Rotational and vibrational temperatures of electronically excited BiN radicals in a chemiluminescent flame

Rotational and vibrational temperatures of electronically excited BiN radicals in a low-pressure Bi_x+N/N₂*/N₂+Ar chemiluminescent flame have been deduced from high-resolution Fourier-transform emission spectra. Bands of three electronic transitions, a³Σ⁺(a₁1)→X¹Σ⁺(X0⁺), b⁵Σ⁺(b₁0⁺)→X¹Σ⁺(X0⁺), and b⁵Σ⁺(b₁0⁺)→a ³Σ⁺(a₁1), were analysed to determine the optical temperatures in the a³Σ⁺(a₁1) and b⁵Σ⁺(b₁0⁺) states. The rotational temperatures characterising the rotational populations in the a₁1, v=0 and 1 states were determined from the a₁→X, 0-2, 0-3, 0-4, 1-1, and 1-2 bands. The b₁→X, 0-8 and 0-11 bands, and the b₁→a₁, 0-0 bands served to determine the rotational temperature of the radicals in the b₁0⁺, v=0 state. The temperatures derived from the various bands and transitions were well consistent and the mean rotational temperature was determined to be 353±18 K, which is close to the translational temperature of the gas.Vibrational temperatures of the radicals in the a₁1 and b₁0⁺ states were derived from band intensities of the a₁→X and from the b₁→X as well as b₁→a₁ systems, respectively. The Franck-Condon factors needed were calculated with RKR potentials deduced from literature values of the rotational and vibrational constants in the three states involved. The a₁1 vibrational temperature (336±21 K) was close to the rotational temperature, while the b₁0⁺ vibrational temperature (438±36 K) differed, likely due to the previously observed perturbation of the b₁0⁺ state.     

The bΣ(b0) → XΣ(X10,X21) and aΔ(a2) → X21 transitions of AsBr

Emission spectra of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺,X₂1) and a¹Δ(a2) → X₂1 transitions of AsBr have been measured in the near-infrared spectral region with a Fourier-transform spectrometer. The arsenic bromide radicals were generated in fast-flow systems by reaction of arsenic vapor (As_x) with bromine and were excited by microwave-discharged oxygen. The most prominent features in the spectrum are the Δv = +1,0,−1, and −2 band sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺) transition in the range 11 700-12 700 cm⁻¹. With lower intensities, the Δv = 0 and −1 sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₂1) sub-system show up in the same range. Further to the red, between 6000 and 6700 cm⁻¹, the Δv = 0, +1, and −1 sequences of the hitherto unknown a¹Δ(a2) → X₂1 transition are observed. Analyses of medium- and high-resolution spectra have yielded improved molecular constants for the X₁0⁺, X₂1, and b0⁺ states and first values of the electronic energy and the vibrational constants of the a2 state.     

Crystal and magnetic structures of Y2CrS4

Chromium(II) sulfide, Y₂CrS₄, prepared by a solid-state reaction of Y₂S₃ and CrS, showed an antiferromagnetic transition at 65 K. The neutron diffraction patterns at 10 and 90 K were both well refined with the space group Pca2₁. At 90 K, cell parameters were a=12.5518(13) Å, b=7.5245(8) Å, and c=12.4918(13) Å. At 10 K, magnetic peaks were observed, which could be indexed on the same unit cell. Magnetic moments of chromium ions were parallel to the b-axis and antiferromagnetically ordered in each set of the 4a sites.     

Functional properties of quantum logics

A quantum logic is defined as a setL of functions from the set of all statesS into [0, 1] satisfying the orthogonality postulate: for any sequencea ₁,a ₂, ... of members ofL satisfyinga _i+a _j≤1 fori≠j there isb∈L such thatb+a ₁+a ₂+...=1. Every logicL is in a natural way an orthomodular σ-orthocomplemented partially ordered set (L, ≤, ′) with members ofS inducing a full set of measures onL. It is shown that a logicL is quite full if and only if (L,≤,′) is isomorphic to an orthocomplemented set lattice of subsets ofS. Sufficient conditions are given in order that a quite full logic be representable in the set of projection quadratic formsf(u)=(Pu, u) on a complex Hilbert space, or in the set of trace functionsf(A)=Trace (AP) generated by projectionsP, where the domain off is the set of non-negative self-adjoint trace operators of trace 1 in a complex Hilbert space.     

Universality Limits of a Reproducing Kernel for a Half-Line Schrödinger Operator and Clock Behavior of Eigenvalues

We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schrödinger operators on the half-line. In particular, we define a reproducing kernel S _L for Schrödinger operators and we use it to study the fine spacing of eigenvalues in a box of the half-line Schrödinger operator with perturbed periodic potential. We show that if solutions u(ξ, x) are bounded in x by ${e^{\epsilon x}}We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schr?dinger operators on the half-line. In particular, we define a reproducing kernel S _L for Schr?dinger operators and we use it to study the fine spacing of eigenvalues in a box of the half-line Schr?dinger operator with perturbed periodic potential. We show that if solutions u(ξ, x) are bounded in x by e^ex{e^{\epsilon x}} uniformly for ξ near the spectrum in an average sense and the spectral measure is positive and absolutely continuous in a bounded interval I in the interior of the spectrum with x₀ ? I{\xi_0\in I}, then uniformly in I,

\fracSL(x0 + a/L, x0 + b/L)SL(x0, x0)? \fracsin(pr(x0)(a - b))pr(x0)(a - b),\frac{S_L(\xi_0 + a/L, \xi_0 + b/L)}{S_L(\xi_0, \xi_0)}\rightarrow \frac{\sin(\pi\rho(\xi_0)(a - b))}{\pi\rho(\xi_0)(a - b)},      6. New analysis of the C2 Ballik-Ramsay system from flame emission spectra      C. Amiot  J. Chauville  J.-P. Maillard 《Journal of Molecular Spectroscopy》1979,75(1):19-40 The C2b3Σg? → a3Πu Ballik-Ramsay system has been studied through emission flame spectra recorded with a Fourier transform interferometer. The 14 bands 0-0, 1-0, 1-1, 2-0, 2-1, 3-0, 3-1, 3-2, 4-1, 4-2, 5-2, 5-3, 6-3, and 7-4 were identified in the 4850- 9900-cm?1 spectral range. They have been reduced to molecular constants using an iterative, nonlinear, least-squares method. Rotational perturbations, observed in the b3Σg?v = 0, 1, 2, 5, and 6 levels, have been reduced. Dunham coefficients are obtained for both the b3Σg? and a3Πu states.      7. Optical anisotropy of orthorhombic InS      Kencichi Takarabe  Taneo Nishino 《Journal of Physics and Chemistry of Solids》1983,44(7):681-684 The optical anisotropy of InS single crystals in the range of photon energy from 1.8 to 3.5 eV has been studied by absorption, electroreflectance and wavelength-derivative reflectance measurements. These systematic optical measurements for the polarizations, E//a and E//b, have revealed that the transition at the fundamental absorption edge of InS is allowed for E//b, and there exist three distinct doublet transitions having different selection rules in the photon energy region from 2 to 3.5 eV; Bo and B'0doublet allowed only for E//b, A0 and A'0 allowed only for E//a, and E1 and E'1 allowed for both polarizations. The observed results are discussed based on the anisotropic nature of two chemical bonds in InS, cation-cation and cation-anion.      8. How chaotic is a state of a quantum system?      A. Wehrl 《Reports on Mathematical Physics》1974,6(1):15-28 A concept related to the entropy is studied. Let A and B be two density matrices, with eigenvalues a1, a2,… and b1, b2,…, arranged in decreasing order and repeated according to multiplicity. Then A is said to be “more mixed”, or “more chaotic”, than B, if a1?b1, a1+a2?b1+b2,…,a1+…+am?b1+…+bm,…; It turns out that if A is more mixed than B, then the entropy of A is larger than the entropy of B. However, more generally, let v be an arbitrary concave function, ?0, and vanishing at 0. Then, if A is more mixed than B, trv(A)?trv(B). It is shown that also the converse is true. Furthermore, a variety of other characterizations of the relation “A is more mixed than B” is obtained, and several applications to quantum statistical mechanics are given.      9. Structural phase transitions at high-temperature in double perovskite Sr2GdRuO6      C.A. Triana  L.T. CorredorD.A. Landínez Téllez  J. Roa-Rojas 《Physica B: Condensed Matter》2012,407(16):3150-3154 The crystal structure evolution of the Sr2GdRuO6 complex perovskite at high-temperature has been investigated over a wide temperature range between 298 K≤T≤1273 K. Powder X-ray diffraction measurements at room temperature and Rietveld analysis show that this compounds crystallizes in a monoclinic perovskite-type structure with P21/n (#14) space group and the 1:1 ordered arrangement of Ru5+ and Gd3+ cations over the six-coordinate M sites, with lattice parameters a=5.81032(8) Å, b=5.82341(4) Å, c=8.21939(7) Å, V=278.11(6) Å3 and angle β=90.311(2)o. The high-temperature analysis shows that this material suffers two-phase transitions. At 373 K it adopts a monoclinic perovskite structure with I2/m space group, and lattice parameters a=5.81383(2) Å, b=5.82526(4) Å, c=8.22486(1) Å, V=278.56(2) Å3 and angle β=90.28(2)o. Above of 773 K, it suffers a phase transition from monoclinic I2/m to tetragonal I4/m, with lattice parameters a=5.84779(1) Å, c=8.27261(1) Å, V=282.89(5) Å3 and angle β=90.02(9)o. The high-temperature phase transition from monoclinic I2/m to tetragonal I4/m is characterized by strongly anisotropic displacements of the anions.      10. Probing the sign-changeable interaction between dark energy and dark matter with current observations      Juan-Juan Guo  Jing-Fei Zhang  Yun-He Li  Dong-Ze He  Xin Zhang 《中国科学:物理学 力学 天文学(英文版)》2018,61(3):030011 We consider the models of vacuum energy interacting with cold dark matter in this study, in which the coupling can change sigh during the cosmological evolution. We parameterize the running coupling b by the form b(a) = b_0 a + b_e(1-a), where at the earlytime the coupling is given by a constant b_e and today the coupling is described by another constant b_0. We explore six specific models with(i) Q = b(a)H_0ρ_0,(ii) Q = b(a)H_0ρ_(de),(iii) Q = b(a)H_0ρ_c,(iv) Q = b(a)Hρ_0,(v) Q = b(a)Hρ_(de), and(vi) Q = b(a)Hρ_c.The current observational data sets we use to constrain the models include the JLA compilation of type Ia supernova data, the Planck 2015 distance priors data of cosmic microwave background observation, the baryon acoustic oscillations measurements,and the Hubble constant direct measurement. We find that, for all the models, we have b_0 0 and b_e 0 at around the 1σ level,and b_0 and b_e are in extremely strong anti-correlation. Our results show that the coupling changes sign during the evolution at about the 1σ level, i.e., the energy transfer is from dark matter to dark energy when dark matter dominates the universe and the energy transfer is from dark energy to dark matter when dark energy dominates the universe.      11. General two-mode squeezed states      R. F. Bishop  A. Vourdas 《Zeitschrift für Physik B Condensed Matter》1988,71(4):527-529 The states |A 1 A 2 are considered, where the operators are associated with a unitary representation of the groupSp(4,), and the two-mode Glauber coherent states |A 1 A 2> are joint eigenstates of the destruction operatorsa 1 anda 2 for the two independent oscillator modes. We show that they are ordinary coherent states with respect to new operatorsb 1 andb 2, which are themselves general linear (Bogolibov) transformations of the original operatorsa 1,a 2 and their hermitian conjugatesa 1 ,a 2 . We further show how they may be regarded as the most general two-mode squeezed states. Most previous work on two-mode squeezed states appears to be based on more restrictive definitions than our own, and thereby reduces to special cases which are unified within our treatment.      12. Superposition model (SPM) analysis of zero-field splitting parameters of Mn doped ZnAl2S4 crystal      M. Acikgoz 《Journal of Physics and Chemistry of Solids》2009,70(10):1366-1368 In this study, superposition model (SPM) is employed to investigate the local environment around the different Mn2+ centers in ZnAl2S4 spinel. Using SPM and crystallographic data, the zero-field splitting (ZFS) parameters b20, b40, and b43 are calculated for Mn2+ at the B-site (with local symmetry D3d), whereas b40 and b44 for the A-site (Td). The lattice relaxation due to Mn2+ impurities is analyzed in terms of the bonding lengths and the angles between the Mn-S bond and the crystallographic axis [1 1 1]. Our SPM analysis of ZFS parameters indicates that satisfactory agreement can be achieved between the theoretical and the experimental results. Additional structural information about Mn2+ impurity centers is also obtained.      13. The millimeter-wave rotational spectrum of fluorobenzene      Z. Kisiel  E. Bia?kowska-Jaworska  L. Pszczó?kowski 《Journal of Molecular Spectroscopy》2005,232(1):47-54 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, v18b = 1, v16a = 1, v16b = 1, and v6a = 1. Accurate quartic-level spectroscopic constants were determined for all states, allowing spectral predictions well into the submillimeter region. The states v18b = 1 and v16a = 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.      14. Linear scaling of the interlayer relaxations of the vicinal Cu(p,p,p − 2) surfaces with the number of atom-rows in the terraces      Juarez L.F. Da Silva  Kurt Schroeder  Stefan Blügel 《Surface science》2006,600(15):3008-3014 We investigate the multilayer relaxation trends in the vicinal Cu(p,p,p − 2) surfaces employing the all-electron full-potential linearized augmented plane-wave method. Calculations are performed for the (3 3 1), (2 2 1), (5 5 3), (3 3 2), (7 7 5), and (4 4 3) surfaces, which have 3, 4, 5, 6, 7, and 8 atom-rows in the terrace, respectively. The following trends are identified: (i) The interlayer relaxations perpendicular to the surface scale almost linearly with the number of atom-rows in the terraces. (ii) The nearest-neighbor distances do not depend on the surface termination, but only on the local coordination. (iii) For Cu(p,p,p − 2) in which the topmost n surface layers have nearest-neighbor coordination smaller than the bulk Cu (calculated for the unrelaxed surfaces), the topmost (n − 1) interlayer spacings (d12, … , dn−1,n) contract compared with the unrelaxed spacing, while the nth interlayer spacing (dn,n+1) expands. The next (n − 2) interlayer spacings (dn+1,n+2, … , d2n−2,2n−1) contract, while the interlayer spacing indicated by d2n−1,2n expands. A similar rule was found for the relaxations parallel to the surfaces. These trends provide a better understanding of the atomic structure of vicinal Cu surfaces.      15. A Laser-Induced Fluorescence Study of the Visible Spectrum of Rhodium Monoxide      Romey F HeuffWalter J Balfour  Allan G Adam 《Journal of Molecular Spectroscopy》2002,216(1):136-150 A first analysis of an electronic spectrum of RhO is presented. The molecular species has been produced in a jet-cooled molecular beam following reaction in a laser ablation plasma. Laser excitation spectra have been recorded between 600 and 640 nm at 200 MHz resolution. Two transitions have been identified of 2Πr(a)-X4Σ−(b) type and six subbands have been rotationally analyzed, four being (0,0) components. Molecular parameters for the X4Σ − state are B0=0.41320 cm−1, λ0=−0.5733 cm−1, γ0=−0.10276 cm−1, and r0=0.1717 nm. An analysis of the hyperfine structure involving the 103Rh nucleus has been made. It shows that the ground state of RhO conforms to Hund's coupling case bβJ with b=− 0.0203 cm−1. Hyperfine effects in the excited states are negligible.      16. Dipole moment of the HO2 radical from its microwave spectrum      Shuji Saito  Chi Matsumura 《Journal of Molecular Spectroscopy》1980,80(1):34-40 Stark effects are measured for the 101 ← 000, 717 ← 808, and 909 → 818 transitions of the HO2 free radical. The unresolved Stark patterns of the b-type transitions are analyzed by the use of computer simulation. Second-order perturbation theory, including the effect of spin-doublings in the denominators, is used for the calculation of the Stark effect coefficients. The dipole moment determined is μa = 1.412 ± 0.033 D, μb = 1.541 ± 0.016 D, and μtotal = 2.090 ± 0.034 D.      17. Synthesis and characterization of Co7(OH)12(C2H4S2O6)(H2O)2—a single crystal structural study of a ferrimagnetic layered cobalt hydroxide      Paul M Forster 《Journal of Physics and Chemistry of Solids》2004,65(1):11-16 A novel layered hydrotalcite-like material, Co7(H2O)2(OH)12(C2H4S2O6), has been prepared hydrothermally and the structure determined using single crystal X-ray diffraction (a=6.2752(19) Å, b=8.361(3) Å, c=9.642(3) Å, α=96.613(5)°, β=98.230(5)°, γ=100.673(5)°, R1=0.0551). The structure consists of brucite-like sheets where 1/6 of the octahedral sites are replaced by two tetrahedrally coordinated Co(II) above and below the plane of the layer. Ethanedisulfonate anions occupy the space between layers and provide charge balance for the positively charged layers. The compound is ferrimagnetic, with a Curie temperature of 33 K, Curie-Weiss θ of −31 K, and a coercive field of 881 Oe at 5 K.      18. Variable-temperature Raman scattering and X-ray diffraction studies of Bi3.25Nd0.75Ti3O12 ceramics      Y.H. Wang  C.P. Huang 《Solid State Communications》2006,138(5):229-233 Neodymium-substituted bismuth titanate (Bi3.25Nd0.75Ti3O12, BNT0.75) ceramics was prepared by chemical co-precipitation along with calcinations. The lattice instability has been investigated by variable-temperature Raman scattering and X-ray diffraction. The results showed that there was an orthorhombic to pseudo-tetragonal phase transition at about 695 K, in terms of the evolution of temperature dependence of Raman scattering frequencies. Some changes at about 695 K in the XRD lines, the lattice parameters (a, b, and c) as well as the orthorhombic distortion b/a have been detected in the high temperature X-ray diffraction, which confirmed the conclusion that the BNT0.75 ceramics undergoes a ferroelectric to paraelectric phase transition at about 695 K.      19. Theoretical Analysis of the Fluorescence Spectra of 7-Azaindole and Its Tautomer      G. N. Ten  O. E. Glukhova  M. M. Slepchenkov  V. I. Baranov 《Optics and Spectroscopy》2016,120(3):359-366 The electronic—vibrational fluorescence spectra of the first, S0 → 1Lb, and second, S0 → 1La, electronic transitions of 7-azaindole and its tautomer for an isolated state have been calculated. Specific features of structural changes in 7-azaindole and its tautomer upon electronic excitation are determined. Vibrational spectra are assigned for the ground state, and the vibrational structure of fluorescence spectra is interpreted. It is shown that the intensity redistribution between the 6a and 6b oscillations, which is observed in the fluorescence spectrum of the S0 → 1Lb transition in 7-azaindole, can be explained as a result of intensity borrowing (according to the Herzberg—Teller mechanism) from the 1La state.      20. Sub-Doppler laser-Stark and high-resolution Fourier transform spectroscopy of the ν3 band of formic acid      《Journal of Molecular Spectroscopy》1987,121(2):243-260 The 5.6-μm band of HCOOH, which is the strong carbonyl stretch mode, is analyzed using a combination of sub-Doppler resolution laser-Stark data obtained with a CO laser and Fourier transform data obtained from a Bomem interferometer. The Fourier transform data, including 647 lines with J′ ≤ 22 and Ka ≤ 11, are fit with a Watson-type Hamiltonian to determine excited state constants. The Coriolis interactions with v5+9 and v6+9, previously noted by Kuze et al., are included in the analysis; the former by using an exact diagonalization technique, the latter via perturbation theory. Taking the molecular parameters from this fit, the laser-Stark data are then analyzed to give ground and excited state dipole moments, yielding the following results in Debyes: μ″a=1.4071(8)μ″b=0.227(10)μ′a=1.4353(9)μ′b=0.214(9), where the errors are 3σ estimates. The laser-Stark data are limited to J′ ≤ 7 and give a ± 14 MHz fit to 191 lines.

New analysis of the C2 Ballik-Ramsay system from flame emission spectra

The C₂b³Σ_g^? → a³Π_u Ballik-Ramsay system has been studied through emission flame spectra recorded with a Fourier transform interferometer. The 14 bands 0-0, 1-0, 1-1, 2-0, 2-1, 3-0, 3-1, 3-2, 4-1, 4-2, 5-2, 5-3, 6-3, and 7-4 were identified in the 4850- 9900-cm^?1 spectral range. They have been reduced to molecular constants using an iterative, nonlinear, least-squares method. Rotational perturbations, observed in the b³Σ_g^?v = 0, 1, 2, 5, and 6 levels, have been reduced. Dunham coefficients are obtained for both the b³Σ_g^? and a³Π_u states.     

Optical anisotropy of orthorhombic InS

The optical anisotropy of InS single crystals in the range of photon energy from 1.8 to 3.5 eV has been studied by absorption, electroreflectance and wavelength-derivative reflectance measurements. These systematic optical measurements for the polarizations, E//a and E//b, have revealed that the transition at the fundamental absorption edge of InS is allowed for E//b, and there exist three distinct doublet transitions having different selection rules in the photon energy region from 2 to 3.5 eV; Bo and B^'₀doublet allowed only for E//b, A₀ and A^'₀ allowed only for E//a, and E₁ and E^'₁ allowed for both polarizations. The observed results are discussed based on the anisotropic nature of two chemical bonds in InS, cation-cation and cation-anion.     

How chaotic is a state of a quantum system?

A concept related to the entropy is studied. Let A and B be two density matrices, with eigenvalues a₁, a₂,… and b₁, b₂,…, arranged in decreasing order and repeated according to multiplicity. Then A is said to be “more mixed”, or “more chaotic”, than B, if a₁?b₁, a₁+a₂?b₁+b₂,…,a₁+…+a_m?b₁+…+b_m,…; It turns out that if A is more mixed than B, then the entropy of A is larger than the entropy of B. However, more generally, let v be an arbitrary concave function, ?0, and vanishing at 0. Then, if A is more mixed than B, trv(A)?trv(B). It is shown that also the converse is true. Furthermore, a variety of other characterizations of the relation “A is more mixed than B” is obtained, and several applications to quantum statistical mechanics are given.     

Structural phase transitions at high-temperature in double perovskite Sr2GdRuO6

The crystal structure evolution of the Sr₂GdRuO₆ complex perovskite at high-temperature has been investigated over a wide temperature range between 298 K≤T≤1273 K. Powder X-ray diffraction measurements at room temperature and Rietveld analysis show that this compounds crystallizes in a monoclinic perovskite-type structure with P2₁/n (#14) space group and the 1:1 ordered arrangement of Ru⁵⁺ and Gd³⁺ cations over the six-coordinate M sites, with lattice parameters a=5.81032(8) Å, b=5.82341(4) Å, c=8.21939(7) Å, V=278.11(6) Å³ and angle β=90.311(2)^o. The high-temperature analysis shows that this material suffers two-phase transitions. At 373 K it adopts a monoclinic perovskite structure with I2/m space group, and lattice parameters a=5.81383(2) Å, b=5.82526(4) Å, c=8.22486(1) Å, V=278.56(2) Å³ and angle β=90.28(2)^o. Above of 773 K, it suffers a phase transition from monoclinic I2/m to tetragonal I4/m, with lattice parameters a=5.84779(1) Å, c=8.27261(1) Å, V=282.89(5) Å³ and angle β=90.02(9)^o. The high-temperature phase transition from monoclinic I2/m to tetragonal I4/m is characterized by strongly anisotropic displacements of the anions.     

Probing the sign-changeable interaction between dark energy and dark matter with current observations

We consider the models of vacuum energy interacting with cold dark matter in this study, in which the coupling can change sigh during the cosmological evolution. We parameterize the running coupling b by the form b(a) = b_0 a + b_e(1-a), where at the earlytime the coupling is given by a constant b_e and today the coupling is described by another constant b_0. We explore six specific models with(i) Q = b(a)H_0ρ_0,(ii) Q = b(a)H_0ρ_(de),(iii) Q = b(a)H_0ρ_c,(iv) Q = b(a)Hρ_0,(v) Q = b(a)Hρ_(de), and(vi) Q = b(a)Hρ_c.The current observational data sets we use to constrain the models include the JLA compilation of type Ia supernova data, the Planck 2015 distance priors data of cosmic microwave background observation, the baryon acoustic oscillations measurements,and the Hubble constant direct measurement. We find that, for all the models, we have b_0 0 and b_e 0 at around the 1σ level,and b_0 and b_e are in extremely strong anti-correlation. Our results show that the coupling changes sign during the evolution at about the 1σ level, i.e., the energy transfer is from dark matter to dark energy when dark matter dominates the universe and the energy transfer is from dark energy to dark matter when dark energy dominates the universe.     

General two-mode squeezed states

The states |A ₁ A ₂ are considered, where the operators are associated with a unitary representation of the groupSp(4,), and the two-mode Glauber coherent states |A ₁ A ₂> are joint eigenstates of the destruction operatorsa ₁ anda ₂ for the two independent oscillator modes. We show that they are ordinary coherent states with respect to new operatorsb ₁ andb ₂, which are themselves general linear (Bogolibov) transformations of the original operatorsa ₁,a ₂ and their hermitian conjugatesa ¹ ,a ² . We further show how they may be regarded as the most general two-mode squeezed states. Most previous work on two-mode squeezed states appears to be based on more restrictive definitions than our own, and thereby reduces to special cases which are unified within our treatment.     

Superposition model (SPM) analysis of zero-field splitting parameters of Mn doped ZnAl2S4 crystal

In this study, superposition model (SPM) is employed to investigate the local environment around the different Mn²⁺ centers in ZnAl₂S₄ spinel. Using SPM and crystallographic data, the zero-field splitting (ZFS) parameters b₂⁰, b₄⁰, and b₄³ are calculated for Mn²⁺ at the B-site (with local symmetry D_3d), whereas b₄⁰ and b₄⁴ for the A-site (T_d). The lattice relaxation due to Mn²⁺ impurities is analyzed in terms of the bonding lengths and the angles between the Mn-S bond and the crystallographic axis [1 1 1]. Our SPM analysis of ZFS parameters indicates that satisfactory agreement can be achieved between the theoretical and the experimental results. Additional structural information about Mn²⁺ impurity centers is also obtained.     

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.     

Linear scaling of the interlayer relaxations of the vicinal Cu(p,p,p − 2) surfaces with the number of atom-rows in the terraces

We investigate the multilayer relaxation trends in the vicinal Cu(p,p,p − 2) surfaces employing the all-electron full-potential linearized augmented plane-wave method. Calculations are performed for the (3 3 1), (2 2 1), (5 5 3), (3 3 2), (7 7 5), and (4 4 3) surfaces, which have 3, 4, 5, 6, 7, and 8 atom-rows in the terrace, respectively. The following trends are identified: (i) The interlayer relaxations perpendicular to the surface scale almost linearly with the number of atom-rows in the terraces. (ii) The nearest-neighbor distances do not depend on the surface termination, but only on the local coordination. (iii) For Cu(p,p,p − 2) in which the topmost n surface layers have nearest-neighbor coordination smaller than the bulk Cu (calculated for the unrelaxed surfaces), the topmost (n − 1) interlayer spacings (d₁₂, … , d_n−1,n) contract compared with the unrelaxed spacing, while the nth interlayer spacing (d_n,n+1) expands. The next (n − 2) interlayer spacings (d_n+1,n+2, … , d_{2n−2,2n−1}) contract, while the interlayer spacing indicated by d_2n−1,2n expands. A similar rule was found for the relaxations parallel to the surfaces. These trends provide a better understanding of the atomic structure of vicinal Cu surfaces.     

A Laser-Induced Fluorescence Study of the Visible Spectrum of Rhodium Monoxide

A first analysis of an electronic spectrum of RhO is presented. The molecular species has been produced in a jet-cooled molecular beam following reaction in a laser ablation plasma. Laser excitation spectra have been recorded between 600 and 640 nm at 200 MHz resolution. Two transitions have been identified of ²Π_r(a)-X⁴Σ⁻(b) type and six subbands have been rotationally analyzed, four being (0,0) components. Molecular parameters for the X⁴Σ ⁻ state are B₀=0.41320 cm⁻¹, λ₀=−0.5733 cm⁻¹, γ₀=−0.10276 cm⁻¹, and r₀=0.1717 nm. An analysis of the hyperfine structure involving the ¹⁰³Rh nucleus has been made. It shows that the ground state of RhO conforms to Hund's coupling case b_βJ with b=− 0.0203 cm⁻¹. Hyperfine effects in the excited states are negligible.     

Dipole moment of the HO2 radical from its microwave spectrum

Stark effects are measured for the 1₀₁ ← 0₀₀, 7₁₇ ← 8₀₈, and 9₀₉ → 8₁₈ transitions of the HO₂ free radical. The unresolved Stark patterns of the b-type transitions are analyzed by the use of computer simulation. Second-order perturbation theory, including the effect of spin-doublings in the denominators, is used for the calculation of the Stark effect coefficients. The dipole moment determined is μ_a = 1.412 ± 0.033 D, μ_b = 1.541 ± 0.016 D, and μ_total = 2.090 ± 0.034 D.     

Synthesis and characterization of Co7(OH)12(C2H4S2O6)(H2O)2—a single crystal structural study of a ferrimagnetic layered cobalt hydroxide

A novel layered hydrotalcite-like material, Co₇(H₂O)₂(OH)₁₂(C₂H₄S₂O₆), has been prepared hydrothermally and the structure determined using single crystal X-ray diffraction (a=6.2752(19) Å, b=8.361(3) Å, c=9.642(3) Å, α=96.613(5)°, β=98.230(5)°, γ=100.673(5)°, R1=0.0551). The structure consists of brucite-like sheets where 1/6 of the octahedral sites are replaced by two tetrahedrally coordinated Co(II) above and below the plane of the layer. Ethanedisulfonate anions occupy the space between layers and provide charge balance for the positively charged layers. The compound is ferrimagnetic, with a Curie temperature of 33 K, Curie-Weiss θ of −31 K, and a coercive field of 881 Oe at 5 K.     

Variable-temperature Raman scattering and X-ray diffraction studies of Bi3.25Nd0.75Ti3O12 ceramics

Neodymium-substituted bismuth titanate (Bi_3.25Nd_0.75Ti₃O₁₂, BNT_0.75) ceramics was prepared by chemical co-precipitation along with calcinations. The lattice instability has been investigated by variable-temperature Raman scattering and X-ray diffraction. The results showed that there was an orthorhombic to pseudo-tetragonal phase transition at about 695 K, in terms of the evolution of temperature dependence of Raman scattering frequencies. Some changes at about 695 K in the XRD lines, the lattice parameters (a, b, and c) as well as the orthorhombic distortion b/a have been detected in the high temperature X-ray diffraction, which confirmed the conclusion that the BNT_0.75 ceramics undergoes a ferroelectric to paraelectric phase transition at about 695 K.     

Theoretical Analysis of the Fluorescence Spectra of 7-Azaindole and Its Tautomer

The electronic—vibrational fluorescence spectra of the first, S₀ → ¹L_b, and second, S₀ → ¹L_a, electronic transitions of 7-azaindole and its tautomer for an isolated state have been calculated. Specific features of structural changes in 7-azaindole and its tautomer upon electronic excitation are determined. Vibrational spectra are assigned for the ground state, and the vibrational structure of fluorescence spectra is interpreted. It is shown that the intensity redistribution between the 6a and 6b oscillations, which is observed in the fluorescence spectrum of the S₀ → ¹L_b transition in 7-azaindole, can be explained as a result of intensity borrowing (according to the Herzberg—Teller mechanism) from the ¹L_a state.     

Sub-Doppler laser-Stark and high-resolution Fourier transform spectroscopy of the ν3 band of formic acid

The 5.6-μm band of HCOOH, which is the strong carbonyl stretch mode, is analyzed using a combination of sub-Doppler resolution laser-Stark data obtained with a CO laser and Fourier transform data obtained from a Bomem interferometer. The Fourier transform data, including 647 lines with J′ ≤ 22 and K_a ≤ 11, are fit with a Watson-type Hamiltonian to determine excited state constants. The Coriolis interactions with v₅₊₉ and v₆₊₉, previously noted by Kuze et al., are included in the analysis; the former by using an exact diagonalization technique, the latter via perturbation theory. Taking the molecular parameters from this fit, the laser-Stark data are then analyzed to give ground and excited state dipole moments, yielding the following results in Debyes: μ″_a=1.4071(8)μ″_b=0.227(10)μ′_a=1.4353(9)μ′_b=0.214(9), where the errors are 3σ estimates. The laser-Stark data are limited to J′ ≤ 7 and give a ± 14 MHz fit to 191 lines.