Theoretical study of the 5p56s – 5p6 spectra of neutral xenon

Recent high precision measurements on the lifetime of the metastable 6s[3/2]₂ state of atomic xenon display a difference with previous predictions by a factor of 2–3. In the present work, a systematic relaxation and correlation approach, which has been developed on the basis of a widely used multi-configuration Dirac-Fock method, is applied to study the electric dipole allowed E1 and forbidden M1, E2 and M2 transitions between the 5p⁵ 6s and 5p⁶ configurations. We systematically include the correlation effects which arise from all the single and double excitations from the occupied shells into the (n=6–10) active sets and the relaxation effects caused by change of the electron density between the radiative initial- and final-states. This study not only reduces greatly the existing discrepancy in the lifetime of the 6s[3/2]₂ state, but also presents rather consistent results for both the lifetime of the metastable 6s'[1/2]₀ state and the oscillator strength of the 5p⁵ 6s - 5p⁶ E1 resonant transitions.     

Internal conversion investigations for the 127·37 keV E3 transition in134Cs

Relative conversion line intensities of the 127·37 keV E3 isomeric transition in¹³⁴Cs have been measured for ten atomic subshells, using the (/2) 13 beta-ray spectrometer. The multipolarity E3 + (0·07±0·04)% M4 was determined. Internal conversion coefficients were calculated in different physical approximations. Precise calculations were performed for two atomic models (non-relativistic Hartree-Fock-Slater and relativistic Hartree-Fock-Slater). Experimental data were found in agreement with tabulations of Hager and Seltzer and mentioned calculations. An upper limit for the -branching ratio (138·6 keV M4)/(127·37 keV E3) was found to be 0·2%. The measurement of the half-life of the isomeric state has been carried out with a NaJ(Tl) crystal. The result obtained isT _1/2 = (2·95 ± 0·02) h.The authors would like to thank Prof. U.Schmidt-Rohr for the interest in this work.     

Mittlere Energien und Driftgeschwindigkeiten von Elektronen in Stickstoff,Argon und Xenon,ermittelt aus Bildverstärkeraufnahmen von Elektronenlawinen

Local and temporal development of electron avalanches in a pulsed discharge gap (d=3,00 cm) are investigated in N₂, Ar, Xe and mixtures of N₂ and CH₄ by simultaneously applying high gain image intensifier- and photomultiplier techniques. Electron drift velocities are obtained from time-of-flight and way-of-flight measurements in these gases. The mean energy of agitation of the electrons is derived both from electron mobility and avalanche image trace profile (diffusion broadening). The results obtained (for 20°C), being in fair agreement with one another, read N₂: (4·6...5·0) eV forE/p=50...200 V/cm Torr; Ar: (9·0...9·5) eV forE/p=24... 45 V/cm Torr; Xe: (4·8...5·0) eV forE/p= 40... 90 V/cm Torr; CH₄(10% N₂): 6·3 eV forE/p= 89 V/cm Torr. The mean energy of agitation does not change very much withE/p in the ranges investigated. Some results concerning the radiation properties of these gases are included such as lifetime of the excited states, quenching pressure etc.     

Stiffness exponents for lattice spin glasses in dimensions $\mathsf{d = 3,\ldots,6}$

The stiffness exponents in the glass phase for lattice spin glasses in dimensions are determined. To this end, we consider bond-diluted lattices near the T = 0 glass transition point p^*. This transition for discrete bond distributions occurs just above the bond percolation point p_c in each dimension. Numerics suggests that both points, p_c and p^*, seem to share the same 1/d-expansion, at least for several leading orders, each starting with 1/(2d). Hence, these lattice graphs have average connectivities of near p^* and exact graph-reduction methods become very effective in eliminating recursively all spins of connectivity , allowing the treatment of lattices of lengths up to L = 30 and with up to 10⁵-10⁶ spins. Using finite-size scaling, data for the defect energy width over a range of p > p^* in each dimension can be combined to reach scaling regimes of about one decade in the scaling variable . Accordingly, unprecedented accuracy is obtained for the stiffness exponents compared to undiluted lattices (p = 1), where scaling is far more limited. Surprisingly, scaling corrections typically are more benign for diluted lattices. We find in for the stiffness exponents y₃ = 0.24(1), y₄ = 0.61(2), y₅ = 0.88(5), and y₆ = 1.1(1).Received: 29 October 2003, Published online: 20 April 2004PACS: 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Nr Spin-glass and other random models - 02.60.Pn Numerical optimization     

Rapid increase in the delay time for the breakdown of gas-filled gaps in high electric fields

An experimental study is reported of the delay-time statistics for electrical breakdown in air in intense electric fields E = 100–200 kV/cm. The dependence of the statistical delay time t_st for the breakdown on the gap width is obtained for various fields E. With E = 100 kV/cm and with an air pressure of p = 1 atm, the delay time is 20 nsec and depends weakly on in the range 5 = 3–10 mm. As the gap width is reduced from 3 to 2 mm, t_st increases sharply, reaching 3000 nsec. The gap width at which the sharp increase in t_st sets in decreases with increasing E. The gap-width dependence of t_st has the same nature at different pressures. The minimum delay time has been measured to be 8 nsec.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 2, pp. 36–39, February, 1969.     

Finite-Size Scaling in the p-State Mean-Field Potts Glass: A Monte Carlo Investigation

The p-state mean-field Potts glass with bimodal bond distribution (±J) is studied by Monte Carlo simulations, both for p = 3 and p = 6 states, for system sizes from N = 5 to N = 120 spins, considering particularly the finite-size scaling behavior at the exactly known glass transition temperature T _c. It is shown that for p = 3 the moments q ^(k) of the spin-glass order parameter satisfy a simple scaling behavior, being the appropriate scaling function and T the temperature. Also the specific heat maxima have a similar behavior, , while moments of the magnetization scale as . The approach of the positions T _max of these specific heat maxima to T _c as N is nonmonotonic. For p = 6 the results are compatible with a first-order transition, q ^(k) (q _jump)^k as N but since the order parameter q _jump at T _c is rather small, a behavior q ^(k) N ^-k/3 as N also is compatible with the data. Thus no firm conclusions on the finite-size behavior of the order parameter can be drawn. The specific heat maxima c _V ^max behave qualitatively in the same way as for p = 3, consistent with the prediction that there is no latent heat. A speculative phenomenological discussion of finite-size scaling for such transitions is given. For small N (N 15 for p = 3, N 12 for p = 6) the Monte Carlo data are compared to exact partition function calculations, and excellent agreement is found. We also discuss ratios , for various quantities X, to test the possible lack of self-averaging at T _c.     

A theoretical study of c-C5H8 adsorption on Ge (0 0 1)-2 × 1 and on dimer vacancies on the surface: Electronic structure and bonding

In this work we analyzed the geometry and the chemical interactions for c-C₅H₈ adsorption on Ge (0 0 1), using density functional theory calculations (DFT). We examined the changes in the atomic interactions using a slab model. We considered two cases, the cyclopentene adsorption on Ge(0 0 1) and on dimer vacancies on the surface. We found an average distance H-Ge, -C-Ge and C-Ge of 1.50, 1.70 and 1.65 Å, respectively, on dimer vacancies; and an average C-Ge distance of 2.05 Å on Ge-Ge dimer. We also computed the density of states (DOS) and the DOS weighted overlap populations (OPDOS) corresponding to C-C, C-Ge, C-H, and Ge-Ge bonds. During adsorption the main contribution are the CC double bond in both cases, and the next C and the H's belonging to this bonds in the case of adsorption on dimer vacancies. The orbital contribution includes participation of the 2p_y and 2p_z orbitals corresponding to unsaturated C atoms, 2p_z corresponding to side saturated C, and the 4p orbitals of Ge for the adsorption on dimer vacancies; 2s and 2p_z orbitals corresponding to double bond C atoms, 4s and 4p_z orbitals of Ge for the adsorption on Ge(0 0 1).     

An expansion of Hartree-Fock and correlation energies,relativistic corrections and the dipole matrix element in the powers of of 1/Z

Feynman diagrammatic technique was used for the calculation of Hartree-Fock and correlation energies, relativistic corrections, dipole matrix element. The whole energy of atomic system was defined as a polen-electron Green function. Breit operator was used for the calculation of relativistic corrections. The Feynman diagrammatic technique was developed for 〈H_B>. Analytical expressions for the contributions from diagrams were received. The calculations were carried out for the terms of such configurations as 1s² 2sⁿ¹ 2pⁿ² (2 ≧n₁≧ 0, 6≧ n₂ ≧ 0). Numerical results are presented for the energies of the terms in the form $$E = E_0 Z^2 + \Delta {\rm E}_2 + \frac{1}{Z}\Delta {\rm E}_3 + \frac{{\alpha ^2 }}{4}(E_0^r + \Delta {\rm E}_1^r Z^3 )$$ and for fine structure of the terms in the form $$\begin{gathered} \left\langle {1s^2 2s^{n_1 } 2p^{n_2 } LSJ|H_B |1s^2 2s^{n_1 \prime } 2p^{n_2 \prime } L\prime S\prime J} \right\rangle = \hfill \\ = ( - 1)^{\alpha + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 1} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 [E^{(0)} (Z - B) + \varepsilon _{co} ] + \hfill \\ + ( - 1)^{L + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 2} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 \varepsilon _{cc} . \hfill \\ \end{gathered} $$ Dipole matrix elements are necessary for calculations of oscillator strengths and transition probabilities. For dipole matrix elements two members of expansion by 1/Z have been obtained. Numerical results were presented in the form P(a,a′) = a/Z(1+τ/Z).     

Electrical properties (dc and ac) of vanadium-borate glass

The results of an investigation into the temperature and frequency dependence of the electrical conductivity [dc and ac (10²–10⁵ Hz)] of glass of the composition 35% B₂O₃-15% CaO-20% V₂O₄-30% V₂O₅ (weight %) are discussed. The resistivity of the glass at T=300°K is =1.2·10¹¹ ·cm. The activation energy of the dc conductivity is E=(0.652±0.004) eV and equal to E for ₂ at high temperatures. The temperature-frequency dependences of the polarization component _p, the dielectric loss coefficient, and the permittivity are explained on the basis of the Fröhlich model proposed for uncoupled relaxation oscillators for which the heights of the potential barriers are uniformly distributed in some range of energies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika. No. 3, pp. 35–38, March, 1981.     

Nuclear moments and the change in the mean square charge radius of neutron deficient thallium isotopes

The hyperfine structure, isotope and isomeric shifts in the atomic transition 6p ² P _3/2–7s ² S _1/2, =535 nm have been measured for theI=7 andI=2 states of^{190, 192, 194, 196}Tl; theI=1/2 andI=9/2 states of¹⁹¹Tl and the I=7 isomer of¹⁸⁸Tl. The thallium isotopes were prepared as fast atomic beams at the GSI on-line mass separator following fusion reactions and — in some cases — subsequent-decay. The nuclear dipole moments, electric quadrupole moments and the change in the nuclear mean square charge radius are evaluated. Theuu-isotopes show an isomeric shift which changes sign between¹⁹²Tl and¹⁹⁴Tl.Dedicated to P. Armbruster on the occasion of his 60th birthday     

Note on the quantum displacement of the critical point

The quantum corrections to the law of corresponding states are studied by calculating the critical pressure, temperature, and density to first order in Planck's constanth on an exactly soluble model. The ratio of the critical parameters to the corresponding classical values are found to be (p _c/p _c ⁰)^1/2=_c/_c ⁰ = T_c/T_c ⁰ = 1–0.67, with=h _c ^1/3(mkT _c)^–1/2. The critical ratio is independent ofh to first order. The results are compared with critical data for noble gases and hydrogen isotopes.     

No Zero Energy States for the Supersymmetric x 2 y 2 Potential

We show that the positive supersymmetric matrix-valued differential operator H = p _x ² + p _y ² + x ² y ² + x₃ + y₁ has no zero modes, i.e., H = 0 implies = 0. The result depends on a virial type argument for the corresponding supercharge. The model may be regarded as a simple relative of dimensional reductions of supersymmetric Yang–Mills theories.     

Fermi Surface Topology in the Case of Spontaneously Broken Rotational Symmetry

The relation between the broken rotational symmetry of a system and the topology of its Fermi surface is studied for the two-dimensional system with the quasiparticle interaction f(p, p') having a sharp peak at |p ? p'| = q₀. It is shown that, in the case of attraction and q₀ = 2p_F the first instability manifesting itself with the growth of the interaction strength is the Pomeranchuk instability. This instability appearing in the L = 2 channel gives rise to a second order phase transition to a nematic phase. The Monte Carlo calculations demonstrate that this transition is followed by a sequence of the first and second order phase transitions corresponding to the changes in the symmetry and topology of the Fermi surface. In the case of repulsion and small values of q₀, the first transition is a topological transition to a state with the spontaneously broken rotational symmetry, namely, corresponding to the nucleation of L ? π(p_F/q₀ ? 1) small hole pockets at the distance p_F ? q₀ from the center and the deformation of the outer Fermi surface with the characteristic multipole number equal to L. At q₀ → 0, when the model under study transforms to the two-dimensional Nozières model, the multipole number characterizing the spontaneous deformation is L → ∞, whereas the infinitely folded Fermi curve acquires the Hausdorff dimension D = 2 which corresponds to the state with the fermion condensate.     

Analogs of q-Serre relations in the Yang-Baxter algebras

Yang-Baxter bialgebras, as previously introduced by the authors, are shown to arise from a double crossproduct construction applied to the bialgebra R ₁₂ T ₁ T ₂ = T ₂ T ₁ R ₁₂, E ₁ T ₂ = T ₂ E ₁ R ₁₂, (T)=TT, (E)=ET + 1E and its skew dual, with R being a numerical matrix solution of the Yang-Baxter equation. It is further shown that a set of relations generalizing q-Serre ones in the Drinfeld-Jimbo algebras U _q(g) can be naturally imposed on Yang-Baxter algebras from the requirement of non-degeneracy of the pairing.     

Quantum Hamiltonian for the Rigid Rotator

An excess term exists when using hermitian form of Cartesian momentum p _i (i = 1,2,3) in usual kinetic energy 1/(2) p ² _i for the rigid rotator, and the correct kinetic energy turns to be 1/(2) (1/f _i ) p _i f _i p _i where f _i are dummy factors in classical mechanics and nontrivial in quantum mechanics.     

Messung der Hyperfeinstruktur-Aufspaltung des metastabilen3 P 2-Zustandes des Kr83 nach der Atomstrahl-Resonanzmethode

The hyperfine structure splitting of the metastable³ P ₂-state of Kr⁸³ has been measured by the atomic beam magnetic resonance method. A glow discharge served as a source of metastable atoms which were detected by surface ejection of electrons from a metal. In order to improve the signal-to-noise-ratio the magnetic C-field was modulated at a frequency of 37 cps. From the measured splittings the following hfs coupling constants were determined:

$$A(^3 P_2 ) = - (243 \cdot 970 \pm 0 \cdot 004)Mc/sec,B(^3 P_2 ) = - (452 \cdot 12 \pm 0 \cdot 08)Mc/sec.$$     

Collective states in highly symmetric atomic configurations and single-photon traps

We study correlated states in circular and linear-chain configurations of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective behavior is mediated by exchange of transverse photons between the atoms. For a circular atomic configuration containing N atoms, the collective energy eigenstates can be determined by group-theoretical means making use of the fact that the configuration possesses a cyclic symmetry group Z _N . For these circular configurations, the carrier spaces of the various irreducible representations of the symmetry group are at most two-dimensional, so that the effective Hamiltonian on the radiationless subspace of the system can be diagonalized analytically. As a consequence, the radiationless energy eigenstates carry a Z _N quantum number p = 0, 1, …, N, which is analogous to the angular momentum quantum number l = 0, 1, … carried by particles propagating in a central potential, such as a hydrogen-like system. Just as the hydrogen s states are the only electronic wave functions that can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the circular atomic sample can occupy the central atom only for vanishing Z _N quantum number p. When a central atom is present, the p = 0 state splits into two, showing level crossing at certain radii; in the regions between these radii, damped oscillations between two “ extreme” p = 0 states occur, where the excitation occupies either the outer atoms or the central atom only. For large numbers of atoms in a maximally subradiant state, a critical interatomic distance of λ/2 emerges both in the linear-chain and in the circular configuration of atoms. The spontaneous decay rate of the linear configuration exhibits a jumplike “critical” behavior for next-neighbor distances close to a half-wavelength. Furthermore, both the linear-chain and the circular configurations exhibit exponential photon trapping once the next-neighbor distance becomes less than a half-wavelength, with the suppression of spontaneous decay being particularly pronounced in the circular system. In this way, circular configurations containing sufficiently many atoms may be natural candidates for single-photon traps.     

Surface (110) of elementary semiconductors with diamond-type structure during stratified growth from an atomic beam in a vacuum

The stratified growth of an ideal crystal with diamond structure from an atomic beam in a vacuum is investigated by using the kinetic method of the theory of crystal growth. Equations are obtained to determine the mean concentrations _n of molecules consisting of n atoms on the (110) surface of the crystal. In the stationary case, an approximate analytic solution is obtained with a nonlinear dependence of ₁, ₂, and on the atomic beam density.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 92–96, Decmeber, 1981.