On spectral representations for the functions Wi(v, q2) (i = 1, 2) describing electroproduction process

It is shown that the Deser, Gilbert, Sudarshan representation (DGSR) does not follow from microcausality and spectrality only. Examples of the functions W_i(v, q²) satisfying the microcausality and spectrality conditions are given which cannot be written as the DGSR with spectral function h(a, α) that is a temperature distribution. Instead of the DGSR the spectral representation for W_i(v, q²) has been proved (eq. (3)) which follows only from microcausality and spectrality.     

Measured integrated band intensities and simulated line-by-line spectra for 12C2HD between 25 and 2.5 μm,and new global vibration–rotation parameters for the bending vibrations

The global analysis of published high-resolution vibration–rotation spectra of ¹²C₂HD in the bending spectral range is presented, resulting in an extension of the known vibration–rotation assignments, including a new band 2v₄+v₅←2v₄ (^IΠ←Δ). Experimental integrated band intensities are reported in the range from 25 to 2.5 μm, and both v₄ and v₅ bending fundamentals are simulated line by line. An extensive line list is produced in the bending energy range, to supply previously missing information in databases.     

Determination of the isotopic shift of192Hg in the line λ=2537 Å by Zeeman scanning the Hanle signal

The Hanle signal in theλ=2 537 Å resonance line of an line mass separated¹⁹²Hg was Zeeman scanned from a spectral lamp containing isotopically pure²⁰⁴Hg. The isotopic shift was redetermined asδv ^192/204=v ²⁰⁴?v ¹⁹²=?27.7(3) GHz. The application of this method to even-even isotopes still further from stability is discussed.     

Spectator and participator processes in the resonant photon-in and photon-out spectra at the Ce L3 edge of CeO2

We study both theoretically and experimentally the photon-in and photon-out spectra of CeO₂, which are caused by the Ce 2p to Ce 5d excitation followed by the three different de-excitation channels: (i) Ce 3d to Ce 2p (denoted by 3d-RXES), (ii) O 2p to Ce 2p (v-RXES), and (iii) Ce 5d to Ce 2p (RIXS). In 3d- and v-RXES, the 5d electron plays a role of a spectator, but in RIXS it is a participator. By extending our single impurity Anderson model (SIAM), which was used recently for our calculations of v- and 3d-RXES spectra of CeO₂, we study the polarization dependence in the spectator and participator spectra, and we perform more detailed calculations for 3d- and v-RXES spectral features, as well as new calculations for the RIXS spectrum with charge transfer excitations. The polarization dependence is different for the spectator and participator spectra; we have no polarization correlation between the incident and emitted photons for the spectator spectra but a strong polarization correlation for the participator spectrum. The theoretical calculations predict that the charge transfer excitations in RIXS occur in the transfer-energy range overlapped with v-RXES, but the RIXS and v-RXES spectra can be discriminated by taking advantage of the different polarization dependence. The overlapped RIXS and v-RXES spectra are observed successfully by our experiments and well reproduced by our SIAM calculations.     

Numerical and analytical study of high-resolution limb spectral radiance from nonequilibrium atmospheres

Emission line shapes are calculated numerically for isolated optically thick infrared lines in the earthlimb as a function of tangent height using a general nonlocal thermodynamic equilibrium (non-LTE), upper-atmospheric line-by-line radiation transport code. It is shown that the exact integral form of the transport equation can be written in a form that is easily amenable to analytical approximation of high accuracy. In this form, the limb spectral radiance I_v appears as a weighted average of n_u/n_l, the ratio of upper-state to lower-state population density, multiplied by the absorptivity 1 - exp[-τ(v)], where τ(v) is the total optical path along the line of sight. In the wings the variation of I_v is governed by the absorptivity; in the core of the optically thick line, I_v is determined by the averaged population ratio. The analytical forms enable us to calculate all of the important features of the self-absorbed line and agree remarkably well with more time-intensive numerical calculation. These results are illustrated by calculations on the 15-μm CO₂v₂ (01¹0-00⁰0) vibrational transition for tangent heights ranging through the mesosphere and lower thermosphere. Even though the collision linewidth is less than 1% of the Doppler width at these altitudes, it is shown that it is essential to use the Voigt line profile in this calculation rather than the Doppler profile. Failure to do so leads to a total band radiance that is in error by up to a factor of three, as well as incorrect band shapes and line shapes.     

Infrared radiation properties of methane at elevated temperatures

The spectral absorptivity of the v₃ and v₄ fundamental and the v₁ + v₄ combination bands of methane have been measured at low resolution for temperatures between 290 and 850 K. Spectral mean (narrow-band) parameters for the fundamental bands have been correlated from the Elsasser model, while total band absorptance data for all three bands have been correlated using the Edwards exponential wide band model. A total emissivity chart has been developed, based on the wide band absorption models.     

The vibration-rotation spectrum of 14CO in the spectral range 2.40–3 μm

The infrared emission spectrum of the Δv = 2 sequence of the ¹⁴C¹⁶O molecule has been recorded at high resolution by Fourier transform spectrometry. More than 750 spectral lines have been assigned for a wide range of rotational quantum numbers (J = 0–60) and vibrational quantum numbers (v = 0–13). Using a variational method, a fully quantum mechanical potential energy curve (IPA potential) is determined. A comparison of this potential with the semiclassical RKR potential, which is based on a first-order WKB method, is carried out.     

Probabilities for electronic transitions of molecular systems of high-temperature air components—I. The schumann-runge system of the O2-molecule and the first positive system of the N2-molecule

The results for absolute and relative probabilities for electronic transitions of the Schumann-Runge system of the O₂-molecule and the first positive system (1+) of the N₂-molecule published elsewhere have been critically analyzed. For the S-R system, statistical processing of the experimental results for absolute and relative probabilities on a joint basis made it possible to establish a new dependence of the electronic transition strength on the internuclear separations S_e(r_v′v″), which reliably describes the behaviour of S_e over the whole spectral range. For the (1+) system of the N₂-molecule, it has been shown that none of the published dependences S_e(r_v′v″) provide acceptable fits to the measured results on absolute intensities and life-times. In practical calculations, one should use the dependence given in Ref. 41, which is derived from relative intensities and corroborated by absolute intensity measurements.     

Spectral dependence of erythrocyte response to low-intensity irradiation at 570–590 nm

Red blood cells irradiated with copper laser pumped by a dye laser exhibit a photoresponse whose spectral dependence corresponds to the molecular oxygen absorption band [2³Σ _g ^? →¹Δ _g (v=0)+¹Δ _g (v=1)].     

Predictions for the A2∑-X2Π system of LiO

Theoretical potential well constants for the ⁷Li¹⁶O molecule were used to predict the spectral and intensity distribution (equal level population assumption) of the A²∑-X²Π emission band system, so far not experimentally detected. Morse Franck-Condon factors were computed and are given. The system should be sought in the infrared, via the Δv = 0 sequence (0, 0 at 4.3 μ) and stronger but overlapped sequences Δv = -1 (3.2 μ), Δv = -2(2.5 μ), and Δv = -3 (2.1 μ).     

Adequate representation of the dipole moment function for diatomic molecules and the matrices of vibration-rotation transition moments

An exponential representation of perturbations is used as a basis of the perturbed Morse oscillator approach which is applied, in a matrix form, for calculating the radial matrix elements for diatomic molecules. An analytic procedure is developed to deduce an exponential-power series expansion for the dipole moment function M(r) from experimental spectral intensities. It is shown that for real anharmonic molecules, the series expansion in powers of e^ar (α being the Morse parameter) is an adequate form for representing transition operators, just as the usual series expansion in powers of internuclear distance r is adequate for the case of a harmonic oscillator, and it is equivalent to a series expansion in vibrational wavefunctions. An exponential-power series expansion is derived as well for a model dipole moment function which has a correct long-range dependence and limit. To exemplify the accuracy and efficiency of the technique proposed, the (40 × 40) matrices of vibration-rotation transition moments 〈vJ|M(r)|v′J′〉(v, v′ = 0, 1, …, 39) have been calculated for the ground state of CO. Typical results of these computations are presented (up to v = 35, J = 100, and v′ ? v = 1–4) to illustrate the dependence of vibration-rotation interaction functions on the vibrational and rotational quantum numbers.     

Weakly forbidden vibration-rotation transitions ΔR ≠ 0 in CF4 laser

Known spectroscopic data on the 16 μm CF₄ laser are completely explained by considering weakly forbidden ΔR ≠ 0 vibration-rotation transitions. A rich fine structure of the v₂ + v₄ pumping band with specific spectral interval 0.01 + 0.03 cm^-1 has been experimentally observed. The components of this structure have been used for optical pumping of a CF₄ laser by a quasi-single mode continuously tunable high-pressure CO₂ laser.     

On blocks in quantum logics

Let L be a quantum logic, Ω(L) the convex set of states on L and M a property, i.e. a convex subset of Ω(L). For any P?L we define A_M(P)={pεL∣μ, vεM and μ|P=v|P?μ(p)=v(p)}. The subset A_M(P)?L is orthomodular and A_M is a closure operator on the subsets of L. We call P?LM-dense, provided A_M(P)=L.We show that a non-classical quantum logic satisfying the chain condition and having a full and unital property M has no block which is M-dense. We also prove that a quantum logic with a property M for which every counter is expectational and no block is M-dense necessarily has uncountably many blocks. In this setting we then discuss projection lattices of von Neumann algebras.     

Probabilities for electronic transitions of molecular systems of high-temperature air components—II. The γ and β systems of NO and the (4+) system of CO

Literature results on absolute and relative probabilities for electronic transitions and on lifetimes of electronically excited states in the γ and β systems of the NO molecule and in the (4+) system of the CO molecule are critically analyzed. The results of previous studies to establish the dependence of the electronic transition strength on the r-centroid for these molecular systems are shown to be inadequate. Using a combined analysis of absolute and relative probabilities, new normalized functions S_e(r_v′v″) are obtained that describe the behaviour of the transition strengths in the spectral ranges occupied by the γ and β systems of NO and by the (4+) system of CO.     

Nitrogen-broadened lines of ethane at 150 K

Spectral transmittance has been measured in the v₉ fundamental band of C₂H₆ at 150 K using a Fourier transform spectrometer with apodized spectral resolution of 0.06 cm^-1. Comparison of observed spectral transmittance with a line-by-line computation using the spectral catalog of Atakan et al. has yielded N₂-broadened half-widths at 150 K.     

The microwave spectrum of IF5 in excited vibrational states: Accidental degeneracy and avoided crossing of the kl = 3 and kl = −1 levels in the state v9(E) = 1

Measurements of the microwave spectrum of the C_4v molecule IF₅ in the excited vibrational states v₉(E) = 1 and v₅(B₁) = 1 are reported for the transitions J12 ← 11 and J13 ← 12 (65–72 GHz). The considerable spectral perturbations produced by an accidental degeneracy and avoided crossing of the ψ^? (kl = 3) and ψ^? (kl = ?1) levels of the v₉(E) = 1 state have been measured and analyzed. A spectroscopic determination of the axial rotation constant C₉ is reported and its implications for the molecular structure of IF₅ discussed.     

On the Solutions of the Yang-Baxter Equations with General Inhomogeneous Eight-Vertex R-Matrix: Relations with Zamolodchikov’s Tetrahedral Algebra

We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent R _ij (u)-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation by mod(2). A complete classification of the solutions is performed. We have obtained also two spectral parameter dependent particular solutions R _ij (u,v) of YBE. The application of the non-homogeneous solutions to construction of Zamolodchikov’s tetrahedral algebra is discussed.     

电子-质子的深度非弹性散射(Ⅱ)

本文应用戴逊表示来研究层子的一般图形,以考察不依赖击出图形是否也能得到无标度性。结果表明,只要流对易子矩阵元的戴逊表示中的谱函数在m²大时具有合适的行为,在ν大时就可以得到无标度性。至于q²的值,则并无限制。q²很小甚至趋于零都是允许的。此特点似与实验相符合。另外,对于一定的ν,结构张量W_μv只决定于谱函数在m²M_pν范围内的值,而与真正的m²→∞时的渐近行为并无关系。因此,目前所观测到的无标度性也许只是一定范围内的现象,当ν更大时,很可能会出现质的变化。     

Infrared spectral line parameters of HBr and DBr at elevated temperatures

The electric dipole matrix elements <v'J'μvJ> for pure rotation and vibration-rotation transitions, with |;m|;<-40 and v<-v'<-6, have been derived for HBr and DBR by using the Rydberg-Klein-Rees (RKR) potentials and numerical solutions of the Schrödinger equation. An improved dipole-moment expansion was determined by fitting these matrix elements to the available experimental data on line intensities. A least squares analysis of the available line position constants gave an improved set of Dunham coefficients good for spectral lines with both large and small quantum numbers v and J. The results were then used to generate a compilation of individual line parameters for the Δv = 1 bands of HBr and DBr at temperatures up to 3000K. These parameters, together with previously compiled line parameters for HCl, HF, CO and NO, are being used for line-by-line calculations of radiance from a hot source as seen through an atmospheric path.     

Analysis of the ν6 band of 12CH3D at 8.6 μm

The ν₆(E) fundamental vibration-rotation band of monodeuteromethane (¹²CH₃D) has been recorded in the spectral range 1033–1270 cm^?1 with a resolution of approximately 0.04 cm^?1. Of the 669 transitions with J′ ≤ 17 identified, 633 have been retained for the determination of the rotational levels in the upper state v₆ = 1. The Coriolis interaction between the v₆ = 1(E) and v₃ = 1 (A₁) vibrational states of ¹²CH₃D results in large A₁A₂ splittings of levels with v₆ = 1 and |K ? l₆| = 0 or 3; the mixing in K and l₆ also gives rise to some ten forbidden transitions observed in the spectra. These effects have been very well explained within the formulation based on the contact transformation method. Values of 15 molecular structure constants of the v₆ = 1 state have been determined from a least-squares analysis of the 633 retained transitions. These constants can be used to estimate values of the upper-state energies up to fourth order, and through them the spectral positions of the 633 retained transitions are reproduced with an overall standard deviation of 0.013 cm^?1, which is within experimental uncertainties.