Static structure factor of electrons around a heavy positively charged impurity in a one-component quantum rare plasma

An expression for the static structure factor,g ⁺⁻ (r), of electrons at a distancer from an infinitely heavy positively charged particle in a one component quantum rare plasma has been obtained in linear response theory using an appropriate quantum dielectric function of the rare plasma. The expression is a complicated function of the electron plasma frequency, Debye screening length andr, but reduces to that of classical plasma when quantum corrections are neglected. Forr<r _s (2r _s being the mean distance between two electrons), the temperature dependentg ⁺⁻ (r) has larger values in quantum case in comparison to that in classical situation and keeps increasing with decrease inr, more so at low temperatures when de-Broglie wavelength becomes larger and a considerable fraction ofr _s.     

Improved (1s)<Superscript>2</Superscript> variational model for helium

The ground-state energy of neutral helium is estimated variationally with a trial wavefunction of the form ϕ≈e ^−γ(rA/a _o)ⁿe^−γ(rB/a _o)ⁿ. This model represents a modification of traditional textbook examinations of this problem via inclusion of the power “n” as a second nonlinear variational parameter in addition to the usual effective nuclear charge γ and leads to an upper-limit on the ground state energy of −2.86107 E _h (E _h =1 hartree) in comparison with the traditional (n=1) result of −2.84766 E _h . This result represents a reduction of the percentage overestimate from the true ground-state energy (−2.90373 E _h ) of from 1.93 to 1.47. In comparison with the maximum accuracy obtainable from an uncorrelated trial wavefunction, −2.86168 E _h , the present trial wavefunction reduces the percentage overestimate from 0.49 (n=1) to 0.021. The optimum values of (n, γ) are determined to be ≈(0.897, 1.825).     

Quantum geometry and quantum mechanics of integrable systems

Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter ħ to produce a new (classical) integrable system. The new tori selected by the ħ-equidistance rule represent the spectrum of the quantum system up to O(ħ ^∞) and are invariant under quantum dynamics in the long-time range O(ħ ^−∞). The quantum diffusion over the deformed tori is described. The analytic apparatus uses quantum action-angle coordinates explicitly constructed by an ħ-deformation of the classical action-angles.     

ESR study of exchange coupled pairs in copper diethyldithiocarbamate

ESR investigations on exchange coupled pairs of Cu ions in single crystals of Cu(dtc)₂, isomorphously diluted with the corresponding diamagnetic zinc salt, are reported. The spin Hamiltonian parameters for the coupled species (S=1) are:g _‖=2.1025,g ₊=2.031,A=75.1×10⁻⁴ cm⁻¹,B=14.8×10⁻⁴,D=276.0×10⁻⁴ cm⁻¹ andE=46.7×10⁻⁴ cm⁻¹. While theg andA tensors show tetragonal symmetry, the zeor-field splitting tensor is rhombic and has principal axes different from those of theg andA tensors. Intensity measurements made down to 4.2 K indicate that the exchange is ferromagnetic with |FFF| ∼ 10 cm⁻¹. Direct dipole-dipole interaction appears to be the major contribution to the zero-field splitting. A calculation on the distributed point dipole model shows that dipolar interaction is considerably modified by the high covalency of the Cu-S bond and accounts for the rhombic nature of the tensor. The possible exchange mechanisms in Cu(dtc)₂—direct exchange and superexchange through the bridging sulphurs—are discussed.     

ESR of V4+ in α-RbTiOPO4 single crystals

We have recorded and investigated the ESR spectrum of vanadium-doped α-RbTiOPO₄ single crystals in the temperature interval 77–300 K. Two types of structurally distinct centers, V1 and V2, with a 4:1 ratio of the peak intensities were observed. The angular dependences of the resonance magnetic fields are described by a spin Hamiltonian corresponding to axial symmetry with the parameters g _∥1=1.9305, g _⊥1=1.9565, A _∥1=−168.2×10⁻⁴cm⁻¹, and A _⊥1=−54.3×10⁻⁴cm⁻¹ for V1 centers and g _∥2=1.9340, g _⊥2=1.9523, A _∥2=−169.0×10⁻⁴cm⁻¹, and A _⊥2=−55.2×10⁻⁴cm⁻¹ for V2 centers. A model of a paramagnetic center is proposed: The vanadium ions replace titanium ions in two structurally distinct positions Ti1 and Ti2 (V1 and V2 centers, respectively). The possibility that a VO²⁺ ion forms when α-RbTiOPO₄ crystals and crystals of the KTP group (KTiOPO₄, NaTiOPO₄, α-and β-LiTiOPO₄), studied earlier, are doped with vanadium is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 534–536 (March 1998)     

Renormalization group functions of the φ<Superscript>4</Superscript> theory from high-temperature expansions

It has been previously shown that calculation of the renormalization group (RG) functions of scalar ϕ⁴ theory reduces to analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG functions of the four-dimensional theory can be calculated for arbitrary coupling constant g with an accuracy of 10⁻⁴ for the Gell-Mann-Low function β(g) and with an accuracy of 10⁻³–10⁻² for anomalous dimensions. The expansions of the renormalization group functions up to the 13th order in g ^−1/2 have been obtained.     

Quantization of a nonlinear oscillator as a model of the harmonic oscillator on spaces of constant curvature: One- and two-dimensional systems

The quantum version of a nonlinear oscillator, previously analyzed at the classical level, is studied first in one dimension and then in two dimensions. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx ²)⁻¹ and with a λ-dependent nonpolynomial rational potential. The quantization procedure analyzes the existence of Killing vectors and makes use of an invariant measure. It is proved that this system can be considered as a model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature. The text was submitted by the authors in English.     

Mixing of excitonic states containing light and heavy holes in an isolated GaAs/AlGaAs quantum well in a magnetic field

The Zeeman splitting of the ground states 1s(hh) and 1s(lh) of excitons with heavy and light holes, respectively, in a 15-nm isolated Al_0.3Ga_0.7As/GaAs quantum well in magnetic fields of up to 20 T is investigated according to the photoluminescence excitation spectra in the Faraday geometry (σ⁺− σ⁻ components). The observed anomalous pattern of nonlinear Zeeman splitting and the nonmonotonic behavior of the effective hole g factor are interpreted in terms of the strong mixing of the magnetoexcitonic states containing light and heavy holes. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 52–56 (10 July 1996)     

EPR and Optical Study of Cu<Superscript>2+</Superscript> Ions Doped in Sodium Zinc Sulfate Tetrahydrate Single Crystals

Electron paramagnetic resonance (EPR) study of Cu²⁺-doped sodium zinc sulfate tetrahydrate is done at liquid nitrogen temperature. Two magnetically equivalent sites for Cu²⁺ are observed. The spin-Hamiltonian parameters determined by fitting the EPR spectra to the rhombic-symmetry crystalline field are g _x  = 2.2356, g _y  = 2.0267, g _z  = 2.3472, A _x  = 27 × 10⁻⁴ cm⁻¹, A _y  = 54 × 10⁻⁴ cm⁻¹and A _z  = 88 × 10⁻⁴ cm⁻¹. The ground state wave function is also determined. The g-anisotropy is evaluated and compared with the experimental value. With the help of optical study, the nature of bonding in the complex is discussed.     

The Ground State Energy per Site of the Quantum and Classical Edwards-Anderson Spin Glass in the Thermodynamic Limit

We derive general rigorous lower bounds for the average ground state energy per site e ^(d) of the quantum and classical Edwards-Anderson spin-glass model in dimensions d=2 and d=3 in the thermodynamic limit. For the classical model they imply that e ⁽²⁾≥−3/2 and e ⁽³⁾≥−2.204⋯.     

Calculation of conformations and vibrational spectra of a monomeric fragment of the 2,6-carboxymethyl cellulose molecule

A theoretical conformational analysis has been carried out for the side substituents of a fragment of the molecule for 2,6-carboxymethyl cellulose (a water-soluble cellulose ether), and the frequencies and the potential energy distribution of the normal vibrations have been calculated for the most stable conformers of the ether groups of this fragment in the approximation of the molecular mechanics method. It has been shown that the most stable conformers are those that have the conformations gg, t, g⁻, g⁻, g⁻-for the groups of atoms on the bonds C5-C6, C6-O6, C13-O6, C10-C13, C10-O9 and the conformations g⁺g⁻, g⁺, g⁻, g⁻; g⁺g⁻, g⁻, g⁻, g⁻; g⁺g⁻, g⁻, g⁺, t for the groups of atoms on the bonds C2-O2, C11-O2, C7-C11, C7-O8. Comparative analysis of the calculated frequencies and the potential energy distribution of the normal vibrations for 13 of the most stable conformers showed, as in the case of the 2,6-hydroxyethyl cellulose molecule, that the frequencies and modes of the normal vibrations are highly sensitive to conformational transitions in the analyzed spectral region (800–1500 cm⁻¹). The characteristic patterns for the change in the frequencies and modes of the normal vibrations have been established in connection with conformational transitions within both side substituents. The observed conformational lability of the bulky substituents in the cellulose ether molecules and its manifestations in the vibrational spectrum provide a basis for hypothesizing that one of the major mechanisms for the process of their thermal gelation in aqueous solutions is conformational transitions within these substituents. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 1, pp. 5–15, January–February, 2007.     

Spectral coincidences between CO-Laser and nitric-oxide. A reinvestigation

The distribution of the localized levelsg(ε) in the forbidden gap of amorphous silicon is calculated from the dependence of the Fermi energy on the doping concentration of phosphorus donors and boron acceptors. The minimum ofg(ε) is verified by this method to be in the order of 10¹⁷ to 10¹⁸ cm⁻³eV⁻¹, whereas the maxima ofg(ε), which have been reported in the literature, are not confirmed.     

Oscillations of the magnetoresistance in an inclined magnetic field for MIS structures on (100) silicon with a high electron density

At electron densities N _S>6×10⁻² cm⁻²² a second series of oscillations, which are tentatively attributed to population of the second energy subband, is observed in addition to the main series of Shubnikov-de Haas oscillations. A change in phase of the oscillations of the second series is observed at some angle of inclination α_e of the field. The measured value of α_e is used to calculate the ratio of the cyclotron mass to the effective g factor. The maximum possible cyclotron mass is also determined as m _H< 0.32m _e. On this basis it is concluded that the second series of oscillations is due to electrons which have an in-plane effective mass m*≈0.2m _e and which belong to the same valleys of the Fermi surface as in the case of the main oscillations. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 136–140 (25 January 1998)     

Investigating the excitation of 8<Superscript>−</Superscript> isomers in the odd-odd nuclei of <Superscript>116–120</Superscript>Sb in the (<Emphasis Type="Italic">p,n</Emphasis>)-reaction

Isomeric cross-section ratios in ^116m,g Sb, ^118m,g Sb and ^120m,g Sb were measured in the (p, n)-reaction for an energy of protons of ∼6.7 MeV. Experimental values of σ ^m /σ ^g were obtained: (4.6 ± 0.4) × 10⁻⁴ for ¹¹⁶Sb, (5.4 ± 0.6) × 10⁻³ for ¹¹⁸Sb and (7.4 ± 0.7) × 10⁻³ for ¹²⁰Sb. Experimental values of the isomeric crosss-ection ratios are compared to the theoretical values calculated using the TALYS-1.0 code. The statistical nature of the (p, n) reaction is demonstrated in the excitation region of residual nuclei 0.8–3.5 MeV.     

Measurement of the Magnetic Moment of the First Excited State in 93Sr Using on-line TDPAC technique

The g-factor of the first excited state of ⁹³Sr (E = 213 keV, T _1/2 = 4.6 ns) was measured by an on-line TDPAC technique with use of the strong hyperfine field in Fe metal. The Larmor frequency ω _L = (2.60 ± 0.15) × 10⁸ rad/s was obtained. The g-factor is derived as g = −0.227 ± 0.013 from g = −ℏω _L/B _hf μ _N. If the spin of the first excited state of ⁹³Sr is assumed to be 3/2, the g-factor is predicted by a simple core-excitation model as g = −0.22, which is in good agreement with the present experimental result.     

Magnetooptical microwave spectroscopy of the coherent magnetic state in the mixed valence compound SmB6 in the frequency range 40–120 GHz

In undoped pure single crystals of the mixed valence compound SmB₆ anomalous ESR absorption is observed in the frequency range v=40–120 GHz at temperatures of 1.8–4.2 K. The ESR for the case of the coherent ground state consists of two components corresponding to g-factors g ₁=1.907±0.003 and g ₂=1.890±0.003. The amplitude of both ESR lines strongly depends on temperature in the temperature range studied: the amplitude of the first line with g=g ₁ increases and the amplitude of the second line decreases with temperature. A model based on consideration of intrinsic defects in the SmB₆ crystalline lattice, with a densit ∼10¹⁵−10¹⁶ cm⁻³, is suggested as an explanation for the anomalous ESR-behavior. In the frequency range v>70 GHz at T=4.2 K, in addition to the main ESR lines, a new magnetic resonance with a hysteretic field dependence is discovered. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 10, 707–712 (25 November 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

EPR and Optical Absorption Studies of Cu2+-Doped Bis(l-Asparaginato)Mg(II)

The electron paramagnetic resonance study of Cu²⁺-doped bis(l-asparaginato)Mg(II) is performed at room temperature. Two magnetically non-equivalent sites for Cu²⁺ are observed. The spin-Hamiltonian parameters evaluated by fitting spectra to the crystalline field of rhombic symmetry are as follows: g _x  = 2.0420 ± 0.0002, g _y  = 2.0808 ± 0.0002, g _z  = 2.3600 ± 0.0002, A _x  = (99 ± 2) × 10⁻⁴ cm⁻¹, A _y  = (108 ± 2) × 10⁻⁴ cm⁻¹, A _z  = (140 ± 2) × 10⁻⁴ cm⁻¹. The ground state wave function of Cu²⁺ is also determined. The g-anisotropy is estimated and compared with the experimental value. Further, with the help of optical study the nature of bonding of a metal ion with different ligands in the complex is discussed.     

Semiempirical study of perturbations of the Landé g factors of electronic-vibrational-rotational levels of hydrogen: II. i 3 g − and j 3Δ g − states of the H2, HD,and D2 molecules

The values of the Landé g factors of the i ³Π _g ⁻ , v, N and j ³Δ _g ⁻ , v, N states of the H₂, HD, and D₂ molecules have been found semiempirically for the following vibrational and rotational quantum numbers: v≤3; N≤7 for H₂; N≤5 for HD; and N≤11 for D₂. These values were obtained in terms of the nonadiabatic model, which takes into account the interaction between the 3dπ³Π_g and 3dδ³Δ_g states with the same values of v and N in the approximation of pure precession, with the use of semiempirical values of the expansion coefficients of the wave functions in the Born-Oppenheimer basis determined by us previously and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. The results obtained for the H₂ molecule are in good agreement with the data in the literature. For the i ³Π _g ⁻ and j ³Δ _g ⁻ states of the HD and D₂ molecules, the g factors were found for the first time. This made it possible to study for the first time the role of the isotopic effect in the perturbation of the dependences of the g factors of rovibrational levels on v and N for the triplet electronic states of the hydrogen molecule. It was found that the interference effects of interaction between the 3dπ³Π_g and 3dδ³Δ_g states lead both to significant differences—up to 8, 6, and 11 times for H₂, HD, and D₂, respectively (the i ³Π _g ⁻ state), 20 times for H₂ and HD, and two orders of magnitude for D₂ (the j ³Δ _g ⁻ state)—between the nonadiabatic values of the g factors and the corresponding adiabatic values for some isotopomers of the hydrogen molecule and to significant differences—up to 9 and 1.5 times for the j ³Δ _g ⁻ and i ³Π _g ⁻ states, respectively—in the nonadiabatic values of the g factors of rovibrational levels of different isotopomers of the hydrogen molecule. __________ Translated from Optika i Spektroskopiya, Vol. 96, No. 1, 2004, pp. 42–54. Original Russian Text Copyright ? 2004 by Astashkevich.