Ultraviolet bands of mercury bromide

The ultraviolet bands of mercury bromide have been excited in uncondensed discharge and photographed with a quartz Littrow spectrograph. The class II system, lying betweenλ 2900 å to 2700 å, suggested byWieland as due to the triatomic molecule, has been studied in detail and ascribed to the diatomic molecule. The bands in the regionλ 2900 å to 2770å have been analysed into two systems which may form the two components of a² II ?² σ electronic transition with a² II interval equal to 969·4 cm^?1. Another system most probably due to² σ?² σ has been observed in the regionλ 2770 to 2720.     

Ultra-violet bands of mercury chloride

The Ultra violet bands of mercury chloride have been excited in uncondensed discharge and photographed with a quartz Littrow Spectrograph. The Class II system betweenλ 2900 to 2700 suggested by Wieland as due to the triatomic molecule has been studied in detail. In addition to the bands already recorded by previous investigators, a number of new bands has been recorded in the present investigation. A new vibrational analysis of these bands is given. The entire bands are ascribed to the longer wavelength component of² π-² ?, the other component being the system in the regionλ 2650 to 2400 with a² π interval of 3335 cm^?1 which is in keeping with the corresponding intervals obtained in the case of HgF and Hg I respectively. The following vibrational constants have been determined.Ν _e Ω′ _e Ω″ _e 36346 cm?1 385 cm?1 292.5 cm?1     

A multiwavelength low-pressure radiation source based on argon and xenon chlorides

The characteristics of an excimer radiation source pumped by a subnormal dc glow discharge in an Ar/Xe/Cl₂ mixture with the source operating in a spectral range of 160–310 nm were studied. The emission intensities of the 175, 236, 258, and 308 nm bands due to the transitions ArCl (B-X), XeCl (D-X), Cl₂ (D′-A′), and XeCl (B-X), respectively, were optimized in relation to the pressure, composition, and discharge current of the mixture.     

A new emission band spectrum of sulphur

A new emission band system of S₂ has been obtained in the region λ 3050–λ 2670 when sulphur is excited in a 30 mc/S. high frequency discharge from a 1/2 kW oscillator. The bands appear single sharp headed and are degraded towards red. Analysis of these new bands as belonging to a single system has led to the following vibrational formula.ν=36624·7+428·5(v′+1/2)?3·45(v′+1/2)² ?699·2(v″+1/2)+3·2(v″+1/2)². This system disignated as (b?x) is tentatively assigned to the electronic transition¹∑ _u ⁺ ?¹∑ _g ⁺ . The¹∑ _g ⁺ (x) state is found as the common lower state of three of the far ultraviolet systems of S₂ recently reported byTanaka andOgawa.     

On the calculation of the two-point function for the thirring-model by the method of functional integration

By the method of functional integration the two-point functionS _F for the spinor model with the interaction\( - \lambda (\bar \psi \psi )^2 \) is calculated in a two-dimensional space-time. After Fourier-transformationS _F (p) results as a power series with respect to 1/√λ. If we change the order of terms, we get a series in powers of γp. Each coefficient is a series in powers of 1/√λ. The first terms of this series are considered as a good approximation for bigλ. By reasons of convergence of the integrals we must displace the expansion centre of the series in powers ofγ p fromp ²=0 top ²=a ².     

Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel

We consider mass-conserving self-similar solutions for Smoluchowski’s coagulation equation with kernel K(ξ,η)=(ξη) ^λ with λ∈(0,1/2). It is known that such self-similar solutions g(x) satisfy that x ^?1+2λ g(x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h _λ x ^?1+2λ g(x) in the limit λ→0. It turns out that \(h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)\) as x→0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.     

Emission und Schwingungsverteilung der 1. neg. Gruppe und der 2. pos. Gruppe in einem Stickstoffplasma

The intensity of the first negative system ofN ₂ ⁺ (B ² Σ _u ⁺ -X ² Σ _g ⁺ and of the second positive system ofN ₂(C ³ Π _u -B ³ Π _g ) was observed in the discharge and in the afterglow as function of discharge current. An a. c. discharge in pure nitrogen was used at pressures of about 5 torr. The intensity of the first negative system ofN ₂ ⁺ — in the discharge and in the afterglow — rises to a maximum and decreases with further increase of the discharge current. The afterglow intensity of the second positive system ofN ₂ shows a maximum too. In the discharge, however, the intensity of the second positive system ofN ₂ increases with increasing discharge current. The relative population of the vibrational levelsN _v′ =i/N _v′ =0 (i=1,2,3,4) of theB ² Σ _u ⁺ state ofN ₂ ⁺ , in the discharge and in the afterglow, increases with increasing discharge current, while the relative population of the vibrational levelsN _v′ =i/N _v′ =0 (i=1, 2, 3, 4) of theC ³ Π _u state ofN ₂ reaches a maximum in the discharge. There seems to be evidence that the first negative system ofN ₂ ⁺ is not excited by electron impact withN ₂ molecules in ground state under the discharge conditions in question.     

Possible check of neutral weak vector-bosons that couple to μ+μ− only

In connection with recent assumptions, that weak vector-bosons might couple only toμ ⁺ μ ^? currents (and not toe ⁺ e ^?-ones) the question arises, how to check these bosons, since no collidingμ ⁺ μ ^? beams are available. We have shown in this paper that this check could be performed by means of the resonance appearing in a pair production process fromμ-beams and that this process would work atμ-energies beyond 20 Bev.     

Niederenergetische Gammalinien vom Neutroneneinfang in Lu 175 und Lu 176

The low energy gamma-rays from neutron-capture in Lu 175 and Lu 176 have been investigated by means of the bent crystal-spectrometer at the DR-3-reactor at Risø. From the transitions in Lu 177 3 rotational bands have been determined. The levels of the (404)K=7/2⁺ groundstate rotational band are: 121,62 keV (I=9/2), 268,79keV (I=11/2), 440,66 keV (I=13/2), 636,22 keV (I=15/2), 854,34 keV (I=17/2). The level-sequence of the (514)K=9/2^?-band is: 150,39 keV (I=9/2), 288,99 keV (I=11/2), 451,49 keV (I=13/2), 637,05 keV (I=15/2) and 844,88 keV (I=17/2). At 457,92 keV is the basis for the (402)K=5/2⁺-band the higher levels of which are 552,05 keV (I=7/2), 671,89 keV (I=9/2), 816,63 keV (I=11/2), 985,23 keV (I=13/2), 1176,73keV (I=15/2) and probably 1389,5 keV (I=17/2). The energies of the levels apart from the 1389 keV-level have an accuracy of 7×10^?5. The energy differences between the 3 bands agree very well with the values expected from the Bohr-Mottelson-formulaE=A·I(I+1)+B·I ²(I+1)². The calculated branching-ratios within the 3 bands are in fairly good agreement with the experimental values. Theg _K -factors have been determined for 2 bands: It was found that for the (514)-bandg _K =1,16±0,04 and for the (402)-bandg _K =1,33±0,07.     

The emission spectrum of the NS molecule

The investigation of the emission spectrum of NS molecule has been carried out by using a Littrow-type quartz spectrograph and a two meter normal incidence type vacuum spectrograph. Theγ-system (² σ-² π), in which only the bands havingv′=0 and 1 were known previously, has been extended tov′=4. TheδG values of the upper state do not show much regularity indicating some perturbation in this state. The vibrational constants for theΒ-system (² δ-² π) have also been modified slightly by observing more bands for this system. Four new systems, all of which have the ground state as their common lower state, have been observed in the ultraviolet and the vacuum ultraviolet regions.     

Solutions of a Particle with Fractional <Emphasis Type="Italic">δ</Emphasis>-Potential in a Fractional Dimensional Space

A Fourier transformation in a fractional dimensional space of order λ (0<λ≤1) is defined to solve the Schrödinger equation with Riesz fractional derivatives of order α. This new method is applied for a particle in a fractional δ-potential well defined by V(x)=?γ δ ^λ (x), where γ>0  and δ ^λ (x) is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if 0<λ<α. The results for λ=1 and α=2 are in exact agreement with those presented in the standard quantum mechanics.     

Band interaction in <Superscript>162</Superscript>Dy, <Superscript>168</Superscript>Er,and <Superscript>172</Superscript>Yb

Coriolis interaction between levels of two rotational bands in ¹⁷²Yb with K ^π = 2⁺ and 3⁺ and in ¹⁶⁸Er between levels with K ^π = 0^?, 1^?, and 2^? is studied. The values of the interaction parameters are obtained. The mutual influence of two bands in ¹⁶²Dy with ΔK = 2, K _i ^π = 0 ₂ ⁺ and 2 ₁ ⁺ due to Coriolis interaction is demonstrated.     

Investigation of low-lying levels of the <Stack><Subscript>4</Subscript><Superscript>8</Superscript></Stack>Be nucleus in the multiquantum approximation of the orthogonal scheme

In the multiquantum approximation of the orthogonal scheme, specific calculations for the energies and radii of the ₄ ⁸ Be nucleus are performed with allowance for all states characterized by the λ=[44] Young diagram, the quantum numbers K_min and K_min+2 of the O(3(A?1)) group, and the quantum numbers E=K+2N (N≤9) of the U(3(A?1)) group. The convergence of the results with respect to the extension of the basis is studied, and the structure of relevant wave functions is revealed. The results of these calculations are compared with the results obtained in the analogous approximation of the unitary scheme.     

Frequency reference for atomic transitions of Rb D<Subscript>2</Subscript>-line based on the effect of selective reflection

On an example of the D₂-line of the Rb atoms the work of the frequency reference of atomic transitions is demonstrated, based on the application of the spectrum of a selective reflectance (SR) from the boundary of atom vapors with the use of nano-cell (NC) with the thickness L ~ λ/2, where λ is the laser wavelength equal to 780 nm. When changing the thickness of the nano-cell near the thickness L ~ λ/2, we observe the inversion of sign of the SR slope profile which is positive when L < λ/2 and negative when L > λ/2. In the case when the incidence angle of the laser beam on the surface of the nano-cell is close to the normal, in real-time it is possible to form the derivative of the SR which represents a resonance peak with ~35 MHz spectral linewidth and located at the atomic transition. The phenomenon of oscillation of the sign of slope while changing the nano-cell thickness from L ~ λ/2 up to L ~ 3/2λ is demonstrated. The practical application of the SR is noted.     

Signature splitting in two quasiparticle rotational bands of <Superscript>180,182</Superscript>Ta

The signature splittings in K^π = 1 ⁺: 7 /2[404] _π?9 /2[624] _ν, K^π = 0^?: 9 /2[514] _π?9 /2[624] _ν bands of ¹⁸⁰Ta and K^π = 0^?: 7 /2[404] _π?7 /2[503] _ν, K^π = 1^?: 5 /2[402] _π?3 /2[512] _ν, K^π = 1⁺: 7 /2[404] _π?9 /2[624] _ν bands of ¹⁸²Ta are analysed within the framework of two-quasiparticle rotor model. The phase as well as magnitude of the experimentally observed signature splitting in K^π = 1⁺ band of ¹⁸⁰Ta, which could not be explained in earlier calculations, is successfully reproduced. The conflict regarding placement of a 12 ⁺ level in K^π = 1 ⁺: 7 /2 ⁺[404] _π?9 /2 ⁺[624] _ν ground-state rotational band of ¹⁸⁰Ta is resolved and tentative nature of K^π = 0^?: 7 /2[404] _π?7 /2[503] _ν, K^π = 1⁺: 7 /2[404] _π?9 /2[624] _ν bands observed in ¹⁸²Ta is confirmed. As a future prediction for experimentalists, these two-quasiparticle structures observed in ¹⁸⁰Ta and ¹⁸²Ta are extended to higher spins.     

Spectroscopic diagnostics of barrier-discharge plasma in mixtures of cadmium diiodide vapor with gases

The spectral characteristics of the emission of atmospheric-pressure gas-discharge plasma in mixtures of cadmium diiodide vapor with gases (Ne, Ar, Kr, Xe, and N₂) were investigated along with the time characteristics of the voltage and current. The gas-discharge plasma was produced and excited by a barrier discharge at a repetition rate of sine voltage pulses of up to 140 kHz. The discharge emission was analyzed in the spectral range 200–900 nm with a high resolution (0.05 nm). Radiation from exciplex CdI(B-X) molecules and excimer I₂* molecules was revealed, as well as the atomic lines of cadmium, iodine, and inert gases. In a mixture with xenon, radiation from exciplex molecules XeI(B-X, B-A) was also found. This radiation prevailed in the spectra at mixture temperatures up to 150°C. The further increase of the temperature leads to the prevalence of the CdI(B-X) radiation. It was found that the most intense CdI(B-X) radiation is observed in mixtures CdI₂/Xe(N₂)/Ne. Regularities in the spectral characteristics of the emission of the gas-discharge plasma are discussed.     

Investigation of the optical constants of arsenic chalcogenide films in the wavelength range 0.5–2.5 μm

Thin films of chalcogenide glasses deposited on quartz glass substrates by thermal evaporation in vacuum have been investigated. The dependences n(λ) and k(λ) for films of different composition have been determined from the transmission spectra. Expressions of the n = A + BL + CL ² + Dλ ² + Eλ ⁴ type (L = (λ ² ? 0.028)^?1 and A, B, C, D, and E are constants) for calculating the refractive indices of As₂Se₃, AsSe₄, AsS₄, and AsS_16.2Se_16.2 films in the wavelength range from 0.5 to 2.5 μm are reported.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. II. Distributions with Heavy Tails

We study the asymptotic structure of the first K largest eigenvalues λ _k,V and the corresponding eigenfunctions ψ(?;λ _k,V ) of a finite-volume Anderson model (discrete Schrödinger operator) \(\mathcal{H}_{V}= \kappa \Delta_{V}+\xi(\cdot)\) on the multidimensional lattice torus V increasing to the whole of lattice ? ^ν , provided the distribution function F(?) of i.i.d. potential ξ(?) satisfies condition ?log(1?F(t))=o(t ³) and some additional regularity conditions as t→∞. For z∈V, denote by λ ⁰(z) the principal eigenvalue of the “single-peak” Hamiltonian κΔ _V +ξ(z)δ _z in l ²(V), and let \(\lambda^{0}_{k,V}\) be the kth largest value of the sample λ ⁰(?) in V. We first show that the eigenvalues λ _k,V are asymptotically close to \(\lambda^{0}_{k,V}\). We then prove extremal type limit theorems (i.e., Poisson statistics) for the normalized eigenvalues (λ _k,V ?B _V )a _V , where the normalizing constants a _V >0 and B _V are chosen the same as in the corresponding limit theorems for \(\lambda^{0}_{k,V}\). The eigenfunction ψ(?;λ _k,V ) is shown to be asymptotically completely localized (as V↑?) at the sites z _k,V ∈V defined by \(\lambda^{0}(z_{k,V})=\lambda^{0}_{k,V}\). Proofs are based on the finite-rank (in particular, rank one) perturbation arguments for discrete Schrödinger operator when potential peaks are sparse.     

Charged <Emphasis Type="Italic">ρ</Emphasis>-meson production in neutrino-induced reactions at &lt;<Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">ν</Emphasis></Subscript>&gt;≈ 10 GeV

The production of charged ρ mesons on nuclei and nucleons is investigated in charged current neutrino interactions at moderate energies (〈E _〉 ≈ 10 GeV), using the data obtained with SKAT bubble chamber. No strong nuclear effects are observed in ρ ⁺ and ρ ^? production. The fractions of charged and neutral pions originating from ρ decays are obtained and compared with higher-energy data. From analysis of the obtained and available data on ρ ⁺ and K*⁺(892) neutrino production, the strangeness suppression factor is extracted: λ _s = 0.18 ± 0.03. Estimation is obtained for cross section of coherent ρ ⁺ neutrino production on nuclei.     

Inverse Scattering at Fixed Energy on Surfaces with Euclidean Ends

On a fixed Riemann surface (M ₀, g ₀) with N Euclidean ends and genus g, we show that, under a topological condition, the scattering matrix S _V (λ) at frequency λ > 0 for the operator Δ+V determines the potential V if \({V\in C^{1,\alpha}(M_0)\cap e^{-\gamma d(\cdot,z_0)^j}L^\infty(M_0)}\) for all γ > 0 and for some \({j\in\{1,2\}}\) , where d(z, z ₀) denotes the distance from z to a fixed point \({z_0\in M_0}\) . The topological condition is given by \({N\geq \max(2g+1,2)}\) for j = 1 and by N ≥ g + 1 if j = 2. In \({\mathbb {R}^2}\) this implies that the operator S _V (λ) determines any C ^{1, α} potential V such that \({V(z)=O(e^{-\gamma|z|^2})}\) for all γ > 0.