Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

Spin-0 and spin-1/2 particles in a constant scalar-curvature background

We study the Klein-Gordon and Dirac equations in the presence of a background metric ds²=−dt²+dx²+e^−2gx(dy²+dz²) in a semi-infinite lab (x>0). This metric has a constant scalar-curvature R=6g² and is produced by a perfect fluid with equation of state p=−ρ/3. The eigenfunctions of spin-0 and spin-1/2 particles are obtained exactly, and the quantized energy eigenvalues are compared. It is shown that both of these particles must have nonzero transverse momentum in this background. We show that there is a minimum energy E²_min=m²c⁴+g²c²?² for bosons (E_KG>E_min), while the fermions have no specific ground state (E_Dirac>mc²).     

High-resolution infrared spectra of OOO ozone isotopomer in the range 900-5000 cm: line positions

Continuing the systematic study of ozone high-resolution infrared spectra, we present in this paper the measurements and analyses of line positions for the ¹⁸O¹⁶O¹⁸O isotopomer. In the range 900-5000 cm⁻¹, corresponding to the observed spectra, 15 bands are analysed: ν₁, ν₃, ν₂+ν₃, ν₁+ν₂, 2ν₃, ν₁+ν₃, 2ν₁, ν₂+2ν₃, ν₁+ν₂+ν₃, 3ν₃, 2ν₁+ν₃, ν₂+3ν₃, ν₁+3ν₃, ν₁+ν₂+3ν₃, and 5ν₃. As in the case of ¹⁶O₃, ¹⁸O₃, and ¹⁶O¹⁸O¹⁶O, the analysis of these bands is performed using effective rovibrational Hamiltonians for nine polyads of interacting upper vibrational states. To correctly reproduce all observed transitions, we have to account for resonance perturbations due to 13 “Dark” states: (0 3 0), (0 4 0), (2 1 0), (0 3 1), (1 0 2), (0 4 1), (1 1 2), (3 1 0), (0 3 2), (0 0 4), (3 2 0), (0 1 4), and (0 4 2). We present the range of observed transitions, the results for spectroscopic parameters (vibrational energy levels, rotational and centrifugal distortion constants, and resonance coupling parameters), as well as the statistics for rovibrational energy levels, calculations and measurements. A comparison of observed band centres with those predicted from an isotopically invariant potential function is discussed. The RMS deviation between predicted and directly observed band centres is ≈0.03 cm⁻¹ up to 3000 and ≈0.25 cm⁻¹ for all 16 bands up to 5000 cm⁻¹.     

Vortex structure of Gross-Pitaevskii model

The vortex line of the Gross-Pitaevskii model is studied. The kinetic helicity of the vortex is discussed, and vortex structure is classified by the Hopf index, linking number in geometry. A mechanism of generation and annihilation of vortex lines is given by the method of phase singularity theory. The dynamic behavior of the vortex at the critical points is discussed in detail, and three kinds of length approximation relations at the neighborhood of a critical point are given: l ∝ (t − t^∗)^1/2, l ∝ t − t^∗, l = const.     

Preliminary analysis of CH3D from 3250 to 3700 cm

The infrared spectrum of CH₃D from 3250 to 3700 cm⁻¹ was studied for the first time to assign transitions involving the ν₂ + ν₃, ν₂ + ν₅, ν₂ + ν₆, ν₃ + 2ν₆ and 3ν₆ vibrational states. Line positions and intensities were measured at 0.011 cm⁻¹ resolution using Fourier transform spectra recorded at Kitt Peak with isotopically enriched samples. Some 2852 line positions (involving over 900 upper state levels) and 874 line intensities were reproduced with RMS values of 0.0009 cm⁻¹ and 4.6%, respectively. The strongest bands were found to be ν₂ + ν₃ at 3499.7 cm⁻¹ and ν₂ + ν₆ at 3342.5 cm⁻¹ with integrated strengths, respectively, of 8.17 × 10⁻²⁰ and 2.44 × 10⁻²⁰ (cm⁻¹/molecule · cm⁻²) at 296 K (for 100% CH₃D). The effective Hamiltonian was expressed in terms of irreducible tensor operators and adapted to symmetric top molecules. Its present configuration in the MIRS package permitted simultaneous consideration of the four lowest polyads of CH₃D: the Ground State (G.S.), the Triad from 6.3 to 9.5 μm, the Nonad from 3.1 to 4.8 μm and now the Enneadecad (19 bands) from 2.2 to 3.1 μm. The CH₃D line parameters for this interval were calculated to create a new database for the 3 μm region.     

High resolution infrared spectrum and global analysis of ν5, ν12, and ν12 + ν6 − ν6 in CH3SiH3

The vibration-torsion-rotation spectrum of CH₃SiH₃ has been measured from 470 to 725 cm⁻¹ at near-Doppler resolution. The full-width at half - maximum of the lines observed near 600 cm⁻¹ was 0.0011 cm⁻¹. The spectra were obtained using a Bruker IFS 125 HR Fourier transform spectrometer with the broadband source radiation being supplied from the synchrotron emission of the storage ring at the Canadian Light Source. Three vibrational bands were investigated: the lowest lying perpendicular fundamental ν₁₂ centred near 524 cm⁻¹, the lowest lying parallel fundamental ν₅ near 703 cm⁻¹, and the torsional hot band ν₁₂ + ν₆ − ν₆ near 534 cm⁻¹. For ν₁₂ and ν₅, the resolution and sensitivity are much improved over those in earlier studies, with many of the torsional multiplets now being resolved even in the cases where the upper levels are unperturbed. The primary motivation for the present work was the hot band, here reported for the first time, where the dependence of the silyl rock in ν₁₂ on the torsional motion is much more pronounced. In addition, for the vibrational ground state (gs), two “forbidden” high torsional overtones v₆ = 3 ← 0 and 5 ← 0 have been observed that become allowed through resonant mixing of the upper states with ν₁₂ and ν₅, respectively. In each case, two (K, σ) series have been measured where the mixing is largest. Here σ = 0, 1, −1 labels the torsional sub-levels. Using the Fourier transform waveguide spectrometer at E. T. H., the three σ-components of the (J = 1 ← 0) transition in ν₁₂ + ν₆ were observed, and a series of direct l-doubling transitions in ν₁₂ + ν₆ were measured for σ = 0. In a global fit, all the new data have been analysed along with the frequencies for other transitions obtained in earlier investigations. The analysis takes into account the relevant interactions among the torsional stacks of levels in the gs, ν₁₂, and ν₅. These include the previously known (gs, ν₁₂) Coriolis-like and (gs, ν₅) Fermi-like interactions along with a higher order (ν₁₂, ν₅) Coriolis-like coupling introduced here. This last is responsible for the strong perturbation of the ν₅ series with K = 10, 11, and 12, and of the corresponding hot band series. A good fit to 9282 frequencies including 7942 new measurements was obtained both with the Free Rotor model in which the torsion is classified as a rotation, and with the High Barrier model in which the torsion is classified as a vibration. The Hamiltonian is discussed with emphasis on the new terms required for treating ν₁₂ + ν₆ − ν₆.     

Passively Q-switched laser performance of c-cut Nd:Gd0.63Y0.37VO4 crystal

Passively Q-switched c-cut Nd:Gd_0.63Y_0.37VO₄ laser performance at 1.06 μm was demonstrated with Cr⁴⁺:YAG as saturable absorbers for the first time to our knowledge. This c-cut mixed crystal was found to have large energy storage capacity. The shortest pulse width, largest pulse energy, and highest peak power were obtained to be 6.6 ns, 201.7 μJ, and 30.6 kW, respectively.     

Global fit analysis including the ν9 + ν4 − ν4 hot band of ethane: Evidence of an interaction with the ν12 fundamental

The ν₉ fundamental band of ethane occurs in the 12 μm region. It is the strongest band of ethane in a terrestrial window and is commonly used for the identification of ethane in the Jovian planets. The ν₉ + ν₄ − ν₄ band occurs in the same region; neither can be analysed as an isolated band, since both are embedded in the torsional bath of the ground vibrational state. We report here two global fit models including data from both of these bands as well as the ν₃ fundamental and the ν₄, 2ν₄ − ν₄, and 3ν₄ torsional transitions. The first is restricted to −5 ? KΔK ? 15 in the hot band and gives an excellent fit to the included data. Three resonant interactions are identified in this fit—a Coriolis interaction with two resonant cases between the ν₉ torsional stack and that of the ground vibrational state (gs) and a resonant Fermi interaction between the ν₃ fundamental and the gs. Hot band lines with KΔK < −5 are influenced by a fourth perturbation, with a crossing at −11 < KΔK < −10, which has been attributed to an interaction with the ν₁₂ fundamental. A second fit, demonstrating a promising treatment of this interaction, is also presented.     

The high-resolution, jet-cooled infrared spectrum of pentafluoroethane

The jet-cooled spectrum of pentafluoroethane (C₂HF₅) has been recorded between 1100 and 1325 cm⁻¹ at a resolution of 0.0022 cm⁻¹. A rotational temperature of approximately 10 K was achieved by expanding 50 Torr of C₂HF₅ in 500 Torr of helium. Transitions belonging to five different fundamental vibrations have been assigned and fit to a Watson Hamiltonian: the ν₃ band at 1309.880494(189) cm⁻¹, ν₄ at 1200.734645(67) cm⁻¹, ν₅ at 1142.78147(33) cm⁻¹, ν₁₃ at 1223.334098(115) cm⁻¹, and ν₁₄ at 1147.394185(163) cm⁻¹. The fit of the ν₄ band has an rms deviation of 0.000436 cm⁻¹ compared to the uncertainty in the experimental line position of 0.0002 cm⁻¹. Satisfactory fits were achieved for the other four bands (ν₃, ν₅, ν₁₃, ν₁₄) at this cold temperature, with most of the centrifugal distortion constants fixed at the ground state values. Joint fits with previous work were attempted for the ν₄ and ν₁₃, successfully in the former case and unsuccessfully in the latter.     

High-resolution ro-vibrational spectroscopy of HDO in the region of 8900-9600 cm

The high-resolution absorption spectrum of the HDO molecule was recorded with a Fourier-transform interferometer in the region of 8900-9600 cm⁻¹, where the strongly interacted bands 2ν₁ + ν₃, 3ν₁ + ν₂, ν₁ + 2ν₂ + ν₃, 2ν₁ + 3ν₂, 4ν₂ + ν₃, ν₁ + 5ν₂, and 7ν₂ are located. About 1000 transitions were assigned to these seven bands based on the ab initio predictions [J. Chem. Phys. 106 (1997) 4618]. Altogether, 375 upper energy levels were determined, including 24 energy levels of the highly excited bending (070) state. On that basis, the necessity of the “Effective Hamiltonian” concept in the spectroscopic analysis is discussed.     

High resolution analysis of the ethylene-1-C spectrum in the 8.4-14.3-μm region

Fourier transform spectra of mono-¹³C ethylene have been recorded in the 8.4-14.3-μm spectral region (700-1190 cm⁻¹) using a Bruker 120 HR interferometer at a resolution of 0.0017 cm⁻¹ allowing the extensive study of the set of resonating states {10¹, 8¹, 7¹, 4¹, 6¹}. Due to the high resolution available as well as the extended spectral range involved in this study, a much larger set of line assignments are now available. The present analysis has lead to the determination of more accurate spectroscopic constants, including interaction constants, than were obtained in earlier studies. In particular, the following band centers were derived: ν₀(ν₁₀) = 825.40602(30) cm⁻¹, ν₀(ν₈) = 932.19572(15) cm⁻¹, ν₀(ν₇) = 937.44452(10) cm⁻¹, ν₀(ν₄) = 1025.6976(14) cm⁻¹. Finally a synthetic spectrum was generated leading to the assignment of a number of ¹³C¹²CH₄ lines observed in an earlier heterodyne spectroscopic study.     

Intracavity laser absorption spectroscopy of D2O between 11 400 and 11 900 cm

The weak absorption spectrum of dideuterated water, D₂O, has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) between 11 400 and 11 900 cm⁻¹. This spectrum is dominated by the 3ν₁ + ν₂ + ν₃ and the ν₁ + ν₂ + 3ν₃ centered at 11 500.25 and 11 816.64 cm⁻¹, respectively. A total of 530 energy levels belonging to eight vibrational states were determined. The rovibrational assignment process of the 840 lines attributed to D₂O was mostly based on the results of new variational calculations consisting in a refinement of the potential energy surface of Shirin et al. [J. Chem. Phys., 120 (2004) 206] on the basis of recent experimental observations, and a dipole moment surface from Schwenke and Partridge [J. Chem. Phys. 113 (2000) 6592]. The overall agreement between these calculations and the observed spectrum is very good both for the line positions and the line intensities.     

The high resolution infrared bands ν1, ν2, ν4 and ν2 + ν5 of FClO3

The high resolution infrared spectrum of mono-isotopic F³⁷Cl¹⁶O₃ has been studied in the regions of ν₁, ν₂, ν₄ and ν₂ + ν₅ bands, centered at 1060.20, 707.16, 1301.71 and 1292.15 cm⁻¹, respectively. The ν₁ and ν₂ parallel bands are unperturbed so their analysis was straightforward and 3355 and 2433 transitions were assigned, respectively. The band origins, the rotational and centrifugal molecular constants in the v₁ = 1 and v₂ = 1 states have been determined, with standard deviation of the fits σ = 0.00019 and 0.00018 cm⁻¹. The ν₄ fundamental is affected by an anharmonic resonance with the ν₂ + ν₅ combination band. The kl > 0 sublevels cross at kl ? 27 because of the opposite values of and . The anharmonic resonance constant  cm⁻¹ has been derived. The Δl = Δk = ±2 and Δl = 0, Δk = ±3 essential resonances have been found to be effective in ν₄, while in ν₂ + ν₅ only the Δl = Δk = ±2 one was active. A total of 5721 transitions have been assigned, 25% of them belonging to ν₂ + ν₅. The rovibrational parameters and the interaction constants of F³⁷Cl¹⁶O₃ have been obtained. The standard deviation of the fit is 0.0006 cm⁻¹, six times the estimated data precision. The equilibrium geometry of perchloryl fluoride has been determined from the A_e and B_e constants of F³⁵Cl¹⁶O₃ and F³⁷Cl¹⁶O₃. Using the A₀ and B₀ constants of all the symmetric species the r₀ geometry has also been derived.     

Analysis of some combination-overtone infrared bands of SO3

Several new infrared absorption bands for ³²S¹⁶O₃ have been measured and analyzed. The principal bands observed were ν₁+ν₂ (at 1561 cm⁻¹), ν₁+ν₄ (at 1594 cm⁻¹), ν₃+ν₄ (at 1918 cm⁻¹), and 3ν₃ (at 4136 cm⁻¹). Except for 3ν₃, these bands are very complicated because of (a) the Coriolis coupling between ν₂ and ν₄, (b) the Fermi resonance between ν₁ and 2ν₄, (c) the Fermi resonance between ν₁ and 2ν₂, (d) ordinary l-type resonance that couples levels that differ by 2 in both the k and l quantum numbers, and (e) the vibrational l-type resonance between the A₁^′ and A₂^′ levels of ν₃+ν₄. The unraveling of the complex pattern of these bands was facilitated by a systematic approach to the understanding of the various interactions. Fortunately, previous work on the fundamentals permitted good estimates of many constants necessary to begin the assignments and the fit of the measurements. In addition, the use of hot band transitions accompanying the ν₃ band was an essential aid in fitting the ν₃+ν₄ transitions since these could be directly observed for only one of four interacting states. From the hot band analysis we find that the A₁^′ vibrational level is 3.50 cm⁻¹ above the A₂^′ level, i.e., r₃₄=1.75236(7) cm⁻¹. In the case of the 3ν₃ band, the spectral analysis is straightforward and a weak Δk=±2, Δl₃=±2 interaction between the l₃=1 and l₃=3 substates locates the latter A₁^′ and A₂^′ “ghost” states 22.55(4) cm⁻¹ higher than the infrared accessible l₃=1 E^′ state.     

High resolution study of the six lowest doubly excited vibrational states of PH2D

The five lowest doubly excited deformational vibrational bands ν₄ + ν₆, 2ν₆, ν₃ + ν₄, ν₃ + ν₆, and 2ν₃ of PH₂D have been recorded for the first time using a Bruker 120 HR interferometer with a resolution 0.0033 cm⁻¹ and analysed. Some transitions belonging to a very weak band 2ν₄ have been also assigned. From the fit 24 and 86, respectively, diagonal and resonance interaction parameters were obtained which reproduce 1089 upper energy levels obtained from more than 4600 assigned transitions with the rms deviation of 0.00059 cm⁻¹.     

The multiphoton ionization spectrum of jet-cooled pyrimidine in the 3p Rydberg and B1 (π,n) states

Resonance-enhanced multiphoton ionization (REMPI) has been applied to study the n → 3p Rydberg transition of pyrimidine (jet-cooled sample and mass resolved spectrum). Only the one component, the 3p_z(B₂), appears in the (2 + 1) REMPI and the active vibrations are ν_6a = 622, ν₁ = 946, and ν_9a = 1116 cm⁻¹. The symmetry of the state was determined by polarization measurements (linear, circular polarization). The first (π^∗,n) ³B₁ triplet state appears as a one-photon resonance in the three-photon ionization process.     

Ab initio dipole moment and theoretical rovibrational intensities in the electronic ground state of PH3

We report a six-dimensional CCSD(T)/aug-cc-pVTZ dipole moment surface for the electronic ground state of PH₃ computed ab initio on a large grid of 10 080 molecular geometries. Parameterized, analytical functions are fitted through the ab initio data, and the resulting dipole moment functions are used, together with a potential energy function determined by refining an existing ab initio surface in fittings to experimental wavenumber data, for simulating absorption spectra of the first three polyads of PH₃, i.e., (ν₂, ν₄), (ν₁, ν₃, 2ν₂, 2ν₄, ν₂ + ν₄), and (ν₁ + ν₂, ν₃ + ν₂, ν₁ + ν₄, ν₃ + ν₄, 2ν₂ + ν₄, ν₂ + 2ν₄, 3ν₂, 3ν₄). The resulting theoretical transition moments show excellent agreement with experiment. A line-by-line comparison of the simulated intensities of the ν₂/ν₄ band system with 955 experimental intensity values reported by Brown et al. [L.R. Brown, R.L. Sams, I. Kleiner, C. Cottaz, L. Sagui, J. Mol. Spectrosc. 215 (2002) 178-203] gives an average absolute percentage deviation of 8.7% (and a root-mean-square deviation of 0.94 cm⁻¹ for the transition wavenumbers). This is very remarkable since the calculations rely entirely on ab initio dipole moment surfaces and do not involve any adjustment of these surfaces to reproduce the experimental intensities. Finally, we predict the line strengths for transitions between so-called cluster levels (near-degenerate levels formed at high rotational excitation) for J up to 60.     

High-resolution infrared spectrum of cyanogen

The high-resolution spectrum of cyanogen (¹⁴N¹²C¹²C¹⁴N) has been measured from 500 to 4900 cm⁻¹. For this isotopomer many combination levels with both degenerate fundamentals, ν₄ and ν₅, have been measured for the first time and the effects of vibrational l-type resonance are observed as well as rotational l-type resonance. The effects of the vibrational resonance coupling ν₂ and 2ν₄ have also been studied. The data have been combined with earlier measurements below 500 cm⁻¹ to give a comprehensive catalog of the vibrational energy levels and the rovibrational constants for the normal isotopomer of cyanogen. A comparison of the term value constants for the three major symmetric isotopomers is given and they are compared with a recent ab initio calculation. The present data were combined with earlier work on the two symmetric isotopomers, ¹³C₂¹⁴N₂ and ¹²C₂¹⁵N₂, to obtain the equilibrium bond lengths, r_CC = 138.109(60) pm and r_CN = 115.976(40) pm.     

The absorption spectrum of phosphine (PH3) between 2.8 and 3.7 μm: Line positions, intensities, and assignments

Over 8000 line positions and intensities of phosphine (PH₃) at 3 μm have been measured at 0.0115 cm⁻¹ resolution with the McMath-Pierce Fourier Transform spectrometer at Kitt Peak. The observed line intensities ranged from 4.13 × 10⁻⁶ to 4.69 × 10⁻² cm⁻² atm⁻¹ at 296 K, for line positions between 2724.477 and 3601.652 cm⁻¹. This region spans eight interacting vibrational states: 3ν₂ (2940.8 cm⁻¹), 2ν₂ + ν₄ (3085.6 cm⁻¹), ν₂ + 2ν₄ (3214.9 cm⁻¹), ν₁ + ν₂ (3307.6 cm⁻¹), ν₂ + ν₃ (3310.5 cm⁻¹), 3ν₄ (∼3345 cm⁻¹), ν₁ + ν₄ (3426.9 cm⁻¹), and ν₃ + ν₄ (3432.9 cm⁻¹). Assignments have been determined for all the bands except 3ν₄ (a weak band in a highly congested area) for a total of 4232 transitions. The total integrated intensity for this region is 5.70 cm⁻² atm⁻¹ near 296 K, and assigned lines account for 79% of the observed absorption. The two strongest bands in the region are ν₁ + ν₄ and ν₃ + ν₄ with band strengths at 296 K of 1.61 and 2.01 cm⁻² atm⁻¹, respectively. An empirical database of PH₃ line parameters (positions, intensities, and assignments) is now available. Lower state energies (corresponding to assignments from this study) and line widths from the literature are included; default values are used for unassigned features.     

High-resolution infrared spectroscopy of the interacting ν9, ν5 + ν6 and 3ν6 levels of CH2BrF

The high-resolution (0.0030 cm⁻¹) Fourier transform infrared spectrum of CH₂⁷⁹BrF has been studied in part of the atmospheric window between 910 and 980 cm⁻¹, the region of the ν₉ (935.847 cm⁻¹) and ν₅ + ν₆ (961.239 cm⁻¹) bands. The ν₉ fundamental consists of a pseudo a-type band induced by Coriolis coupling with ν₅ + ν₆, in turn exhibiting a predominant a-type structure. Several interactions connecting these levels and the dark state 3ν₆ have been assessed. The whole data set is treated using Watson’s A-reduced Hamiltonian in the I^r representation implemented with first order a- and b- and c-type Coriolis terms. A detailed analysis of the rotational structure yields a set of accurate upper-state parameters up to quartic distortion terms for ν₉ and ν₅ + ν₆. In addition, spectroscopic information about the dark ternary overtone of ν₆ has been obtained.