Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.     

Inverse Problem for a General Bounded Domain inR3 with Piecewise Smooth Mixed BoundaryConditions

We study the influence of a finite container on an ideal gas. The trace of theheat kernel (t) = _{= 1}exp(–t), where {} _{= 1}are the eigenvalues of the negative Laplacian – ² = – ³ _{= 1}(/x )² in the (x ¹, x ², x ³)-space,is studied for a general bounded domain with a smooth bounding surface S, where afinite number of Dirichlet, Neumann, and Robin boundary conditions on thepiecewise smooth parts S _i (i = 1, ..., n) of S are considered such that S =U _{i = 1} S _i . Some geometrical properties of (the volume, the surface area, the meancurvature, and the Gaussian curvature) are determined. Furthermore,thermodynamic quantities, particularly the energy, for an ideal gas enclosed inthe general bounded domain with Dirichlet, Neumann, and Robin conditionsare examined with the help of the asymptotic expansions of (t) for short timet. We show that these thermodynamic quantities depend on some geometricproperties of .     

Far-infrared laser stark spectroscopy of CH3OH and13CH3OH

The high resolution laser Stark spectra of methanol and¹³C-substituted methanol have been studied up to Stark fields of about 60 000V/cm with the HCN and DCN lasers. Numerous families of absorption lines have been observed in both parallel and perpendicular polarizations. For methanol, the transitions J _k =7₅ 6₄ A, _t=0; J _k =11₄ 10₃ E _l , _t=0; and J _k =17₃ 16₂ E₂, _t=0 have been identified while the assignments for¹³C-substituted methanol are J _k =14₈ 15₇ A, _t=0; J _k =15₃ 14₂ A⁺, _t=0; J _k =10₇ 9₆ A, _t=0; and J _k =27₉ 27₈ E₁, _t=0. Zero-field frequencies for the assigned transitions are given with improved accuracy over those calculated from available molecular constants, especially for¹³CH₃OH.     

Finite size effects in critical dynamics and the renormalization group

Systems representable as a time-dependent Ginzburg-Landau model with nonconserved order parameter are considered in a block (V=L ^d) geometry with periodic boundary conditions, both for space dimensionalitiesd4 andd=4–. A systematic approach for studying finite size effects on dynamic critical behavior is developed. The method consists in constructing an effective reduced dynamics for the lowest-energy (q=0) mode by integrating out the remaining degrees of freedom, and generalizes recent analytic approaches for studying static finite size effects to dynamics. Above four dimensions, the coupling to the other (q0) modes is irrelevant and the probability densityP(,t) for the normalized order parameter=d^d x(x,t)/V satisfies a Fokker-Planck equation. The dynamics is equivalently described by the Langevin equation for a particle moving in a ||⁴ potential or by a supersymmetric quantum mechanical Hamiltonian. Dynamic finite size scaling is found to be broken, e.g. the order parameter relaxation rate varies at the bulk critical temperatureT _c, as (T _c, L)L ^–d/2 asL. By contrast, ford<4, the coupling to the other (q0) modes cannot be ignored and dynamic finite size scaling is valid. The asymptotic behavior of correlation and response functions can be studied within the framework of an expansion in powers of ^1/2. The scaling function associated with is computed to one-loop order. Finally, the many component (n) limit is briefly considered.     

Kinetic studies of laser-induced synthesis of thin vanadium pentoxide films

The kinetics of Ar⁺ laser-induced oxidation of 100 nm thick vanadium films on glass substrates is followed by measuring time-dependent changes in reflected and transmitted intensity of a He-Ne probe beam. The growth rate of the vanadium pentoxide layer increases with increasing laser powerP as = ₀ exp(-a/P). At power densities above kW/cm² vanadium pentoxide crystallizes from the melt.     

Parity operator and quantization of δ-functions

In the Weyl quantization scheme, the -function at the origin of phase space corresponds to the parity operator. The quantization of a functionf() on phase space is the operator f(/2)W()dM, whereM is the parity andW() the Weyl operator.     

τ-Lepton decay in an arbitrary plane-wave electromagnetic field

This paper discuses the , decay process in a field formed by the super-position of two fields: a crossed constant field and and electromagnetic plane-wave field. An expression is derived for the decay probability under the assumption of a nonzero -neutrino mass. The dependence of the decay probability on the lepton spin and on the external-field parameters is analyzed. The variation of the decay probability with the neutrino mass and lepton spin yields information which may be useful for ascertaining the neutrino mass.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 27–32, December, 1985.The authors are indebted to Professor V. R. Khalilov for a formulation of the problem and many valuable comments.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Measurements of rotational energy transfer and quenching in OHA 2 σ +,υ′ = 0 at elevated temperature

Total rotational energy transfer rates have been measured at 1330 K for specific rotational levels in the OHA ^{2 +}, = 0 state in collisions with H₂O. Rotational levels ranging fromN = 0 to 15 were studied. Measurements were performed in the post-flame region of a stoichiometric H₂/O₂/He flame operating at 25 mbar. Quenching rates following excitation of individual upper rotational states were also measured. The RET and quenching rates both exhibit monotonic decreases with increasing rotational quantum number.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Directed compact lattice animals: Exact results

The partially directed compact lattice animal model on the square lattice is solved exactly for the cluster number and average cluster radius along the directed axis in terms of the appropriate generating functions. For the critical exponents we find=0 and =1. Caliper size distribution along the directed axis is also calculated analytically. It is used to confirm =1 and to study some finite-size scaling properties for this model. For the perpendicular cluster radius distribution, a combination of analytic arguments and computer results leads to a conjecture on the exact form of the appropriate generating function and to the result =1/2. Some calculations are reported for the triangular lattice and for hypercubic lattices ind>2.     

Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

Gravitational and Electroweak Interactions

Schrodinger considered the variational principle , whereg is the determinant of the metricg, but noted that ifg is varied, the resultingEuler-Lagrange equations cannot serve as field equations. We writeg =g_ijh ⁱh ^j, where g_ij = diag(-1, 1,1, 1), and express the vectors of the tetradh ⁱ as derivatives ofnonintegrable functions xⁱ of the typecommonly used for phase factors in gauge theory, i.e.,h ⁱ =x_, ⁱ. We have previously shownthat if the xⁱ are varied, the resultingEuler–Lagrange equations serve as field equations which imply the validity of Einstein equationswith a stress-energy tensor for the electroweak fieldand associated currents. In this paper, we express theseEinstein equations into two new forms, and use these forms to derive Lorentz-force-likeequations of motion. The electroweak field appears as aconsequence of the field equations (rather than as acompensating field introduced to secure local gauge invariance). There is no need forsymmetry breaking to accommodate mass, because the gaugesymmetry is approximate from the outset.     

On a Static Solution of the Einstein Equation with Incoming and Outgoing Radiation

The Einstein equation with T = k k + where k, l are null is considered with spherical symmetry and staticity. The solution has a naked singularity and is not asymptotically flat. However, it may be interpreted as an envelope for any static spherical body making it more massive. Such an interpretation and some of its implications are detailed.     

On the question of the existence of a canonically defined distance function for metrics with indefinite signature on a given manifold

Let be the set of all inner products with a given indefinite signature on a finite-dimensional vector spaceV. It is shown that any continuous pseudometricd on which is canonical, i.e., invariant with respect to all automorphisms ofV, is of the formd(g, h)=f( _g / _h ), where _g , _h denote the volume elements associated withg andh, respectively, andf is a real-valued function; i.e., there are no nontrivial distance functions. This result shows that a reasonable distance function between metric fields on a manifoldM cannot be obtained in terms of canonical distances of the inner products induced in the tangent spaces. A similar result is proved even for uniform structures instead of pseudometrics.     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).     

The influence of the shape of load stress pulses on the course of plastic deformation of crystalline materials

The present paper deals with the derivation of the relationship between the course of macroscopic deformation and the dynamic properties of dislocation in loading material with stress pulses of general shape, and duration in tens of microseconds. On the basis of the obtained relationships, the correctness of the definition of the yield point under these conditions of loading, suggested previously (Czech. J. Phys.B 20 (1970), 776) on the basis of the analysis of the phenomenon of delayed deformation at elevated loading rates, is demonstrated.In the calculation we proceed, on the one hand, from the relation for the dislocation rate proposed by J. J. Gilman= exp(-D/) and, on the other hand, the damping mechanism of a viscous type, where=b/B.In both cases the correctness of the suggested definition is shown. The results of the theoretical analysis agree with the hitherto known experimental results.     

High-frequency expansion of relativistic classical plasma dielectric tensor

A high-frequency sum-rule expansion is derived for the transverse elements of the relativistic classical plasma dielectric tensor in an isotropic system. The relativistic results are different from the nonrelativistic ones by a factor of ^–1(1 – ²/3c ²) for ₂ (k) and longitudinal plasmon and transverse photon frequencies, and by ^–2(1–2 ²/3c ²) for ₂ (k).     

Ferromagnetic resonance in media with an inhomogeneous saturation magnetization

The method of transition probabilities is used to calculate the line width of ferromagnetic resonance in a medium with an inhomogeneous saturation magnetization. It is shown that in addition to linear (with respect to the Fourier components of the function describing inhomogeneities) terms, the perturbation Hamiltonian must include also quadratic terms. The frequency dependence of the contribution of the porosity to H is fundamentally different from the frequency dependence of the magnetic anisotropy contribution. This anisotropy contribution H_a() decreases on increase in the frequency and has a maximum at = (2/3)_M, whereas the porosity contribution H_p increases on increase in the frequency and vanishes at = (2/3)_M.deceasedTranslated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp.48–52, December, 1980.     

Continuity of type-I intermittency from a measure-theoretical point of view

We study a simple dynamical system which displays a so-called type-I intermittency bifurcation. We determine the Bowen-Ruelle measure and prove that the expectation (g) of any continuous functiong and the Kolmogoroff-Sinai entropyh() are continuous functions of the bifurcation parameter. Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.