).     

The determination by an independent method ofP k electron capture probabilities in133Ba and139Ce decays gamma decay of133Ba

The electron capture decays of¹³³Ba (10.4 y) and¹³⁹Ce (140 d) were investigated with high resolution Ge(Li) detectors. By x-ray — γ-ray coincidences values of the quantityP _k ω _k ? _k for various transitions in the decay of¹³³Ba and¹³⁹Ce are obtained. The factor ω _k ? _k was measured independently by means ofK-conversion electron-K x-ray coincidences and was then used to determineP _k , theK-capture probability. The independent measurement of the product ω _k ? _k , together with recent accurate values of ω _k , provides a new method for the accurate calibration of semiconductor x-ray detectors. In the decay of¹³⁹Ce, a value ofP _k =0.78±0.03 is found (where the error represents twice the standard deviation) from whichQ _ec =326 _?30 ⁺⁷⁰ keV to the¹³⁹La ground-state is found by use of theory. In¹³³Ba decay, values are found ofP _k 1=0.72±0.04 for theEC transition to the 437 keV level in¹³³Cs,P _k 2=0.80±0.07 to the 384 keV level, and from an independent measurement, the ratioP _k 1/P _k 2=0.87±0.07. From these results the ground-state value ofQ _ec =522 _?10 ⁺²⁰ keV is derived from theory for¹³³Ba decay. The gamma spectrum of¹³³Ba also was remeasured. From the present gamma intensities and previous conversion electron intensities, new values forK-shell conversion coefficients are obtained. Previously reported γ-rays at 35 and 391 keV are not confirmed.     

A new many-body solution of the Friedel resonance problem

It is numerically shown that the groundstate of the Friedel problem (consisting of a conduction band and a dresonance), occupied with (n+ 1) electrons, can be written as Ψ = (A a ₀ ^* +Bd*) Π _v=1 ⁿ a _v ^* Φ₀, where a ₀ ^* represents a localized conduction electron state, d* is the Friedel resonance state and Π _v=1 ⁿ a _v ⁸ Φ₀ is a Slater determinant of n single electron states a _t ^* , (Φ₀ is the vacuum state). The a _i ^* together with a ₀ ^* are part of a full ortho-normalized basis of the conductions band.     

Structural analysis of three-spin systems of photosystem II by PELDOR

The pulsed electron electron double resonance (PELDOR) pulse sequence is applied to a three-spin system consisting of three radicals (Y _D ^· , Y _Z ^· and Q _A ^? ) generated in spinach PS II. The distance between Y_Z and Q_A has been determined to be 3.4 nm with the previously derived distances of the other radical pairs, 2.9 nm for Y _D ^· -Y _Z ^· and 3.9 nm for Y _D ^· -Q _A ^? . This distance has been derived from the Y _Z ^· -Q _A ^? radical pair trapped in Y_D-less mutants ofChlamydomonas reinhardtii. Furthermore the method was applied to the Y _D ^· -Q _A ^? -Chl _Z ⁺ system to find the unknown distance between Q_A and Chl_Z. The derived distance was 3.4 nm. A triangular configuration was found in the membrane system that gives the relative positions of the electron transfer components.     

Dielectric relaxation phenomena of rigid polar liquid molecules under giga hertz electric field

The dielectric relaxation phenomena of rigid polar liquid molecules chloral and ethyltrichloroacetate (j) in benzene, n-hexane and n-heptane (i) under 4.2, 9.8 and 24.6 GHz electric fields at 30°C are studied to show the possible existence of double relaxation times τ ₂ and τ ₁ for rotations of the whole and the flexible parts of molecules. The probability of showing double relaxation is more in aliphatic solvents indicating their nonrigidity. The symmetric and asymmetric distribution parameters γ and δ are obtained from X _ij ^′ /X _0ij and X _ij ^″ /X _0ij and w _j →0 where X _ij ^′ and X _ij ^″ are real and imaginary parts of the complex orientational susceptibility X _i ^* and X _0ij is the low frequency susceptibility which is real. X _ij ’s are involved with the measured dielectric relative permittivities ε _ij ^′ , ε _in ^″ , ε _0ij and ε _∞ij of solutions. The theoretical weighted contributions c ₁ and c ₂ towards dielectric dispersions by Fröhlich’s method are compared with the experimental ones obtained from the graphical variation of X _ij ^′ /X _0ij and X _ij ^″ /X _0ij with weight fractions w _j ’s at w _j → 0. The measured dipole moments μ ₂ and μ ₁ of the whole and the flexible part of a polar molecule in terms of the linear coefficients β’s of X _ij ^′ ’s with w _j ’s and the estimated τ ₂ and τ ₁ reveal their associations with aliphatic solvents. The theoretical dipole moments μ _theo’s from the available bond angles and bond moments of the substituent polar groups of the molecules with the estimated μ’s suggest the mesomeric, inductive and electromeric effects in them under GHz electric field.     

Bloch electron dynamics

New equations of motion for a Bloch electron [momentum p=h k,energy ε _n(p),zone number n, charge -e]: $$m_j \frac{{dv_j }}{{dt}} = - e(E + v \times B)_j $$ are proposed, where v≡?ε_n(p)/?p is the velocity, and {m_j}are the principal masses m _j ^? 1=?²ε_n/?p _j ² along the normal and the two principal axes of curvatures at each point of the constant-energy surface represented by ε=ε_n(p).Their advantages over the prevalent equations of motion where the left-hand-side is replaced by hk _j are demonstrated by examining de Haas-van Alphen oscillations and orientation-dependent cyclotron resonance peaks.     

Transverse momentum of charged hadrons produced in ν and\bar v deuterium charged current interactions

The transverse momentum properties of charged hadrons produced in charged current ν and \(\bar v\) deuterium interactions are studied. The variation of <P _t ² > withW ²,Q ²,x _F andz ² is analyzed. A study of transverse momentum balance shows that soft gluon emission and some quark primordial transverse momentum with <k _t ² >?(0.4 GeV/c)² are needed to balance highp _t particles. Distributions ofp _tin andP _tout in and out of the event plane are presented. A three jet structure is observed for events withW ²>50 (GeV²) and with a highp _t track, which is compatible with models taking into account hard gluon emission.     

An analysis of Cabibbo-favored two-body decays of charmed mesons withη orη′ in the final state

We have carried out a study of Cabbibbo-favored two-body decays ofD ⁰ andD _s ⁺ involving η and η′ in the final state, $D^0 \to (\eta ,\eta ')\bar K^0 , D^0 \to (\eta ,\eta ')\bar K*^0 $ andD _s ⁺ →(η,η′)π ⁺,D _s ⁺ →(η,η′)ρ ⁺. We have introduced an annihilation term wherever admissible, and investigated its size if it were to bridge the gap between theory and experiment in each case. We have also related the semileptonic rates forD _s ⁺ →(η,η′)e ⁺ v to those of the hadronic rates forD _s ⁺ →(η,η′)π ⁺ and unveiled a puzzle. We offer a possible solution.     

Electric properties of levels of 156Dy rotational bands

The nonadiabaticity of E0 transitions from 0 ₂ ⁺ states and 2 ₁ ⁺ bands in ¹⁵⁶Dy is examined within a phenomenological model that takes into account the mixing of K ^π = 0 ₁ ⁺ , 0 ₂ ⁺ , 0 ₃ ⁺ , 2 ₁ ⁺ states and 1⁺-bands. It is shown that the nonadiabaticity of E0 transitions is due primarily to the mixing of 0 ₂ ⁺ and 0 ₃ ⁺ bands.     

Effective hamiltonian of Bloch electrons in a homogeneous electrical field

In order to construct a band mechanics of Bloch electrons in a homogeneous electrical field E with the interband interaction taken into account, a method of determining the exact single-band Hamiltonian $$H_q = \varepsilon _q^F (\kappa ) + Fi\frac{\partial }{{\partial \kappa }}$$ is proposed, where ε _q ^F (κ) is the renormalized (effective) electron dispersion law for R = 0 and the q-th Bloch band,F= ¦e¦·E. The function ε _q ^F (κ) is expressed in terms of the interband element coordinates as well as in terms of periodic solutions of the system of ordinary differential equations which degenerateinto a common Riccati equation in a two-band approximation. A solution of the system and the form of ε _q ^F (κ), in agreement with the Wanhier result, is found in the quasiclassical approximation.     

Overview on neutrinos and the Daya Bay experiment

Neutrinos are elementary particles in the Standard Model. Neutrino oscillation is a quantum mechanical phenomenon beyond the Standard Model. Neutrino oscillation can be described by two independent mass-squared differences Δm ₂₁ ² , Δm ₃₁ ² (or Δm ₃₂ ² ) and a 3 × 3 unitary matrix, containing three mixing angles θ ₁₂, θ ₂₃, θ ₁₃, and one charge-parity (CP) phase. θ ₁₂ is about 34° and determined by solar neutrino experiments and the reactor neutrino experiment KamLAND. θ ₂₃ is about 45° and determined by atmospheric neutrino experiments and accelerator neutrino experiments. θ ₁₃ can be measured by either accelerator or reactor neutrino experiments. On Mar. 8, 2012, the Daya Bay Reactor Neutrino Experiment reported the first observation of non-zero θ ₁₃ with 5.2 standard deviations. In June, with 2.5× previous data, Daya Bay improved the measurement of sin²2θ ₁₃ = 0.089 ± 0.010(stat) ± 0.005(syst).     

BFKL Pomeron in the reaction γ ⊥ * (Q 2)p→ρ ⊥ 0 p at large Q 2 and W

The reaction γ _⊥ ^* (Q ²)p→ρ _⊥ ⁰ p has been studied at large Q ² and W ²/Q ² and low momentum transfers to the nucleon, k _⊥ ² —that is, in the region where the Pomeron exchange mechanism is operative. At sufficiently large Q ², the Pomeron interacts with quarks occurring at small distances, whereby the hard component of the Pomeron is separated, so that the process is governed by the Pomeron of perturbative QCD (BFKL Pomeron). Our calculations indicate that, in vector-meson electroproduction at low k _⊥ ² , the perturbative regime cannot set in fast because, for Q ²≤100 GeV² and, accordingly, for W ²/Q ²≤10⁷, comparatively large distances of $\rho _{q\bar q} > 0.2$ fm are important.     

Spin states of cobalt and the thermodynamics of Sm1 − x Ca x CoO3 − δ solid solutions

In the rare-earth SmCoO₃ perovskite, Co³⁺ ions at low temperatures appear to be in the low-spin state with S = 0, t _2g ² e _g ⁰ . If Ca²⁺ ions partially substitute Sm³⁺ ions, oxygen deficient Sm_{1 ? x} Ca _x CoO_{3 ? δ} solid solutions with δ = x/2 appear. The oxygen deficiency leads to the formation of pyramidally coordinated cobalt ions Co _pyr ³⁺ in addition to the existing cobalt ions Co _oct ³⁺ within the oxygen octahedra. Even at low temperatures, these ions have a magnetic state, either S = 1, t _2g ⁵ e _g ¹ or S = 2, t _2g ⁴ e _g ² . At low temperatures, the magnetization of Sm_{1 ? x} Ca _x CoO_{3 ? δ} is mainly determined by the response of Co _pyr ³⁺ ions. Owing to the characteristic features of the crystal structure of the oxygen deficient perovskite, these ions form a set of nearly isolated dimers. At high temperatures, the magnetization of Sm_{1 ? x} Ca _x CoO_{3 ? δ} is mainly determined by the response of Co _oct ³⁺ ions, which exhibit a tendency to undergo the transition from the S = 0, t _2g ⁶ e _g ⁰ state to the S = 1, t _2g ⁵ e _g ¹ or S = 2, tt _2g ⁴ e _g ² state. In addition, the magnetization and specific heat of the solid solutions under study include the contribution from the rare-earth subsystem, which undergoes a magnetic ordering at low temperatures.