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A bank of spectral line parameters of the principal isotopologue of the hydrogen sulfide molecule (H232S) is presented. The databank is based on the global simulation of line positions and intensities of this molecule within the method of effective operators. Parameters of the global effective Hamiltonian and effective dipole moment operator were derived from their fitting to the line positions and intensities observed, respectively, which were taken from the literature. The databank covers the 552.76–8424.32 cm−1 spectral range and includes the calculated values of the following spectral line parameters: line position and intensity, energies of lower and upper states, Einstein coefficient for the spontaneous emission, and the statistical weights of the lower and upper states. The intensity cutoff was chosen equal to 10−28 cm/molecule at T = 296 K. In total, the databank contains about 88 thousand lines. This databank is deployed on the website of V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences ( ftp://ftp.iao.ru/pub/H2S/ ).

In a recent paper Castellanos-Jaramillo and Castellanos-Moreno proposed a simple quantum-mechanical model for an electron in the vicinity of an ionized nanostructure with a permanent electric dipole. They chose the interaction of the electron with the charge and the dipole in such a way that the resulting Schr\"{o}dinger equation is separable into radial and angular parts. In this comment we show that those authors did not solve the angular eigenvalue equation with proper periodic boundary conditions and that they also made a mistake in the elimination of the first derivative in the radial equation. Such errors invalidate their results of the Einstein coefficients for the $\left( GaAs\right)_{3}$ system considered.

We present a high-resolution, high-temperature version of the Acetylene Spectroscopic Databank called ASD-1000. The databank contains the line parameters (position, intensity, Einstein coefficient for spontaneous emission, term value of the lower states, self- and air-broadening coefficients, temperature dependence exponents of the self- and air-broadening coefficients) of the principal isotopologue of C 2 H 2 . The reference temperature for line intensity is 296 K and the intensity cutoff is 10 −27 cm −1 /(molecule cm −2 ) at 1000 K. The databank has 33,890,981 entries and covers the 3–10,000 cm −1 spectral range. The databank is based on the global modeling of the line positions and intensities performed within the framework of the method of effective operators. The parameters of the effective Hamiltonian and the effective dipole moment operator have been fitted to the observed values of the line positions and intensities collected from the literature. The broadening coefficients as well as their temperature dependence exponents were calculated using the empirical equations. The databank is useful for studying high-temperature radiative properties of C 2 H 2 . ASD-1000 is freely accessible via the Internet site of V.E. Zuev Institute of Atmospheric Optics SB RAS ftp://ftp.iao.ru/pub/ASD1000/ .

Over a thousand spectral lines in the photoexcitation spectrum of molecular deuterium (D2) to np 1 Σ u + and 1 Π u + Rydberg levels ( n ⩾ 4 ) were measured for rotational levels N ′ = 1 –6 in the 117 000–137 000 cm−1 spectral range by two different types of experiments at two synchrotron radiation sources: a vacuum ultraviolet (VUV) Fourier-transform (FT) spectrometer at SOLEIL, Paris and a 10 m-normal-incidence monochromator (NIM) at BESSY II, Berlin. The experimental energies, the absorption cross sections, Einstein A-coefficients, and line widths are compared with ab initio multi-channel quantum defect (MQDT) calculations for these levels. More than 350 R(0) or P(2) lines were assigned, some 280 R(1) or P(3) lines, some 270 R(2) or P(4) lines, over 100 R(3) or P(5) lines, over 90 R(4) lines, and 24 R(5) lines to extract information on the N ′ = 1 –6 excited levels. Transition energies were determined up to excitation energies of 137 000 cm−1 above the ground state, thereby extending earlier work by various authors and considerably improving the spectral accuracy ( 0.1 cm−1), leading to several reassignments. The absorption and the dissociation, ionization and fluorescence excitation cross sections from the NIM experiment are measured on absolute scale and are used to calibrate intensities in the VUV-FT spectra. The overall agreement between experiment and first principles calculations, without adjustable parameters, is excellent in view of the multi-state interferences treated within the MQDT-framework: For the low N ′ values the averaged deviations between those observed in the FT-SOLEIL spectra and those calculated with MQDT are ∼ 0.1 cm−1 with a spread of ∼ 0.5 cm−1. The line intensities in terms of Einstein coefficients are well represented in the MQDT-framework, as are the level widths representing the lifetimes associated with the sum of the three decay channels. These line intensities follow, in general, the 1 / n 3 scaling behavior as characteristic in Rydberg series, but deviations occur and those are explained by MQDT. The decay dynamics of the excited N Rydberg levels is analyzed on the basis of the measured quantum yields for ionization, dissociation and fluorescence observed in the NIM experiment in terms of absolute cross sections for the distinctive channels. In particular in the n = 4 manifolds dissociation is found to play a major role, where in the n = 5 manifolds the behavior is most erratic due to strong competition between decay channels. At n = 6 , ionization takes over as the dominant channel. Despite the excellent agreement between observations and the outcome of the MQDT calculations for both level energies and dynamics, some pronounced deviations are found as in the splitting of the 5 p π , v = 4 –6, N ′ = 1 levels. The shortcomings of the MQDT calculations are ascribed to the treatment of the excited states in terms of a 1 snp single electron configuration, therewith neglecting possible interferences with 1 snf or 2 s core excited states. Some 27 lines remained unassigned; in view of their observation in fluorescence it is stipulated that these lines probe levels in the nf manifold.

We study the behavior of an electron in the vicinity of a positively charged nanoparticle that has a permanent electric dipole and is of finite size (not point-like) in two dimensions. We place special attention to the fact that a constant of motion, as well as the energy, exists so that the wave functions result from an eigenvalue problem which are classified using two quantum numbers. The (GaAs)3 cluster is used as iconic case. The angular part is solved using Mathieu functions and the radial part by means of a numerical method. The solutions are plotted and the Einstein coefficients are calculated.

In this work, we investigate the potential energy curves (PECs), transition dipole moments (TDMs) and spin-orbit couplings for low-lying electronic states of SiO+ based on ab initio calculations. The PECs of seventeen low-lying electronic states are calculated by the internally contracted multireference configuration interaction (icMRCI) method with the Davidson correction, as well as the basis set extrapolation, core-valence (CV) correction and scalar relativistic correction. The Schrodinger equation of nuclear movement is solved over the PEC to obtain the rotational and vibrational energy levels, which are used to fit the spectroscopic parameters. The Einstein coefficients, Franck-Condon factors and oscillator strengths for dipole-allowed transitions are calculated with the PECs and TDMs. The radiative lifetimes of some excited states are also obtained. Our calculated radiative lifetime of 67.8 ns for B2Σ+(υ′ = 0) is in excellent agreement with the recent experimental measurement of 66 ± 2 ns. The spin-orbit coupling integrals related to the X2Σ+, A2Π, B2Σ+, 14Σ+, 14Π and 14Σ− states are calculated using the Breit-Pauli Hamiltonian. In addition, the effects of spin-orbit couplings on the potential energies of the Λ-S electronic states are discussed.

In this chapter, we start by reviewing Einstein’s derivation of Planck’s radiation law, whereby the Einstein coefficients for stimulated and spontaneous radiative processes are introduced. Generalizing to the case of non-equilibrium, conditions for laser activity are derived. After a brief discussion of possible realizations of the laser principle, we discuss the generation of short laser pulses by the superposition of a fundamental and side-band frequencies. The carrier envelope phase is then discussed as well as the characterization of laser pulses by windowed Fourier transforms that concludes this chapter.

The Einstein coefficients and radiative lifetimes for diatomic molecules such as N-2 and CO have been computed using the Fourier Grid Hamiltonian (FGH) method and a comparison with other methods has been made. The Hamiltonian matrix is constructed using the Hulburt and Hirschfelder (HH) potential model and the Rydberg-Klein-Rees (RKR) potential model for diatomic molecules. The FGH method works well for any model of the potential including the tabulated forms of experimental potential energy data. The eigenvalues and vibrational wave-functions for the ground and the exited state of N-2 and CO molecules have been computed by diagonalizing the Hamiltonian matrix. The vibrational wave-functions and eigenvalues for the ground and the excited states are used to calculate the radiative transition parameters such as Einstein coefficients (A(v '' v')), radiative lifetimes, electronic transition dipole moments (R-e(x)), Franck-Condon factors (FCFs), r-Centroids and average internuclear separations for both the models. FGH method work well for both the models. There are good agreements between our computed values of radiative transition parameters for both the models and the values estimated by other methods. (C) 2015 Elsevier B.V. All rights reserved.

Radiation heat transfer plays an important role in the energy balance of plasma in an electric arc and its accurate prediction is essential for the development of new electrical devices. Unfortunately, a very complex spectrum of the absorption coefficient makes accurate radiation heat transfer calculations a very challenging task, especially with complex geometries. Numerical approximation of the absorption coefficient is therefore commonly used to reduce computing demands. This paper presents our contribution to the topic of computing requirements reduction, namely the problem of frequency band selection for mean absorption coefficients (MACs). We show that, with the proper band distribution and averaging method, even a very low number of bands can be sufficient for an accurate approximation of the real radiation heat transfer. The band selection process is based upon numerical optimization with a mean value of each band being calculated as a line limited Planck MAC. Both the line limiting factor and associated characteristic plasma absorption length are investigated in detail and an optimal value equal to the three plasma radii is proposed. Tables for three bands mean absorption coefficients in air at the pressure of 1 bar and temperature range spanning from 300 K to 30 kK are included in this paper. These tables serve as input parameters for a fast evaluation of radiation transfer using either the P1 or discrete ordinates method (DOM) approximation with satisfactory accuracy.

According to Bohr’s atomic model (1911), which is based on spectroscopic investigations, transitions between discrete energy levels of an atom can lead to emission or absorption of radiation of a frequency that fulfills Bohr’s energy-frequency relation. In an absorption process, a photon is absorbed. In an emission process, a photon is emitted. Einstein found that the emission of a photon is possible by two different processes, spontaneous and stimulated emission, and that the coefficients describing the three processes — absorption, stimulated and spontaneous emission — are related to each other (Einstein relations).

The structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom in interaction with a quantum electromagnetic field is investigated. Our main purpose is to rewrite the formalism in Ref. \cite{zz} and to deduce the general expressions of the Einstein A coefficients of an atom on an arbitrary stationary trajectory. The total rate of change of the energy and Einstein coefficients of the atom near a plate with finite temperature or acceleration are also investigated., Comment: 12pages. arXiv admin note: text overlap with arXiv:gr-qc/0509053, arXiv:quant-ph/0608179 by other authors

The relative band strengths of several absorption bands of the Ag2 C 1 Π u – X 1 Σ g + system are measured for the first time. Ratios of observed strengths for bands with common lower vibronic levels are compared with theoretically predicted absorption band oscillator strengths, which we computed by numerically solving the radial Schrodinger equation for the vibrational wave functions, ψ υ ′ and ψ υ ″ of the Ag 2 107 , 109 C 1 Π u – X 1 Σ g + band system, using Rydberg–Klein–Rees potential energy curves and a suitable choice for the electronic transition moment function. This resulted in a useful set of radiative transition parameters for a large matrix of Ag2 C–X bands. The functional form of the electronic transition moment required by the observed band strength ratios forces good agreement between the observations and diatomic molecular theory. Since the function is highly nonlinear, the commonly applied r-centroid approximation is invalid, and numerical integration of ∫ ψ υ ′ * R e ( r ) ψ υ ″ dr had to be performed instead. As a final check on the reliability of our results, we find good agreement between the experimentally measured displacements of band heads for the Ag 2 107 , 107 and Ag 2 109 , 109 isotopologues and the corresponding isotopic shifts of our calculated band origins.

This paper calculates the potential energy curves of the 14 Λ-S and 49 Ω states, which come from the first three dissociation channels of the SiN− anion. These calculations are conducted using the valence internally contracted multireference configuration interaction and the Davidson correction approach. Core-valence correlation and scalar relativistic corrections are taken into account. The potential energies are extrapolated to the complete basis set limit. The spin-orbit coupling is computed using the state interaction approach with the Breit–Pauli Hamiltonian. We found that the X1Σ+ (υ′′ = 0–23) and a3Σ+ (υ′ = 0–2) states of SiN− are stable at the computed adiabatic electron affinity value of 23,262.27 cm−1 for SiN. Based on the calculated potential energy curves, the spectroscopic parameters and vibrational levels were determined for all stable and metastable Λ-S and Ω states. The computed adiabatic electron affinity of SiN and the spectroscopic constants of SiN− (X1Σ+) are all in agreement with the available experimental data. The d3Σ+, 25Σ+, 15Δ, and 15Σ− quasi-bound states caused by avoided crossings were found. Calculations of the transition dipole moment of a3Σ+1 to X1Σ+0+ are shown. Franck-Condon factors, Einstein coefficients, and radiative lifetimes of the transition from the a3Σ+1 (υ′ = 0–2) to the X1Σ+0+ state are evaluated.

We investigated here temperature dependence of Stark widths for neutral atom spectral lines in order to find a more precise method for scaling with temperature than sometimes used dependence T-1/2, which is often inadequate particularly for Stark broadening of neutral emitter lines. We found here an analytical scaling with temperature within simplified semiclassical approaches of Freudenstein and Cooper and Dimitrijevic and Konjevic. For analysis of the temperature dependence, lines of HeI were used.

Radiative transition parameters are tabulated for the A 1 Σ u + - X 1 Σ g + band system of the silver dimer 107,109 Ag 2 for bands involving vibrational levels up to v ′ = 54 and v ″ = 98 , which amply covers the band transitions empirically studied in the seminal work of Kleman and Lindkvist [B. Kleman, S. Lindkvist, Arkiv for Fysik 9 (1955) 385–390]. The tabulated parameters include band-origin wavelengths and wavenumbers, Franck–Condon factors, r -centroids, electronic transition moments, Einstein coefficients (spontaneous emission rates) and absorption band oscillator strengths. Rydberg–Klein–Rees potential energy curves for both electronic states, based on the latest available spectroscopic constants, were calculated, and then used to solve the radial Schrodinger equation for the vibrational wave functions, ψ v ′ and ψ v ″ . The constant electronic transition moment function R e ( r ) = 3.05 a.u. was fitted to previously reported relative absorption band strength measurements and the radiative lifetime of the A 1 Σ u + state. A numerical integration of ∫ ψ v ′ ∗ R e ( r ) ψ v ″ d r was performed in computing the Einstein coefficients and absorption band oscillator strengths, and these were found to differ negligibly from similar results obtained with the r -centroid approximation, as expected for a constant R e ( r ) function.

Planck, Einstein and Bose all had to introduce statistics, and thus counting , in order to successfully derive an equation for the energy distribution within the black-body radiation spectrum, and what we now call Bose-Einstein statistics. Some of the details involved in the counting procedure vary while still giving the same result. However, the interpretation of what we count may differ dramatically from one another (as, for example, between Planck and Bose), without impacting the final, mathematical result. We demonstrate here a further alternative, which varies both, in the details of the counting, as well as in the interpretation, while still producing the same well known statistics. This approach puts the "quantumness" back into the radiation emission/absorption process, possibly dispensing with the requirement of quantized light, at least in the context of black-body radiation.

The wave function of the electron in a hydrogen atom, which is a solution of the Schrodinger equation, is of the general form

A model potential method is used to investigate photoabsorption from the Na(3p3/2) state. Absorption cross sections into higher Rydberg states and photoionization cross sections are presented as an analytical function of photo electron energy. Einstein coefficients for spontaneous emissions 3p3/2 ← ns1/2, nd5/2, nd3/2 are tabulated for n up to 50. The Einstein coefficients and low-energy ionization cross sections are believed to be accurate to better than 2–3%, above 1 eV the error may increase to 4–6%.

Theoretical Lyman α absorption profiles show a significant dependence on temperature of the H2 satellite at 1600 A, whereas the H + satellite at 1400 A remains unchanged. The use of opacities calculated with different approximations concerning the electric dipole transition moment (constant, dependent on interatomic distance, and modulated by the Boltzmann factor) lead to very different synthetic absorption spectra. Our new Lyman α profiles over the ZZ Ceti range of temperatures have been used to synthesize theoretical spectra which compare very well to existing HST spectra. In Allard et al. (1999) we derived a classical path expression for a pressure-broadened atomic spectral line shape which allows for an electric dipole moment that is dependent on the posi- tion of perturbers. The theory was applied to the atomic hydro- gen Lyman lines broadened by collisions with neutral and ion- ized atomic hydrogen. The far wings of the Lyman series lines exhibit line satellites, enhancements that may be associated with quasi-molecular states of H2 and H + . We showed that the strengths of these features depend on the values of the electric dipole moments at the internuclear separations responsible for the satellites. Profiles were computed with and without spatial dependence of the dipole moment, and were compared with as- tronomical and laboratory observations. We demonstrated that the dependence of the electric dipole transition moment on in- teratomic separation is an important factor which cannot be ne

The spatial distributions of radiation densities emitted by various components (major, minor and traces) of atmospheric low power (100 W) argon microwave induced plasma (MIP), generated by a resonant TM 010 cavity, were determined. The analytes (Ca, V and Zn) were introduced into the plasma in the form of aqueous solutions applying pneumatic nebulization. The obtained distributions were characterized by the value and the position of the maximum of radiation on the axis of the axially symmetric discharge of filament type. The distance of the maximum above the plasma torch depends on physical characteristics of the element. The influence of potassium on spatial radiation densities of all the mentioned species was investigated. The radial distributions of electron number density (1–9×10 14 cm −3 ) were determined from the Stark broadening of the H β line. From the experimentally determined ratio of ionic to atomic spectral line intensity of Ca and electron number density, the radial distributions of the non-equilibrium factor, the degree of ionization of Ca and ionization temperatures of Ca, T ion (Ca), and of Ar, T ion (Ar), were determined. The values of T ion (Ar) are ranging from 6700 to 7600 K and of T ion (Ca) from 4000 to 5600 K in the plasma region from 1.6 to 3.4 mm in axial and up to 0.3 mm in radial direction. The obtained results compared with apparent temperature data from literature confirm that this plasma is not in state of local thermodynamic equilibrium (LTE).

A general theory is developed to describe diffusion phenomena in biased semiconductors and semiconductor superlattices. It is shown that the Einstein relation is not applicable for all field strengths so that the calculation of the field-mediated diffusion coefficient represents a separate task. Two quite different diffusion contributions are identified. The first one disappears when the dipole operator commutes with the Hamiltonian. It plays an essential role in the theory of small polarons. The second contribution is obtained from a quantity that is the solution of a kinetic equation but that cannot be identified with the carrier distribution function. This is in contrast to the drift velocity, which is closely related to the distribution function. A general expression is derived for the quantum diffusion regime, which allows a clear physical interpretation within the hopping picture.

In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that the conditions of thermodynamic equilibrium of electromagnetic radiation and the energy balance of thermal radiation by the matter, between any of its two energy-states, not only result in Planck's radiation law and the Bohr frequency condition, but they remarkably yield the law of the statistical thermal equilibrium of matter: the Maxwell–Boltzmann distribution. Since the transition probabilities of the modern quantum theory of radiation coincide with their definition in Einstein's theory of blackbody radiation, the presented deduction of the Maxwell–Boltzmann distribution is equally valid within the bounds of modern quantum theory. Consequently, within the framework of the fundamental assumptions, the Maxwell–Boltzmann distribution of energy-states is not only a sufficient, but a necessary condition for thermal equilibrium between the matter and radiation.

We define and compute mean absorption coefficients for the macroscopic models of radiative transfer. These coefficients take into account the anisotropic form of the photon emission and lead to a better computation of a photonic flow far from the radiative equilibrium. They are deduced by averaging a specific radiative intensity on the space of frequency and are generalized versions of the Planck means. This intensity is obtained by minimizing the mathematical entropy with the constraint of the reconstruction of radiative moments and constitutes the closure of the M 1 radiative model. We discuss the influence of these coefficients, extend them to the case of multi-frequency problems and perform a numerical comparison with the former Planck mean.

Blackbody radiation is reconsidered using the counterpart of the Bose-Einstein distribution in the $\ensuremath{\kappa}$ statistics arising from the Kaniadakis entropy. The generalized Planck radiation law is presented and compared to the usual law, to which it reduces in the limiting case $\ensuremath{\kappa}\ensuremath{\rightarrow}0$. Effective Einstein's coefficients of emission and absorption are defined in terms of the Kaniadakis parameter $\ensuremath{\kappa}$. It is shown that the Kaniadakis statistics keeps unchanged the first Einstein coefficient $A$ while the second coefficient $B$ admits a generalized form within the present theoretical framework.

We provide systematic calculations about the energy levels, Einstein coefficients and oscillator strengths for electric quadrupole (E2) and magnetic quadrupole (M2) transitions between n=3 and n=2 of Ne-like systems by using the fully relativistic multi-configuration Dirac-Fock method. The oscillator strengths of the E2 transitions under Coulomb and Babshkin gauges are compared with each other and show the differences from 1.2 to 12 percent. We also found that the M2 line (0.37429 nm) with the biggest oscillator strengths in Ne-like Ag37+ mixes with the line (2p3/253s1/23d5/2)3/2 → gs (0.37427 nm) emitted by the Na-like Ag36+.

Einstein coefficients and oscillator strengths for Rydberg–ground and Rydberg–Rydberg transitions in the rare-gas excimer NeH have been calculated with the quantum defect orbital (QDO) method. A comparative study of analogous transitions in NeH and in some of its isoelectronic Rydberg radicals has revealed clear similarities between them.

The nonextensive statistics of a boson gas within the dilute gas approximation is applied to black-body radiation. Einstein's spontaneous emission coefficient A21, stimulated emission coefficient B21, and absorption coefficient B12 are studied in connection with this new statistical mechanics. Relations including nonextensivity between these coefficients are obtained.

The problem of estimating diffusion coefficients has been considered extensively in both discrete and continuous time. We consider here an approach based on counting occupation numbers of diffusing particles. The problem, and our approach, are motivated by statistical mechanics.

Ab initio density functional theory calculations for ethanal and muonium, using the projector augmented-wave technique, are described. The potential binding sites for the muonium are evaluated from total-energy-minimization calculations. At these preferred sites the associated (bond-stretching) vibrational frequencies, Einstein coefficients and isotropic hyperfine coupling constants are then calculated. It is found that the hyperfine parameter at each site depends on the vibrational state, and so muon vibrational spectroscopy of ethanal is predicted to be possible. The effect of a rigid-muonium-bond rotation is also considered. It is found that this can change the sign of the predicted hyperfine coupling constant at certain sites, which is necessary to get reasonable agreement with experimental values. The temperature dependence of the hyperfine coupling constant was calculated from a Boltzmann population of rotational states. This was found to be insufficient to explain the experimentally observed temperature dependence. This is probably due to the neglect of coupling between vibrational and rotational modes. Therefore this common interpretation of the experimental temperature dependence of the hyperfine coupling constant must be reconsidered.

Einstein A-values are given for the electric dipole transitions in the C3 H2-molecule between the rotational levels of the vibrational ground state up to 85cm-1. The mean radiation life-times of the levels are calculated from the Einstein A-values. These values can be used as input parameters for analysing the spectra of C3H2

State-to-state and thermally averaged Einstein A -coefficients have been computed for the fundamental and first three overtone sequences of the NO(X2II-X2II) system with the aim of examining the effects of centrifugal distortion on the high-J transitions that occur as a result of upper atmospheric chemistry. The Einstein coefficients were calculated using an experimentally derived dipole moment function of Rawlins et al (manuscipt in preparation), and the ab initio dipole moment functions of Langhoff et al [Chem. Phys. Lett. 223, 416 (1994)] and de Vivie and Peyerimhoff [J. Chem. Phys. 89, 3027 (1988)], for J′ ranging up to 139.5. The state-specific Einstein coefficients show that, regardless of dipole moment function employed, centrifugal distortion has a relatively small effect on the Δv = 1 sequence which is manifest primarily as a reduction in the high-J R-branch intensities. However, the effect on the overtone rotational intensities is larger and results in enhanced R-branch intensities and reduced P-branch intensities relative to those calculated neglecting centrifugal distortion. For example, in the first overtone system for J′ ≈ 80.5, v′ = 2–14, the ratio of R- to P-branch Einstein coefficients is larger by about 1.7 than the R P ratio predicted in the absence of centrifugal distortion.

New spectroscopic and laser data on monoclinic Ba(Yb 1-x Er x ) 2 F 8 crystals are obtained. Efficient 2 μm stimulated emission of Er 3+ ions in the 4 F 9/2 → 4 I 11/2 channel and 2 and 3 μm cascade lasing of the sequential 4 F 9/2 → 4 I 11/2 → 4 I 13/2 transitions were excited at room temperature under Xe flashlamp pumping. Intensity characteristics of manifold-to-manifold (JJ' transitions) such as Einstein coefficients A JJ' , line strengths s JJ' , branching ratios β JJ' , and radiative lifetimes τ rad for the initial laser states 4 I 13/2 , 4 I 11/2 , 4 I 9/2 , 4 F 9/2 , 4 S 3/2 , and 2 H(2) 9/2 were analyzed in detail. All observed laser transitions between individual Stark levels were identified. Unlike well-known 2 μm lasers with Ho 3+ , Tm 3+ , Co 2+ , and Ni 2+ ions in many oxide and fluoride compounds. BaYb 2 F 8 :Er 3+ crystals operate on a pure four-level generating scheme.

Recently reported measurements of the absorption band strength (i.e., the Einstein B-coefficient for absorption) for the transition O2(X3Σg → a1Δg) at 1.27 µm, when correctly reanalyzed in this paper, indicate that the Einstein A-coefficient for spontaneous emission of radiation is 1.47 × 10−4 s−1. This is a factor of 1.75 smaller than the value of 2.58 × 10−4 s−1 that has been used almost exclusively in the aeronomy field for the past 30 years. The determination of the new A-value is reviewed, with an emphasis on the derivation of the appropriate ratio of the degeneracies of the upper and lower states of this transition. The new A-value implies that ozone concentrations as inferred from measurements of O2(a¹Δg) emission must be increased significantly in existing databases and also that the efficiency of solar heating in the Hartley band of ozone is larger than previously calculated.

Experimental examination of the reflection of light at the surface of noble metals at high temperature shows non existence of the radiative equilibrium condition and the induced emission. Interpretation of the thermal radiation is given without using the Planck's radiation formula and the Kirchhoff's law. Temperature shifts of the spectral peak of the emission band with increasing temperature are calculated by a quantum mechanical model, where the radiation is induced by an electron transition between two potentials and the spectral shape and shifts are determined by the Boltzmann factor in the potentials.

The role of the novel longitudinal vacuum fieldB(3)is discussed in relation to fundamental radiation laws: the Rayleigh-Jeans law, the Planck law, and the Einstein coefficients. The circular index (3) ofB(3)causes electromagnetic energy density to be redistributed from the other indices (1) and (2) of the circular basis, but the presence ofB(3)in the vacuum does not change the value of the Planck constant h. TheB(3)field does not affect, furthermore, the understanding of quantized radiation absorption first proposed by Einstein. Therefore, the experimental observableB(3) does not imply modification of these fundamental, radiation laws, and experimental isolation ofB(3) must take place through its characteristic square root power density dependence when used to magnetize an electron plasma.

We present theoretical and experimental studies of the influence of high intensity laser radiation on light emitted on a branch line inside the resonance cavity of an argon ion laser. We provide a steady-state description of interactions between the two fields. Propagation, saturation and two photon transitions introduce a “correction” to the Einstein's A coefficient. The extent of the correction is different for various branch lines and depends on both the value of the respective A coefficient and the intensity of laser light. The A coefficients are not dependent on collisions of ions with photons within the measurement error. Experimental results appear to confirm our simple theoretical model and show complex behavior of the system.

The famous ‘‘1917 paper’’ of Einstein on the Quantum Theory of Radiation is revisited. Emphasis is placed on the little‐known bulk of the paper dealing with momentum balance. The most difficult part of the calculation is here simplified by regarding the ‘‘drag force’’ on a body moving within a blackbody cavity as due to the same quantized impulses that give rise to random recoil.

We treat the basis of bipolar semiconductor lasers. We discuss: condition of gain; joint density of states; gain coefficient; laser equation; bipolar character of the active medium. And we derive, by use of Planck’s radiation law, the Einstein coefficients for an ensemble of two-level systems that is governed by Fermi’s statistics.

The b 1B1→a 1A1 emission spectrum of the CH2 radical has been studied in the 13 330–18 180 cm−1 region. Methylene (a 1A1) is produced by photolysis of ketene at 308 nm and excited to single rovibrational levels of the b 1B1 state by a tunable pulsed dye laser. The emission from the b 1B1 state is spectrally dispersed with a resolution of 0.25 A. Term values and transitions are reported for new levels of the b 1B1(0,v2,0) (v2=14 and 15) and a 1A1(0,0,0) states with J≥6 and 0≤Ka≤6. Unusually intense ΔKa=3 transitions and several ΔKa=5 transitions are observed. Analysis of the emission spectra gives the relative intensities of transitions from a selected rovibrational level in the upper b 1B1 state to rovibrational levels in the a 1A1 state. These relative intensities together with the fluorescence lifetimes of the b 1B1 levels determine the absolute Einstein emission coefficients for rovibronic transitions in the visible spectrum of methylene. These data permit accurate measurement of rovibrationa...

The Einstein A coefficients are calculated, in all cases of degeneracies of the Dirac transition currents, by means of the energy balance method.

The current state of the art of red-shifted fluorescent dyes is reviewed from the viewpoint of Superconductor Super Collider (SSC) design constraints (emission wavelength, lifetime, radiation-tolerance, quantum yield, etc.) and theoretical limitations (Einstein coefficients, natural lifetimes, oscillator strengths). Improvements to the performance of current red-emitting fluors which are simultaneously optimized to meet these constraints are needed, and the suggestion of applying computational methods to molecular design of fluorescent chromophores is presented by example. Emphasis is placed on dyes which emit at wavelengths longer than 500 nm, and in particular near 630 nm, the window of maximum transmittance of polystyrene plastic optical fiber.

All significant experimental measurements and many theoretical calculations of the spectroscopy and structure of the isotopic lithium hydrides ( 6LiH, 7LiH, 6LiD, 7LiD) are identified and reviewed. Published molecular constant determinations from conventional and laser spectroscopy are evaluated; recommended spectroscopic constants for the X 1Σ+, A 1Σ+, and B 1Π states are tabulated. Potential energy curves (RKR, IPA, and hybrid) for the X 1Σ+, A 1Σ+, and B 1Π states are evaluated and recommended curves are tabulated. Dissociation energy estimates are evaluated and recommended D0 and De values tabulated for X 1Σ+, A 1Σ+, and B 1Π states. Accurate electronic structure calculations (Hartree Fock or better) on this ‘‘workbench of theoretical chemistry’’ are listed and described briefly; all excited electronic states considered are included. Experimental and theoretical radiative and dipole properties are noted and discussed. Adiabatic corrections to the Born–Oppenheimer approximation are also reviewe...

Computational hybrid collision-radiative model of physical-chemical processes and nonequilibrium spectral emissivity of strong shock waves in CH4-N2 and CO2-N2 at velocities 5-9 km/s is presented. Ab-initio data for Einstein coefficients are taken into account for prediction of rates of electronic excitation at collisions with electron and life times of excited states. Electronic temperature is predicted by solving electron energy conservation equation. Several kinetic models based on data of Goksen and Warnatz were tested with the model. It was demonstrated that the model is sensitive even to reasonable variation of kinetic models. Computational data are compared with experimental data. Nomenclature ρ = density u = velocity p = pressure T = translational temperature h = enthalpy i x = molar fraction of i-th species i m = mass of i-th species i µ = molecular weigh of i-th species , A kN = the Boltzmann and the Avogadro constants 0 R = universal gas constant , ij θ = characteristic vibrational temperature of the j-th vibrational mode of i-th molecular species , ij g = degeneration of the j-th vibrational mode M N = number of molecular species , vi T = vibrational temperature for i-th molecular species , Vi N = number of vibrational modes for the i-th molecule 0 fi H ∆ = formation enthalpy at standard conditions with temperature 0 T N = number of chemical species m e = average number of m-th type vibrational quanta rated per one molecule ,m T v = vibrational temperature 0 m e = equilibrium value of m e , mi τ = time of vibrational VT-relaxation for m-th molecule in collisions with i-th particles m T Q V = vibrational energy sources due to the vibrational-translational (VT) interaction m Q vv = vibrational energy sources due to the vibrational-vibrational (VV) interaction m c Q v = vibrational energy sources due to the dissociative-vibration (CV) interaction lnΛ = the Coulomb logarithm

Air fluorescence models require accurate Franck–Condon factors and Einstein coefficients for analyzing the intensities of N2, N+2, and O+2 emissions produced by electron bombardment of air, such as in the aurora, high‐altitude nuclear explosions, and rocket‐borne electron gun experiments. In our previous report, improved vibrational and rotational constants based on the latest available spectroscopic measurements for several excited and ionic states important in air fluorescence modeling were derived. These constants have been used in the present work to calculate band origins, Franck–Condon factors, and r‐centroids for many band systems of nitrogen and oxygen. These results, together with electronic transition moments obtained from published papers or derived here from published emission data and measured upper‐state lifetimes, have been used to compute Einstein coefficients by the r‐centroid method. Einstein coefficients by integration of the product of the electronic transition moment function and vibr...

Extensive arrays of Einstein A coefficients, band oscillator strengths, sums of the squared electronic-vibrational transition moments, and Franck-Condon factors are presented for the N2 first and second positive, NO beta and gamma, N+2 first negative, and O2 Schumann-Runge band systems. These results are based upon recent ab initio calculations of electronic transition moments, and potential curves obtained with updated spectroscopic constants.

A summary of the spectroscopic equations necessary for prediction of the molecular transition energies and the Einstein A and B coefficients for rovibronic lines of the gamma(0,0) band of nitric oxide (NO) is presented. The calculated molecular transition energies are all within 0.57/cm of published experimental values; in addition, over 95 percent of the calculated energies give agreement with measured results within 0.25/cm. Einstein coefficients are calculated from the band A00 value and the known Hoenl-London factors and are tabulated for individual rovibronic transitions in the NO A2sigma(+)-X2Pi(0,0) band.

The quantized electromagnetic field in interaction with nonrelativistic sources, i.e., atoms and molcules, has been the subject of study in the previous papers in this series. The Heisenberg formalism is used to calculate the electric- and magnetic-field operators arising from charges and currents expressed in multipolar form. In this paper, quadratic operators in these fields such as the Thompson energy density and the Poynting vector and their expectation values for specified states are found. The expectation values are, in general, time dependent. For initial conditions given at t=0 it is shown that the fields are causal, i.e., for tr/c the source-dependent fields are zero and the quadratic operators have only their zero-point contributions. For tgr/c they have both time-independent and time-dependent terms. The time-dependent terms, though transient, are shown to obey Poynting's theorem. The steady-state part of the Poynting vector is related to the Einstein coefficients. The corresponding electric-energy density is related to the Casimir-Polder potential for a polarizable test body in the field of the source molecules. Similarly the magnetic-energy density is derived and is used in the calculation of energy shifts. Quadratic operators referring to different field points are also discussed.

A.1 Planck Radiation Law Blackbody objects (i.e., perfect emitters of energy) whose temperatures are greater than absolute zero emit energy E per unit volume and per unit frequency at all wavelengths according to the Planck radiation law (A-1) where h = Planck's constant = 6.6256 x 10-34 J-s, kB = Boltzmann's constant = 1.380662 x 10-23 J/K, c = speed of light = 3 x 108 m/s, T = physical temperature of the emitting object in degrees K, f = frequency at which the energy is measured in Hz. Upon expanding the exponential term in the denominator, Eq. (A-1) may be rewritten as (A-2).