Einstein Coefficients Research Articles

A systematic study on spectroscopic and transition properties of the phosphorus mononitride cation

The potential energy curves (PECs) of 28 Λ–S states of the phosphors mononitride cation have been constructed by using the internally contracted multireference configuration interaction (icMRCI) method plus Davidson correction (+Q). The effect of core correlation and scalar relativistic treatment of electron, and the basis-set extrapolation to the complete basis set limit are considered. The spin–orbit coupling is computed via the full Breit-Pauli Hamiltonian. The transition dipole moments (TDMs) for the dipole-allowed and spin-forbidden transitions are calculated. Utilizing the PECs and TDMs, the spectroscopic and transition properties of bound states are then evaluated. The current spectroscopic parameters, vibrational band origins, Einstein coefficients, and Franck-Condon factors well match the available measured values. And the radiative lifetimes for most excited states are estimated for the first time. These results can be useful in the analysis and assignment of molecular spectra or as guidelines for detecting these states spectroscopically.

Transition probabilities of the AgS(A[formula omitted][formula omitted] X[formula omitted]) emission including spin–orbit coupling effects and evidence of a novel band system

A systematic spectroscopic work using multireference configuration interaction (MRCI) and coupled cluster (CC) calculations was performed in conjunction with large basis sets for AgS. As a result, a more accurate dissociation energy of 17,542 cm−1 is predicted for the X2Π using an analytical potential energy curve, including spin–orbit effects. The calculated energy separation Te(A)∼ 10,500 cm−1 suggests that the AgS(A2Σ+→ X2Π) band system is in near-IR. An unobserved 32Π→ X2Π band system is predicted with Einstein coefficient for spontaneous emission of the orders of 104–105 s−1 in the UV region (342 nm). The radiative lifetimes for the A2Σ+ are of the order of ∼100 microseconds. The AgS(A) state presents a possible predissociation channel caused by interactions with the quartet 14Σ− and 14Π states. The spin–orbit coupling effects are considered in this work by utilizing the Breit–Pauli operator. The present findings are good references for future spectroscopic research concerning heavy-element sulfides.

A new Einstein coefficient method for mesopause-lower thermosphere atmosphere temperature retrieval under a non-local thermal equilibrium situation.

The mesopause-lower thermosphere (MLT) region is an important spatial region in the Earth's atmosphere, making it a valuable area to investigate the temperature variations. Kirchhoff's law fails with the altitude increase due to the non-local thermal equilibrium effect, resulting in an increase in the error of the method to retrieve the atmospheric temperature in the MLT region using the A-band spectral line intensity. In the non-LTE state, the temperature retrieval method based on the Einstein coefficients is proposed to retrieve atmospheric temperature in the 92-140 km height range using the airglow radiation intensity images obtained from the Michelson Interferometer for global high-resolution thermospheric imaging (MIGHTI) measurements. Results show that the temperature deviation of the two-channel combinations does not exceed 15 K in the altitude range of 92-120 km. This deviation increases up to 45 K when the altitude is in the range of 120-140 km due to the influence of the N2 airglow spectrum. The two-channel combinations self-consistency is increased by 85 K compared with the temperature obtained using the spectral line intensity retrieval. Additionally, the comparison of the retrieval results with the spectral line intensity method and the comparison with the atmospheric chemistry experiment Fourier transform spectrometer (ACE-FTS) temperature measurement data shows that the Einstein coefficient method is significantly more rational and accurate than the spectral line intensity method.

A spin–orbit configuration interaction study of the low-lying electronic states of the diatomic lithium antimonide cation

High-level ab initio calculations were performed to determine the structural features, electronic characteristics and transitional properties of LiSb+, which is a hitherto experimentally unknown diatomic cation. We acquired and evaluated the potential energy curves, spectroscopic constants and vibrational energy levels for low-lying Λ-S electronic states and their related Ω states. The spin–orbit coupling effect has a slight impact on these states. Transitional properties, such as transition dipole moments, Einstein coefficients, Franck–Condon factors and vibrational branching ratios, as well as the radiative lifetimes of transitions from excited Ω states to the ground state, have been identified and discussed. We anticipate that these prognostic results will act as guidelines for future research.

Cascade Infrared Thermal Photon Emission

The later stages of cooling of molecules and clusters in the interstellar medium are dominated by emission of vibrational infrared radiation. With the development of cryogenic storage it has become possible to experimentally study these processes. Recent storage ring results demonstrate that intramolecular vibrational redistribution takes place within the cooling process, and an harmonic cascade model has been used to interpret the data. Here we analyze this model and show that the energy distributions and the photon emission rates develop into near-universal functions that can be characterized with only a few parameters, irrespective of the precise vibrational spectra and oscillator strengths of the systems. We show that the photon emission rate and emitted power vary linearly with total excitation energy with a small offset. The time developments of ensemble internal energy distributions are calculated with respect to their first two moments. The excitation energy decreases exponentially with a rate constant which is the average of all k1→0 Einstein coefficients, and the time development of the variance is also calculated.

Ultraviolet spectroscopy of AlO from first principle

The spectrum of AlO is widely used in various applications including the explorations of interstellar space, studies of laser ablation, combustions of Al-containing fuels and so on. In this work, we reported the spectroscopy of the AlO radical at temperatures of 300 ∼ 15,000 K for the wavenumber range of 1 ∼ 55,000 cm−1. Firstly, we extended our previous calculations of the potential energy curves (PECs) and transition dipole moments (TDMs) for AlO (Bai, Qin & Liu, MNRAS, 2022, 510:1649–1656) to higher B2Σ+, D2Σ+, 1′2Π and 1′'2Π electronic states, with the consideration of Davidson correction, scalar relativistic correction and core-valence correlation. Partition functions, Einstein coefficients and radiative lifetimes of AlO were then obtained by solving the nuclear-motion Schrödinger equation. The partition functions reveal that the AlO molecules mainly exist in the X2Σ+ state at temperatures of 10 ∼ 6270 K and in the A2Π state at temperatures of 6270 ∼ 15,000 K in the thermodynamic equilibrium. Finally, line intensities and spectra for different electronic transitions of AlO were calculated. The results show that the X2Σ+ → C2Π and X2Σ+ → D2Σ+ transitions dominate in the ultraviolet waveband. Comparisons of the TDMs, radiative lifetimes, line intensities and spectra with previous theoretical and experimental values indicate that our calculated data in the ultraviolet waveband are reliable and may be used for the radiation field calculation.

Rheological evolution mechanisms of asphalt binder and mastic under freeze-thaw cycles

Perennial freeze-thaw cycles have caused plenty of defects on asphalt pavements. To analyze the effect on asphalt binder and mastic under freeze-thaw cycles, the multiple stress creep recovery (MSCR) tests, frequency sweep tests, linear amplitude sweep (LAS) tests, and bending beam rheological (BBR) tests were performed first. The rheological property of asphalt binder and mastic was evaluated through the Burgers model, 2S2P1D (two springs, two parabolic elements, and one dashpot) model, Sigmoidal model, and viscoelastic continuum damage (VECD) theory. The Einstein coefficient and K.D.Ziegel−B−G∗ (K−B−G∗) model were adopted to investigate the asphalt binder-filler interaction subsequently. Finally, Fourier transform infrared spectroscopy (FTIR) test was conducted to analyze the variation of chemical composition of asphalt binder before and after freeze-thaw cycles. The results showed that as freeze-thaw cycle increased, the percent recovery of asphalt binder increased, and the non-recoverable creep compliance of asphalt binder decreased and that of asphalt mastic increased first but decreased. The rutting factor and fatigue factor of asphalt binder and mastic increased after freeze-thaw cycles. The asphalt mastic showed poorer fatigue resistance than asphalt binder at a given freeze-thaw cycle. The low-temperature stiffness of asphalt binder and mastic increased as freeze-thaw cycle increased. K−B−G∗ value showed that the asphalt binder-filler interaction damaged seriously after fifteen freeze-thaw cycles, and the Einstein coefficient decreased by 52.73% after twenty freeze-thaw cycles. The IS and IC indexes increased, and the IB index decreased after twenty freeze-thaw cycles. The design and construction of asphalt pavement in seasonal frozen regions may benefit from this study.

Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S2 Molecule

Intensity of transitions from the b1∑g+ and a1Δg states to the ground state X3∑g− in the near IR emission spectrum of the S2 molecule has been calculated by the multireference configuration interaction method taking into account spin-orbit coupling (SOC). The intensity of the b1∑g+ − X3∑g,Ms=±1− transition is largely determined by the spin interaction with the electromagnetic wave, which comes from the zero-field splitting of the ground X multiplet and the SOC-induced mixing between b and X3∑g,0− states. The Einstein coefficients for the experimentally detected 0−0, 0−1, 1−1 bands of the b1∑g+−X3∑g,Ms=±1− emission system are calculated in good agreement with observations. The Einstein coefficient of the a1∆g−X3∑g,Ms=±1− magnetic dipole transition is very low, being equal to 0.0014 s−1. Nonetheless, the weakest of all experimentally observed bands (the 0−0 band of the a-XMs=±1 transition) qualitatively corresponds to this calculation. Most importantly, we provide many other IR bands for magnetic dipole b1∑g+ − X3∑g,Ms=±1− and a1∆g−X3∑g,Ms=±1− transitions, which could be experimentally observable in the S2 transparency windows from a theoretical point of view. We hope that these results will contribute to the further experimental exploration of the magnetic infrared bands in the S2 dimer.

FitAik: A package to calculate least-square fitted atomic transitions probabilities

We present a new method implemented in our new package FitAik, to perform least-squares fitting of calculated and experimental atomic transition probabilities, by using the mono-electronic transition integrals 〈nℓ|r|n′ℓ′〉 (with r the electronic radial coordinate) as adjustable quantities. FitAik is interfaced to the Cowan suite of codes, for which it automatically writes input files and reads output files. We illustrate our procedure with the example of Er+ ion, for which the agreement between calculated and experimental Einstein coefficients is found to be very good. The source code of FitAik can be found on GitLab, and the calculated Einstein coefficients are stored in our new database CaDDiAcS. They are also used to calculate the dynamic dipole polarizability of Er+.

Thermometry of stored molecular ion beams

The radiative cooling of a stored, initially rotationally hot OH^{-} ion beam is probed by photodetachment using an electrostatic ion beam trap combined with an in-trap velocity map imaging spectrometer, providing direct measurement of the time-dependent rotational population. The rotational temperatures are estimated from photodetached electron spectra as a function of time using a Boltzmann distribution model and further verified by a rate law model using known Einstein coefficients. We demonstrate that during the entire cooling time, the rotational population can be well described by a Boltzmann distribution.

Ab initio calculation of the potential energy curves and spectroscopic properties of low-lying electronic states of CH+ molecular cation

The combined use of the MRCI-SD(T) method with the cc-pV6Z basis set has enabled us to determine the potential energy curves of the molecular cation whose fundamental state lies above the corresponding state of its neutral parent at the dissociation limit. With the accurate potential energy curves thus obtained, we have calculated spectroscopic constants which show good agreement with the experimental and other theoretical values available in the literature. To account for perturbations where necessary, spin-orbit coupling effects have been introduced. An understanding of the polarity of studied in the various electronic states is made possible by calculating the dipole moments. In addition, transition dipole moments were computed prior to the obtention of molecular parameters such as oscillator strength, Einstein coefficients, radiative probabilities and Franck–Condon factors. Overall good accuracy is observed.

Ab Initio Calculation of Ground- and Low-Excited-State Spectroscopic Data and Transition Properties of SBr.

In this paper, potential energy curves of Λ-S and Ω states of SBr+ are reported for the first time, and the spectrum data of some low excited bound states are obtained. The differences in the spectrum properties of main-group molecules and SBr+ were compared and analyzed, providing a sufficient theoretical basis for the subsequent study of main-group molecules. The avoided crossing that occurs in the Ω state is analyzed, and finally it is concluded that this phenomenon mainly occurs in the energy region between 20,000 and 40,000 cm-1 that is relative to the minimum energy value. Potential transitions in the Ω state capable of achieving laser cooling of SBr+ are explored. The Franck-Condon factor, radiation lifetime, and Einstein coefficient between X3Σ0+- and b1Σ0++ are calculated. From the calculation results, we concluded that direct laser cooling of SBr+ is not feasible. What we have studied in this paper provides a theoretical basis for subsequent computational exploration of the spectrum properties of SBr+.

Equilibrium points, linear stability, and bifurcation analysis on the dynamics of a quantum dot light emitting diode system

Abstract In this paper a quantum dot light emitting diode (QDLED) system is modeled as a three dimensionless differential system. We identified three vital parameters Γ the rate of the output coupling rate of photons in the optical mode to the nonradiative decay rate of the number of carriers in the wetting layer (WL), Γ 1 the rate of the Einstein coefficient to the nonradiative decay rate of the number of carriers in the WL and δ o such that I/We is the divide the injection current on Einstein coefficient multiplying elementary charge. Using these parameters a novel way to stability of the dynamics based on the number of interior equilibrium solutions admitted by the system has been obtained. We investigate the considered model is reach in dynamics and identified various bifurcations that are experienced by the considered system from the parameter space. These are saddle-node bifurcation, trans-critical bifurcation, and pitchfork bifurcation. In this study we offer mathematical proof for the incidence of these bifurcations that take place in the considered dynamical system as the parameters move between the regions presented in the parameter space and accordingly, this method was enhanced with numerical results.

A comparison of indices used to evaluate asphalt-filler interactions

Based on the physicochemical reactions between asphalt and filler, the structural asphalt film is formed. The interaction can significantly affect the strength of structural asphalt film and the mechanical properties of asphalt mastic. The strength of asphalt-filler interaction is hard to intuitively characterize. Hence, we need the index to evaluate the ability of interaction. To select the optimum evaluation index to characterize filler-asphalt interactions, we compared the rationality and reliability of six interaction indices (Palierne C, complex shear modulus coefficient ΔG*, Einstein coefficient ΚE, complex viscosity coefficient Δη*, Ziegel-B and Luis Ibrarra-A). This comparison was based on the complex modulus, phase angle and viscosity of asphalt mastics manufactured from four asphalt binders and nine mineral fillers comprising different fractions of filler volume. Comparing the sensitivity of the evaluation indices to changes in asphalt performance, filler type, and filler volume fraction, respectively, the complex shear modulus coefficient index (ΔG*), Einstein coefficient (KE) and complex viscosity coefficient (Δη*) of the filler volume fraction is the dominant factor, and as the filler volume fraction increases, the values of the indices increase. This observation of interaction indices growing with filler volume fraction is inconsistent with the physical–chemical interactions between asphalt and filler. Therefore, these indices cannot be applied to evaluate the filler-asphalt physical–chemical interactions. When the filler volume fraction changes from 0.23 to 0.68, the range of Palierne C index values is 0.84 ∼ 1.42. The higher the filler volume fraction, the smaller the Palierne C value. When the filler volume fraction is below 0.53, the Palierne C varies little. This changing rule of Palierne C is consistent with the adsorbed asphalt layer theory. Hence, Palierne C was ultimately selected as the optimum interaction index based on the relationship between adsorbed asphalt layer on mineral filler and filler volume fraction. We applied Palierne C to evaluate the interaction between different asphalts and mineral fillers.We used the Palierne C index to analyze the effects of asphalt, filler type and filler volume fraction on the asphalt-filler interaction. The results showed that SBS modified asphalt had the greatest effect on the filler-asphalt interaction, followed by high viscosity modified asphalt, SK 90 matrix asphalt, and finally, KL70 matrix asphalt. We also found that although the filler-asphalt interaction increases as the proportion of cement and hydrated lime increases, the cement and hydrated lime demonstrated an insignificant effect on the interaction. The effects of the hydrated lime-asphalt interaction were stronger than that of cement. The higher the filler volume fraction, the lower the value of Palierne C.Finally, gray system theory was used to analyze the correlation between the asphalt-filler interaction and the composition of filler and asphalt. The correlation degrees of the Palierne C index with filler composition were MgO > GaO > K2O > Fe2O3 > SiO2 > AL2O3 > P2O5 > MnO > Na2O > Ga(OH)2 > TiO2. Results indicate that the filler composition has a stronger effect on the filler-asphalt interaction than the asphalt composition. This result is consistent with previous research. The filler particles absorb the polar composition of asphalt, and the reactions occur between the filler alkaline group and the asphalt acid group. The results showed that the composition of MgO and GaO fillers most significantly affected the filler-asphalt interaction. And this conclusion further confirms the feasibility of using the Palierne C index to evaluate the filler-asphalt interaction.

Measurement of the mercury (6s6p)P13 -state lifetime in the frequency domain from integrated absorbance data

Quantitative UV laser absorption spectroscopy is implemented to measure the strength of the $(6{s}^{2})\phantom{\rule{0.28em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}(6s6p)^{3}P_{1}$ intercombination transition of Hg atoms near the wavelength of 253.7 nm and to retrieve the lifetime of the excited state. Tunable, single-mode, coherent radiation in the deep UV is produced through a double-stage second-harmonic generation process, starting from the output radiation of an external-cavity diode laser at 1014.8 nm. This latter is referenced to an optical frequency comb synthesizer. The measurement strategy exploits the relationship between the strength of an optical transition and the spontaneous emission Einstein coefficient. The complete uncertainty budget leads to an overall relative uncertainty of 0.6%, with a statistical contribution of 0.28 ns, which is the lowest ever obtained for the $(6s6p)\phantom{\rule{0.28em}{0ex}}^{3}P_{1}$ lifetime. The new value, amounting to $125.12\ifmmode\pm\else\textpm\fi{}0.79\phantom{\rule{0.28em}{0ex}}\mathrm{ns}$, compares well with most of the past determinations within two times the quoted uncertainties. Despite this, it does not agree with the weighted average of the 12 prior values, thus suggesting that a critical reassessment of the uncertainty of some of the past measurements is probably necessary.

On the effective temperature of large sunspot umbra using AlH molecular lines

In this work, the radiative transition parameters including Franck–Condon (FC) factors, r-centroids, electronic transition moment, Einstein coefficients, band strength, oscillator strength, lifetime and effective vibrational temperature have been computed for A1Π−X1Σ+ and C1Σ+−A1Π systems of aluminium monohydride (AlH) molecule by the numerical integration method for the experimentally known vibrational levels using Rydberg – Klein – Rees (RKR) potential. The computed radiative transition parameters are tabulated. A significant number of well resolved AlH molecular rotational lines of A1Π−X1Σ+ (0,0), (1,1) and (0,1) bands are identified in the sunspot umbral spectrum and the estimated effective rotational temperature has been determined as 2315 K, 2155 K and 1838 K respectively. The effective vibrational temperatures of the A1Π−X1Σ+ and C1Σ+−A1Π systems are found to be 5682 K and 3472 K respectively. Hence, the radiative transition parameters and the effective temperatures confirm the presence of AlH molecule in sunspot spectra.

The quasi bound spectrum of H2

We compute the radiative ro-vibrational emission spectrum of H involving quasi-bound states via a simple numerical method of resolution of the Schrödinger equation by introducing a modified effective molecular potential. The comparison of the eigenvalues obtained with our approximation and other theoretical methods based on scattering resonance properties is excellent. Electric quadrupole and magnetic dipole contributions are calculated and we confirm the previous computations of Forrey of the electric quadrupole transition Einstein coefficients. The astrophysical relevance of such quasi-bound levels is emphasized.

A computational study of the low-lying electronic states of diatomic beryllium bismuthide

We have performed high-level ab initio computations to provide information associated with potential energy curves, molecular structures, electronic structures and vibrational energy levels of BeBi, which is yet an experimentally unknown species. Spectroscopic constants for twelve Λ-S states of the first four Λ-S dissociation channels are obtained for the first time. The feature of seven low-lying excited Ω states of BeBi, corresponding to the first three Ω dissociation limits, has been reported. The spin-orbit coupling effect is proved to have caused a significant impact on the investigated electronic states and interactions among them. Moreover, transition probabilities, such as transition dipole moments, Franck-Condon factors, Einstein coefficients, vibrational branching ratios and radiative lifetimes, are calculated for selected transition bands. Accompany computations are also been carried out for other Be-VA group diatomics of BeN, BeP and BeAs. Relevant data correlated with BeSb are collected from our previous study [Spectrochim. Acta A 208 (2019) 124]. Regular tendencies associated with molecular structures and spectroscopic constants are demonstrated from BeN to BeBi. We expect this work will extend our knowledge of the Be-VA group species and satisfy demands for experimental detections on BeBi.

Study on the spectroscopy and transition properties of TeCl+

For the first time, the spectroscopy data of TeCl+ ion and the transition data between low excited states are systematically calculated. The potential energy curves of 22 Λ-S states and 51 Ω states are calculated by the internally contracted multiconfiguration interaction and Davidson correction method. By solving the one-dimensional radial Schrödinger equation, the spectroscopy data of Λ-S states and Ω states are obtained. The phenomenon of avoided crossing in Ω state is analyzed in detail, which is mainly concentrated in the region of 20000 cm−1 to 35000 cm−1. The Franck-Condon factors, Einstein coefficients and spontaneous radiative lifetimes of X3Σ0+-↔21Σ0++ transitions are calculated. According to the calculation results, it is preliminarily judged that the direct laser cooling of TeCl+ ion is not feasible.

Calculation of the singlet-triplet magnetic and electro-quadrupole transitions intensity for Ge2 molecule

Intensity of the parity-forbidden singlet-triplet (S-T) transitions of the Ge2 molecule in the near IR region has been studied by the multi-reference configuration interaction (MRCI) approach with spin-orbit coupling (SOC). Intensity of the sub-band is mainly dominated by the spin angular momentum term in the magnetic-dipole transition moment, which arises from the spin current inside the zero-field split sublevels of the ground state. The Einstein coefficients corresponding to vibronic bands 0–(2∼7), 1–(4∼7), 2–(6∼7), 3–7 of the transition are in the range of 0.304–0.463 s−1; these bands could be detected since they are not overlapped by the allowed rovibronic systems. The magnetic-dipole is only defined by the orbital angular momentum term and the band intensity is not sufficient for observation. The electric-quadrupole and transitions have also been calculated to be negligible. The triply forbidden electro-dipole transitions in the IR spectrum of the Ge2 throws new light on this little known domain of diatomic molecular spectroscopy. Highlights The parity-forbidden singlet–triplet transitions of the Ge2 has been studied. Intensity of the sub-band arises from the spin current inside the zero-field split sublevels of the ground state. Contributions of the a1Δg−1Πg and orbital transitions presented in the magnetic-dipole a 1Δg- transition are negligible.