Magnetic and electric hyperfine interactions in the system EuSm

Magnetic and electric hyperfine interactions in the system EuSm were investigated with the isomeric 11/2^– state in¹⁴⁵Eu by applying the time-differential perturbed angular distribution (TDPAD) method. The temperature dependence of paramagnetism was studied between 90 K and 1000 K by measuring the magnetic hyperfine interaction frequency _L=g_NN¹ (T)B_ext. The paramagnetic correction factor strictly follows the Curie-Weiss relation =1+C/(T-), withC=–50(2) K and =–29(5) K. This is compatible with a hyperfine field ofB _int(0)=–25(1) T, a valence of two for Eu in Sm, and antiferromagnetic order at low temperatures.The temperature dependence of the electric quandrupole coupling constant v_Q, investigated between 100 K and 400 K, can be reproduced by a linear temperature variation v_Q(T)=v_Q(0) (1-AT), with v_Q(0)=16.2(4) MHz andA=7.2(8)·10^–4 K^–1.The paramagnetic relaxation time _rel of the nuclear alignment is proportional to the temperature of the sample, with _rel T^–1=3.7(2) ·10^–9s K^–1.This leads to the Korringa relation _J T=const=5.1(5)·10^–11s K for the relaxation time of the 4f electronic spinJ. Assuming that the relaxation ofJ is mainly caused by exchange interaction between conduction electrons and localized 4f electrons at the Eu site, an exchange integral of |J _eff|=0.10(2) eV can be deduced.     

High-resolution FTIR spectroscopy of HNSO—Analysis of the highly perturbed ν4, ν6 and 2ν5 bands

We report a rovibrational analysis of the ν₄ and ν₆ fundamentals and the 2ν₅ overtone of HNSO from high-resolution Fourier transform infrared spectra. The ν₆ band (out-of-plane bend) centred at 757.5 cm⁻¹ is c-type. The ν₄ band (HNS bend) centred at 905.9 cm⁻¹ is predominantly a-type with a very weak b-type component (). Numerous global perturbations and localized avoided crossings affecting the v₄ = 1 rotational levels were successfully treated by inclusion of Fermi and c-axis Coriolis resonance terms between v₄ = 1 and v₅ = 2, and a b-axis Coriolis resonance term between v₄ = 1 and v₆ = 1. The latter term gives rise to an avoided crossing with an extraordinary ΔK_a = 5 selection rule. The Fermi resonance between v₄ = 1 and v₅ = 2 gives rise to strong mixing of their rotational wavefunctions in the vicinity of K_a = 18. The resultant borrowing of intensity made it possible for 2ν₅ transitions in the range K_a = 16–19 to be assigned and included in a global rovibrational treatment of all three band systems.     

New observation of the , 1Δg, and 2Πg states and molecular constants with all Li2, Li2, and LiLi data

This paper reports our new observation of the , 1³Δ_g (v = 2–4), and 2³Π_g (v = 2–8) states of ⁶Li⁷Li by continuous wave perturbation facilitated optical–optical double resonance spectroscopy. Combining our new experimental term values of ⁶Li⁷Li with the available experimental data of ⁶Li₂ and ⁷Li₂, molecular constants and potential energy curves by Rydberg–Klein–Rees and direct-potential-fit techniques have been determined. Born-Oppenheimer breakdown parameters of the Li₂ 1³Δ_g and 2³Π_g states are calculated.     

A tunable frequency stabilized Ar+ laser

The frequency of a single-mode Ar⁺ laser atv=582 THz (=515 nm) is stabilized by means of an external iodine cell to a Doppler broadened absorption profile. The —unmodulated — stabilized laser frequency is reproducible to ±1 MHz or ±1.5×10^–9 v and can be shifted within a 180 MHz wide range.     

Narrow-band extreme-ultraviolet laser radiation tunable in the range 90.5–95 nm

Tunable, narrowband extreme ultraviolet radiation in the range 90.5–95 nm with only limited intensity variations is produced by frequency-tripling ultraviolet light from a frequency-doubled dye laser in a gas-jet of xenon. Acetylene gas is found to be an efficient medium for third-harmonic generation in this wavelength range as well. The extreme-ultraviolet radiation is applied in a spectroscopic study of the b ¹ II _u , v=6–8 and v=10–12, o ¹ II _u , v=0 and b¹ _u ⁺ , v=9 states of molecular nitrogen. From linewidth measurements a value k _p=6×10¹⁰ s^–1 for the predissociation rate of the b ¹ II _u , v=11 state is deduced.     

Determination of the isotopic composition of hydrogentritium mixtures by emission spectroscopy

Absolute effective cross sections for collisions of the second kind are evaluated by studying the dependence of line or molecular band intensification on the partial pressures of mixture components in a glow discharge. Determination of the cross sections is based on measurement of the relative intensities of the corresponding bands in mixtures of different percentage composition. The resulting values for the effective cross sections Q are as follows: N₂(C³ II)_v=3 and Ar(³P_o) 3.10^–15 cm², N₂(C³ II)_v=2 and Ar(³P₂) 0.8.10^–15 cm, N₂(C³ II)_v=0 and CO 2.10^–15 cm, CO(C³ II)_v=0 and Ar(³P₂) 0.3.10^–15 cm².In conclusion, the authors wish to thank V. S. Mel'chenko for discussing the results of the present study.     

Difference-frequency source for very low optical frequencies spectroscopy: CO2 induced spectra

In a previous paper [1] the manufacturing, development and testing of a coherent submillimetric source was exposed. This source was obtained by difference frequency mixing of two CO₂ TEA lasers.In this present work, are presented the first results obtained with this mounting and concerning the collision induced spectrum of gaseous carbon dioxide at room temperature in the 4–40 cm^–1 region.The absorption coefficient is calculated together with the first coefficients of its development as a function of density.The curves ₂/v ²=f(v) and ₃/v ²=f(v), wherev is the frequency, are presented. They permit the calculation of the virial coefficients.The results are then compared with those determined by an extrapolation in this frequency range, of measurements already made in CO₂ in higher (optical) or lower (microwaves) frequencies.     

Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Unfamiliar integrals and motions down the ‘plug-hole’ potential

The orbits in the potentials ψ=−CzR⁻²+ζ(R), (ζ arbitrary) have integrals E, and . Thus the z-velocity is proportional to the number of turns made around the axis! The Poisson Bracket [h,I] is not zero so Liouville’s integrability theorem does not apply. Starting from the self-similar potential with ζ∝R⁻¹, we find some orbits that spiral around cones and explore general orbits in this strange system.     

Inverse muon decay in a steady external field

A standard Weinberg-Salam model has been used to calculate the cross section of +e »v _e+ in steady crossed fields (EH=E ²–H ²=0). The asymptotic behavior of the cross section has been examined as a function of the kinematic and dynamic (field) invariant parameters.M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 106–111, December, 1992.     

Painlevé test of the McKean and Carleman models

The Painlevé test of the system of nonlinear partial differential first-order equations u₁+u_k=k₁v²+k₂u²+k₃uv, v₁–v_x=–k₁v²–k₂u²–k₃uv is performed. The system includes the Carleman and McKean models which are caricatures of the Boltzmann equation. For k ₁=k ₂=0 the system describes the interaction of two waves u and v. The results of the Painlevé test are discussed in connection with whether or not the system is integrable. We also study in detail the constraint on (whose vanishing defines a noncharacteristic hypersurface S) which arises at the resonance.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

The Relativistic Composite-Velocity Reciprocity Principle

Gyrogroup theory [A. A. Ungar, Found. Phys. 27, 881–951 (1997)] enables the study of the algebra of Einstein's addition to be guided by analogies shared with the algebra of vector addition. The capability of gyrogroup theory to capture analogies is demonstrated in this article by exposing the relativistic composite-velocity reciprocity principle. The breakdown of commutativity in the Einstein velocity addition of relativistically admissible velocities seemingly gives rise to a corresponding breakdown of the relativistic composite-velocity reciprocity principle, since seemingly (i) on one hand, the velocity reciprocal to the composite velocity uv is –(uv) and (ii) on the other hand, it is (–v)(–u). But (iii) –(uv)(–v)(–u). We remove the confusion in (i), (ii), and (iii) by employing the gyrocommutative gyrogroup structure of Einstein's addition and, subsequently, present the relativistic composite-velocity reciprocity principle with the Thomas rotation that it involves.     

Wide-range tunable sub-millimetre cyclotron resonance laser

The results of investigation of cyclotron type stimulated emission processes inp-Ge in strong crossedE B fields are presented. Using the optimumE,B field orientation the spectral range of continuous tuning of the emission line frequency was increased substantially. A tunable sub-millimetre laser with the tuning rangev = 25 to 95cm^–1 ( = 105 to 400m), output power 10 to 100mW and emission linewidthv 0.2cm^–1 is described.     

Effect of Microscopic Noise on Front Propagation

We study the effect of the noise due to microscopic fluctuations on the position of a one dimensional front propagating from a stable to an unstable region in the linearly marginal stability case. By simulating a very simple system for which the effective number N of particles can be as large as N=10¹⁵⁰, we measure the N dependence of the diffusion constant D_N of the front and the shift of its velocity v_N. Our results indicate that D_N(log N)^–3. They also confirm our recent claim that the shift of velocity scales like v_min–v_NK(log N)^–2 and indicate that the numerical value of K is very close to the analytical expression K_approx obtained in our previous work using a simple cut-off approximation.     

The millimeter-wave rotational spectrum of fluorobenzene

The room-temperature rotational spectrum of fluorobenzene was studied in the frequency region 167-318 GHz. Rotational transitions were assigned and measured in the ground vibrational state, and all six excited vibrational states with energies below 600 cm⁻¹, i.e., v₁₁ = 1, v₁₁ = 2, v_18b = 1, v_16a = 1, v_16b = 1, and v_6a = 1. Accurate quartic-level spectroscopic constants were determined for all states, allowing spectral predictions well into the submillimeter region. The states v_18b = 1 and v_16a = 1 were found to be connected by a strong Coriolis interaction, which allowed precise determination of their energy separation, ΔE = 7.455088(3) cm⁻¹. Unambiguous assignment of vibrational modes was made on the basis of the calculated inertial defect and nuclear spin statistical weights. Rotational constants for the ¹³C₄ isotopomer have also been redetermined and two new least-squares determinations of the geometry of fluorobenzene, r₀ and are reported.     

Vector-spinor space and field equations

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists a vector-spinor space with N_v vector dimensions and N_s spinor dimensions, where N_v=2k and N_s=2 ^k, k3. This space is decomposed into a tangent space with4 vector and4 spinor dimensions and an internal space with N_v–4 vector and N_s–4 spinor dimension. A variational principle leads to field equations for geometric quantities which can be identified with physical fields such as the electromagnetic field, Yang-Mills gauge fields, and wave functions of bosons and fermions.     

Motion of vortex lines and mutual friction in superfluid4He nearT λ

The motion of a single vortex line in superfluid⁴He nearT is studied within modelF. The linear response of the vortex-line velocityv _L to a homogeneous counterflowv _s –v _n is calculated up to lowest order of renormalized perturbation theory. The critical temperature dependence is taken into account via the renormalizationgroup theory. Non-asymptotic critical effects are found to be important. The results are generalized to describe collective vortex motion and mutual friction in rotating superfluid⁴He. The phenomenological mutual-friction coefficientsB andB of Hall and Vinen are determined without adjustment of parameters. ForB quantitative agreement with experiments nearT is found whereas forB the agreement is only semiquantiative.     

Scaling function for energy-density correlations: Dispersion theory andε-expansion forT>T c

A dispersion representation for the static energy-density correlation function ² (q) ²(–q) _c =C(q,T)=A+Bt ^–h(z ²), wherez=q , t=(T—T)_c/T _c and is the correlation length, is discussed.h(z ²) is calculated to order ² in the zero-field critical region (T>T _c) for the standard isotropicn-component ⁴Ginzburg-Landau-Wilson model. Utilizing a procedure similar to that introduced by Bray for the two-point correlation function, the-expansion results are used in conjunction with an approximant for the spectral functionF(z/2) Imh(—z ²) based on the asymptotically exact short-distance expansion resulth ^–1(z ²)z ^/v[D ₀+D ₁ z ^{–(1 —)/v} +D ₂ z ^–1/v ] to predict quantitatively the full momentum dependence ofC(q,T) forT>T _c. In contrast to the two-point correlation function,C(q,T) is found to be a monotonic function as the critical temperature is approached at fixedq (forT>T _c).