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A spin–orbit coupling electronic structure study of the AlZn molecule is conducted to investigate the molecular properties of the low-lying electronic states and their feasibility toward direct laser cooling. This study uses the complete active-space self-consistent field level of theory, followed by the multireference configuration interaction method with Davidson correction (+Q). The potential energy and dipole moment curves and the spectroscopic constants are computed for the low-lying doublet and quartet electronic states in the 2S+1Λ± and Ω(±) representations. The transition dipole moments, the Franck–Condon factors, the Einstein coefficient, the radiative lifetimes, the vibrational branching ratio, and the slowing distance are determined between the lowest spin–orbit bound electronic states. These results show that the molecule AlZn has a high potential for laser cooling through the X2Π1/2 → (2)2Π1/2 transition by utilizing four lasers at a wavelength in the ultraviolet region, reaching a sub-microkelvin temperature limit. [ABSTRACT FROM AUTHOR]

The absorption spectrum of H219O, a radioactive isotopologue of the water molecule, is predicted using variational nuclear motion calculated based on a high precision potential energy function and ab initio dipole moment surface. Vibrational - rotational energy levels and wave functions, line centers and Einstein coefficients for dipole transitions are calculated. Predicted transition wavenumbers are improved by extrapolating known empirical energy levels of the stable H216O, H217O and H218O isotopologues to H219O. A line list for possible atmospheric application is presented which includes air line broadening coefficients. The calculations span a wide spectral range covering infrared and visible wavelengths, and are appropriate for temperatures up to 1000 K. Windows suitable for observing absorption by H219O are identified and comparisons made with the infrared spectra of water vapor in natural abundance, H215O and H214O. [ABSTRACT FROM AUTHOR]

We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes' shift between forward and reverse transitions required by equilibrium with blackbody radiation. For Boltzmann statistics, the relative strengths of forward and reverse transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal chemical potentials of bands obey the Rydberg-Ritz combination principle. Each stimulated Einstein coefficient spectrum gives a frequency-dependent transition cross-section. Transition cross-sections obey causality and a detailed-balance condition with spontaneous emission, but do not directly obey generalized Einstein relations. Even with an energetic width much less than the photon energy, a predominantly absorptive forward transition with an energetic width much greater than the thermal energy can have such an extreme Stokes' shift that its reverse transition cross-section becomes predominantly absorptive rather than emissive. [ABSTRACT FROM AUTHOR]

There are only limited theoretical results published on the transition properties of the X1Σ+, A1Π, B1Σ+, C1Δ, D1Σ−, E1Δ, a3Π, b3Σ+, and c3Δ states of BeS, and even some of the states have no theoretical and experimental reports on the relevant aspects of these transitions. Therefore, we derived these transition properties in this study. The potential energy curves of X1Σ+, A1Π, B1Σ+, C1Δ, D1Σ−, E1Δ, a3Π, b3Σ+, c3Δ, d3Σ−, and e3Σ− states of the BeS molecule with their Ω states and the transition dipole moments between them were calculated by the complete active space self-consistent field method, followed by the internally contracted multireference configuration interaction method. For the accurate computation of the transition properties, scalar relativistic corrections and core–valence correlation were considered. The radiative lifetimes were approximately 10−6 s for the A1Π and b3Σ+ states, 10−7 s for the E1Δ state, 10−7–10−8 s for the C1Δ and D1Σ− states, and 10−8 s for the B1Σ+, c3Δ, and e3Σ− states. The transition properties of the seven Ω states generated by the X1Σ+, A1Π, B1Σ+, and a3Π electronic states, including several electric dipole-forbidden transitions were researched. In particular, the B1Σ+0+–X1Σ+0+, B1Σ+0+–A1Π1, and A1Π1–X1Σ+0+ systems have strong transitions. In this paper, the radiative lifetimes of A1Π1, B1Σ+0+, a3Π0−, a3Π0+, and a3Π1 electronic states were also computed. For the A1Π1, B1Σ+0+, and a3Π1 states, the distribution of the radiation lifetime with the rotational angular momentum quantum number J at 0 ≤ υ ≤ 15 and J ≤ 70 was evaluated. It is expected that the outcome of the calculations in this paper can contribute some meaningful guidelines for conducting further theoretical and experimental investigations. [ABSTRACT FROM AUTHOR]

The predicted rotation-vibration absorption spectrum of the radioactive isotopically substituted water molecule, H214O, is presented. Variational nuclear-motion calculations are performed using the DVR3D software package based on the use of a high-precision potential energy function and an accurate dipole moment surface. Line centres, intensity and Einstein coefficients are calculated, and air pressure broadening coefficients are estimated. The calculation was carried out over a wide wavenumber range from 0 to 25000 cm $ {}^{-1} $ − 1 and total angular momentum up to J = 20. Isotopologue extrapolation rules based on experimental data on the energy levels of the stable isotopologues H216O, H $ {}_{2}^{16} $ 2 16 O H217O and H218O were also used to improve the predicted line positions. Spectral ranges best suited to the detection of H214O are identified. [ABSTRACT FROM AUTHOR]

Insufficient theoretical investigation is being conducted on the spectroscopic characteristics within the infrared wavelength range of SiP, an identified interstellar molecule. Using the ic-MRCI method, potential energy functions and dipole moment functions for the ground state (⁠|${X^2}\Pi $|⁠) and low excited states (⁠|${{\rm{A}}^2}{\Sigma ^ + }$|⁠) of the SiP molecule were calculated. Based on experimental spectroscopy data, least squares fitting was used for the potential energy functions of the |${X^2}\Pi $| and |${{\rm{A}}^2}{\Sigma ^ + }$| states. By combining these potential energy and dipole moment functions, the one-dimensional Schrödinger equation was solved to obtain the vibronic energy levels and Einstein A coefficients for the electronic states. Partition functions of the SiP molecule from 0.1 to 3000 K and the radiative properties of |${X^2}\Pi \leftrightarrow {X^2}\Pi $| and |${X^{\rm{2}}}\Pi \leftrightarrow {{\rm{A}}^2}{\Sigma ^ + }$| were derived. Infrared spectroscopy of the |${X^2}\Pi $| state and ultraviolet spectroscopy of the |${X^{\rm{2}}}\Pi \leftrightarrow {{\rm{A}}^2}{\Sigma ^ + }$| transition at 100 K, a temperature crucial for astronomical research, were calculated. Results indicate that the spectral-line intensity of the |${X^{\rm{2}}}\Pi \leftrightarrow {{\rm{A}}^2}{\Sigma ^ + }$| transition is greater, making it more suitable for astronomical observation. The obtained computational results in this paper yield spectroscopic parameters for the characterization of the interstellar molecule SiP, furnishing theoretical underpinnings for subsequent experimental observations. [ABSTRACT FROM AUTHOR]

Cool red giant stars exhibit absorption bands of calcium monochloride (CaCl) in the optical region. In this work, the bands of CaCl corresponding to the A2Π − X2Σ+ transition with v ′ ≤ 4 and v ″ ≤ 4, and B2Σ+ − X2Σ+ transition with v ′ ≤ 2 and v ″ ≤ 2 are rotationally analyzed with PGOPHER, a multipurpose program for simulating and fitting molecular spectra. All bands were analyzed using high-resolution absorption spectra collected at the National Solar Observatory in 1985, calibrated with atomic lines from a high-resolution emission spectrum obtained in a separate hollow cathode experiment. The results are compared with previous laser-induced fluorescence measurements. Overall, the accuracy of spectroscopic constants for the A2Π and B2Σ+ states is improved. Scaled transition dipole moment calculations were used to obtain line strengths. Line lists are provided with Einstein A coefficients and oscillator strengths, which can be used to determine CaCl stellar abundances. Additionally, isotope splittings allowed us to estimate band origins for the 40Ca37Cl isotopologue based on band-head positions. [ABSTRACT FROM AUTHOR]

In recent years, an increasing number of experimental results have been published for a wide variety of systems in which high-precision, ultra-fast, and ultra-short laser pulses techniques have been used to study time-resolved dynamical processes. In the absence of a theoretical prediction of the time distribution of the transition probabilities, the lifetimes τ are generally extracted by fitting the decay time with an exponential, bi-exponential or three-exponential function. In fitting the data, the short-time behavior is generally neglected. The purpose of this study is to show that an explicit formula for the time distribution of the transition probability can be determined rigorously using time-dependent perturbation theory. A formula that perfectly fits an important subset of the experimental results from t = 0 to t = ∞ . We show that by following a route different from the usual procedure for deriving transition amplitudes and Einstein coefficients in time-dependent perturbation theory, one ends up with a time-dependent factor, that is, a temporal distribution function of the transition probabilities, and for the Einstein coefficients. The time distribution reported here looks in the time domain similar to the Planck distribution in the frequency domain. In fact, the behavior of the time distribution, with a maximum at 2 τ ln ⁡ 2 , and with τ playing the role of temperature, resembles the behavior of the Planck frequency distribution. We present several examples to demonstrate that the theoretical formula allows for easier fitting of the experimental results reported in the literature. We also show that the time distribution explains the difference in resonance heights between the experimental and theoretical blue laser spectra. [ABSTRACT FROM AUTHOR]

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The operation of a two-level gas laser is theoretically studied in schemes with single- and double-sided transversal diode pumping Some analytical formulas, which describe the operation of a two-level gas laser with single- and double-sided diode pumping and make it possible to find any laser energy characteristics and optimal working medium and pumping radiation parameters necessary for maximally efficient laser operation, are derived for the case when the outer mirror has a not very low reflection coefficient. It is shown that the generation efficiency of a two-level gas laser can be increased by 11–20 by switching from single-sided to double-sided pumping. [ABSTRACT FROM AUTHOR]

Ab initio CASSCF/MRCI + Q calculations have been used to investigate the electronic structure and transition properties of the alkaline earth astatine molecules SrAt and BaAt. The adiabatic potential energy curves have been computed and plotted for the low-lying electronic states in the representations 2S+1Λ+/− and Ω(±) (with and without spin–orbit coupling effect). The spectroscopic and vibrational constants have been deduced for the corresponding bound states. An analysis of the Franck–Condon factors, the Einstein Coefficients, and the branching ratios among different vibrational levels has shown that both SrAt and BaAt molecules are suitable candidates for Doppler and Sysphus laser cooling. Experimental laser cooling schemes and conditions for these two molecules have been proposed. These results may pave the way for new spectroscopic and laser cooling experiments of alkaline earth astatine molecules. [ABSTRACT FROM AUTHOR]

We present a unified variational treatment of the electric quadrupole (E2) matrix elements, Einstein coefficients, and linestrengths for general open-shell diatomic molecules in the general purpose diatomic code Duo. Transformation relations between the Cartesian representation (typically used in electronic structure calculations) to the tensorial representation (required for spectroscopic applications) of the electric quadrupole moment components are derived. The implementation has been validated against accurate theoretical calculations and experimental measurements of quadrupole intensities of 1H2 available in the literature. We also present accurate electronic structure calculations of the electric quadrupole moment functions for the X1Σ+ electronic states of CO and HF, as well as for the a1Δg– b 1 Σ g + quadrupole transition moment of O2 with the MRCI level of theory. Accurate infrared E2 line lists for 12C16O and 1H19F are provided. A demonstration of spectroscopic applications is presented by simulating E2 spectra for 12C16O, H19F, and 16O2 (Noxon a1Δg– b 1 Σ g + band). [ABSTRACT FROM AUTHOR]

Comprehensive and accurate rovibronic line lists for the X 1Σ+ and A 1Π states of 12C1H+ and 13C1H+ which should be applicable up to temperatures of 5000 K are presented. Available empirical potential energy curves and high-level ab initio dipole and transition dipole moment curves are used with the program level to compute rovibronic energy levels and Einstein A coefficients. Λ-doubling is incorporated into the energy levels and A -coefficients involving the A 1Π state using an empirical method. For 12C1H+, line positions are improved by using both laboratory and astronomical observational spectra as input to the MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure. The 12C1H+ line list contains 1505 states and 34 194 transitions over the frequency range of 0–33 010 cm−1 (λ > 300 nm). Comparisons with observed astronomical and laboratory spectra give very good agreement. The PYT CH+ line lists and partition functions are available from the ExoMol database at www.exomol.com. [ABSTRACT FROM AUTHOR]

Rotational temperatures in the Mesosphere‐Lower Thermosphere region are estimated by utilizing the OH(6,2) Meinel band nightglow data obtained with an Ebert‐Fastie spectrometer (EFS) operated at Arecibo Observatory (AO), Puerto Rico (18.35°N, 66.75°W) during February‐April 2005. To validate the estimated rotational temperatures, a comparison with temperatures obtained from a co‐located Potassium Temperature Lidar (K‐Lidar) and overhead passes of the Sounding of the Atmosphere by Broadband Emission Radiometry (SABER) instrument onboard NASA's Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite is performed. Two types of weighting functions are applied to the K‐Lidar temperature profiles to compare them with EFS temperatures. The first type has a fixed peak altitude and a fixed full width at half maximum (FWHM) for the whole night. In the second type, the peak altitude and FWHM vary with the local time. SABER measurements are utilized to estimate the OH(6,2) band peak altitudes and FWHMs as a function of local time and considerable temporal variations are observed in both the parameters. The average temperature differences between the EFS and K‐Lidar obtained with both types of weighting functions are comparable with previously published results from different latitude‐longitude sectors. We found that the temperature comparison improves when the time‐varying weighting functions are considered. Comparison between EFS, K‐Lidar, and SABER temperatures reveal that on average, SABER temperatures are lower than the other two instruments and K‐Lidar temperatures compare better with SABER in comparison to EFS. Such a detailed study using the AO EFS data has not been carried out previously. Plain Language Summary: In the Earth's atmosphere, a strong band of near‐infrared (NIR) emissions exists at ∼90 km altitude due to the vibrational‐rotational excitation of the Hydroxyl (OH) molecules. The intensity of these OH emissions depends on the temperatures of their rotational states. Under the assumption of thermodynamic equilibrium, the rotational temperatures should represent the background atmospheric temperatures. A scanning spectrometer of the Ebert‐Fastie configuration (EFS) was operated on the nights of February‐April 2005 at Arecibo Observatory (AO), Puerto Rico (18.35°N, 66.75°W) to record the intensity of the OH(6,2) band which is used to estimate rotational temperatures in this work. During the same period, a co‐located Potassium temperature Lidar (K‐Lidar) utilized resonance scattering from the atmospheric K‐atoms to measure temperatures in the 80–100 km altitude range. By nature, the EFS‐derived temperatures are an altitude‐integrated quantity while the K‐Lidar provides altitude‐resolved temperatures. First, we followed a commonly used methodology to compare the EFS and K‐Lidar temperatures by using the SABER data onboard NASA Thermosphere Ionosphere Mesosphere Energetics and Dynamics satellite. We found good agreement between our results and previously published studies. Then, we propose a modified methodology with the help of SABER data to show that it provides a better comparison between the EFS and K‐Lidar temperatures. Key Points: Good inter‐comparison is obtained between Arecibo Observatory spectrometer and Lidar temperatures, and results are similar to previous studiesThe temperature comparison improves when time‐varying weighting functions are used instead of a single weighting functionRotational temperature estimation from the spectrometer data depends strongly on the choice of Einstein coefficients for the P1 line transitions [ABSTRACT FROM AUTHOR]

Comprehensive and accurate rovibronic line lists for the X 1Σ+ and A 1Π states of 12C1H+ and 13C1H+ which should be applicable up to temperatures of 5000 K are presented. Available empirical potential energy curves and high-level ab initio dipole and transition dipole moment curves are used with the program level to compute rovibronic energy levels and Einstein A coefficients. Λ-doubling is incorporated into the energy levels and A -coefficients involving the A 1Π state using an empirical method. For 12C1H+, line positions are improved by using both laboratory and astronomical observational spectra as input to the MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure. The 12C1H+ line list contains 1505 states and 34 194 transitions over the frequency range of 0–33 010 cm−1 (λ > 300 nm). Comparisons with observed astronomical and laboratory spectra give very good agreement. The PYT CH+ line lists and partition functions are available from the ExoMol database at www.exomol.com. [ABSTRACT FROM AUTHOR]

A semi-empirical IR/Vis line list, SOLIS, for the sulphur monoxide molecule 32S16O is presented. SOLIS includes accurate empirical rovibrational energy levels, uncertainties, lifetimes, quantum number assignments, and transition probabilities in the form of Einstein A coefficients covering the |$X\, {}^{3}\Sigma ^{-}$| |$, a\, {}^{1}\Delta , b\, {}^{1}\Sigma ^{+}, A\, {}^{3}\Pi , B\, {}^{3}\Sigma ^{-}, A^{\prime \prime }\, {}^{3}\Sigma ^{+}, A^{\prime }\, {}^{3}\Delta$|⁠ , and |$e\, {}^{1}\Pi$| systems and wavenumber range up to 43 303.5 cm−1 (≥230.93 nm) with J ≤ 69. SOLIS has been computed by solving the rovibronic Schrödinger equation for diatomics using the general purpose variational code Duo and starting from a published ab initio spectroscopic model of SO (including potential energy curves, coupling curves, (transition) dipole moment curves) which is refined to experimental data. To this end, a database of 50 106 experimental transitions, 48 972 being non-redundant, has been compiled through the analysis of 29 experimental sources, and a self-consistent network of 8558 rovibronic energy levels for the X, a, b, A, B , and C electronic states has been generated with the marvel algorithm covering rotational and vibrational quantum numbers J ≤ 69 and v ≤ 30 and energies up to 52 350.40 cm−1. No observed transitions connect to the |$B\, {}^{3}\Sigma ^{-}$| (v  = 0) state which is required to model perturbations correctly, so we leave fitting the |$B\, {}^3\Sigma ^-$| and |$C\, {}^3\Pi$| state UV model to a future project. The SO line list is available at ExoMol from www.exomol.com. [ABSTRACT FROM AUTHOR]

A new method of laser radiation generation without population inversion in the red wing of the -line of alkali metal atoms under resonant absorption of broadband radiation of pump laser diodes at the transition is studied theoretically. The appearance of laser generation is caused by the fact that the probability of stimulated emission in the red wing of the spectral line exceeds the probability of absorption if homogeneous broadening due to interaction between active particles and the buffer gas significantly exceeds the natural broadening (under high pressures of the buffer gas). Analytical formulas representing the operation of a transversely diode-pumped alkali metal vapor laser are obtained. It is found that cesium atoms are the most promising object for observation of laser generation without population inversion in the red wing of the -line of alkali metal atoms. In a sufficiently long active medium (the length of the medium is 50 times its width), the efficiency of pumping radiation conversion into laser radiation can reach 57% at a buffer gas pressure of 5 atm, a pump diode radiation intensity of 5 kW/cm , and a half-width of its spectrum of 1 cm . The laser radiation frequency can be tuned by several tens of cm . [ABSTRACT FROM AUTHOR]

We compute the radiative ro-vibrational emission spectrum of H 2 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. [ABSTRACT FROM AUTHOR]

We compute the radiative ro-vibrational emission spectrum of H 2 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. [ABSTRACT FROM AUTHOR]

A study of the generation and subsequent expansion of plasmas using a single beam (532 nm) from the second harmonic generator of a Q-switched Nd:YAG laser is described. The plasmas in air are studied using an intensified charge-coupled device camera over periods of 1000 ns following the laser pulses. The plasma experimental results are interpreted in terms of wave speeds and plasma temperatures. Energy balance equations are considered to estimate the plasma temperatures and the laser-supported radiation (LSR) and the laser-supported detonation (LSD) wave speeds. Within 1000 ns observation time, the circular spectral images turn elliptical because of plasma expansion toward the laser beam. The plasma expansion increases with increasing laser irradiance. A laser irradiance range of 90-450 GW/cm² yields LSR wave speeds between 45 and 170 km/s and LSD wave speeds of 90-130 km/s. The measured wave speeds are compared with the LSR and the LSR wave speed models. The plasma temperatures are between 90,000 and 120,000 K at 15 ns after the laser pulse based on measured emission spectra and are between 640,000 and 760,000 K at 3 ns based on the LSR model. [ABSTRACT FROM AUTHOR]

The simulation of nonideal Lennard-Jones mixtures is carried out by the method of molecular dynamics. The values of pressure, internal energy, chemical potential, and diffusion coefficients are determined depending on the composition and density. The nonideal behavior of the mixtures is specified by the parameters in the mixing rules for the intermolecular interaction potential. Four options for the values of such parameters are considered. The thermodynamic consistency of the calculated thermodynamic properties is verified using the Gibbs–Duhem expression. The value of excess entropy is calculated, and its connection with the Einstein diffusion coefficients is shown. A parameter is determined in the regression equation that relates the excess entropy to the Einstein diffusion coefficients. Its value is 0.8, which is close to the values in similar expressions for other substances. [ABSTRACT FROM AUTHOR]

Intensity of transitions from the b 1 ∑ g +   and a1Δg states to the ground state X 3 ∑ 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   b 1 ∑ g + −   X 3 ∑ g , M s = ± 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 X 3 ∑ g , 0 − states. The Einstein coefficients for the experimentally detected 0−0, 0−1, 1−1 bands of the b 1 ∑ g + − X 3 ∑ g , M s = ± 1 − emission system are calculated in good agreement with observations. The Einstein coefficient of the a 1 ∆ g − X 3 ∑ g , M s = ± 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 b 1 ∑ g + −   X 3 ∑ g , M s = ± 1 − and a 1 ∆ g − X 3 ∑ g , M s = ± 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. [ABSTRACT FROM AUTHOR]

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 CH + whose fundamental X 1 Σ + state lies 111.12 nm above the corresponding X 2 Π state of its neutral parent CH 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 CH + 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. [ABSTRACT FROM AUTHOR]

Single field inflationary models are investigated within Palatini quadratic gravity, represented by R + α R 2 , along with a non-minimal coupling of the form f (ϕ) R between the inflaton field ϕ and the gravity. The treatment is performed in the Einstein frame, where the minimal coupling to gravity is recovered through conformal transformation. We consider various limits of the model with different inflationary scenarios characterized as canonical slow-roll inflation in the limit α ϕ ˙ 2 ≪ (1 + f (ϕ)) , constant-roll k-inflation for α ≪ 1 , and slow-roll K-inflation for α ≫ 1 . A cosine and exponential potential are examined with the limits mentioned above and different well-motivated non-minimal couplings to gravity. We compare the theoretical results, exemplified by the tensor-to-scalar r ratio and spectral index n s , with the recent observational results of Planck 2018 and BICEP/Keck. Furthermore, we include the results of a new study forecast precision with which n s and r can be constrained by currently envisaged observations, including CMB (Simons Observatory, CMB-S4, and LiteBIRD). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The ExoMol database (www.exomol.com) provides molecular data for spectroscopic studies of hot atmospheres. These data are widely used to model atmospheres of exoplanets, cool stars and other astronomical objects, as well as a variety of terrestrial applications. The 2024 data release reports the current status of the database which contains recommended line lists for 91 molecules and 224 isotopologues giving a total of almost 1012 individual transitions. New features of the database include extensive "MARVELization" of line lists to allow them to be used for high resolutions studies, extension of several line lists to ultraviolet wavelengths, provision of photodissociation cross-sections and extended provision of broadening parameters. Some of the in-house data specifications have been rewritten in JSON and moved for conformity with other international standards. Data products, including specific heats, a database of lifetimes for plasma studies, and the ExoMolHR web app which allows exclusively high resolution data to be extracted, are discussed. [Display omitted] [ABSTRACT FROM AUTHOR]

[Display omitted] • A comparison of results using two basis sets, AVQZ-PP and AWCVQZ-PP, was made. • High-precision ab initio calculations were performed for the potential energy functions, dipole functions, and transition matrix functions of TeI+ in 22 Λ-S states. • Spin-orbit coupling effects were considered, and potential energy functions for 51 Ω states and SOC matrix elements were calculated. • The spectroscopic parameters for low-lying Λ-S and Ω states are fitted. • The Franck-Condon factors, Einstein coefficients, and radiative lifetimes for the X 3 Σ 0 + - ↔ 1 1 Σ 0 + + transition are calculated. The molecular potential energy function plays an important role in many fields. In this paper, the icMRCI + Q method was utilized to compute the potential energy and dipole moments for 22 Λ-S states and 51 Ω states of the TeI+ system. Two basis sets (AVQZ-PP and AWCVQZ-PP) were employed to compute the TeI+ system, with the results indicating that the AVQZ-PP basis set yielded more accurate results. Therefore, all calculations in this paper are based on this basis set. Furthermore, to ensure the accuracy of the results, a comparison was conducted on the spectral parameters of the ground state and two excited states of the molecular ion within the same main group. Given the significant impact of spin–orbit coupling, as indicated by the calculated SO matrix elements, our discussion will predominantly center on the avoidance of crossovers in the Ω states. Finally, the Franck-Condon factors, Einstein coefficients and radiative lifetime between these two states were calculated from the data of the transition between the X 3 Σ 0 + - ↔ 1 1 Σ 0 + + of the TeI+ molecule. [ABSTRACT FROM AUTHOR]

Salt-erosion effect can significantly deteriorate the serviceability of asphalt pavements in salt-rich regions. This paper aims to analyze the creep characteristics and the evolution mechanism of asphalt binder/mastic under salt-erosion conditions. The multi-stress creep recovery (MSCR) test and bending beam rheology (BBR) test were conducted to investigate the creep evolution of salt-eroded asphalt binder/mastic under different temperatures. The gel permeation chromatography (GPC) and scanning electron microscopy (SEM) were employed to analyze the creep evolution mechanism of salt-eroded asphalt binder/mastic. Furthermore, the Burgers model and Schapery model were adopted to study the viscoelastic characteristic evolution of salt-eroded asphalt binder/mastic. Results indicated that the proportion of small molecules in asphalt binder was declined, and the mineral filler coated with asphalt binder was exposed, after salt erosion. The nonrecoverable deformation of asphalt binder/mastic at high- and medium-temperature were reduced after salt erosion. Meanwhile, the percentage of recoverable strain increased with the salt freeze-thaw cycles. The low-temperature performance of asphalt binder/mastic was deteriorated after salt erosion. Following 20 times of salt erosion, the stiffness modulus of asphalt binder/mastic increased by 59.77 % and 16.47 %, respectively. Meanwhile, salt erosion can decrease the viscous components in asphalt binder/mastic, the comprehensive compliance (J c) of asphalt binder/mastic increased by 59.65 % and 16.93 %. Furthermore, the asphalt binder-mineral filler interaction was weakened after salt erosion, the Einstein coefficient decreased by an average of 18.52 %. The design and construction of asphalt pavement in salt-rich regions might be benefited from this paper. • Evaluate the creep characteristics of salt-eroded asphalt binder/mastic. • Investigate the evolution of salt-eroded asphalt binder-filler interaction. • Clarify the creep evolution mechanism of salt-eroded asphalt binder/mastic. [ABSTRACT FROM AUTHOR]

Aims : tungsten has been chosen for use as a plasma facing component in the divertor for the ITER experiment, and is currently being used on existing tokamaks such as JET. W+ plays an integral role in assessing the impurity influx from plasma facing component of tokamaks and subsequent redeposition. Together with previously calculated a neutral tungsten electron-impact dataset this study allows us to determine neighbouring spectral lines in the same wavelength window of the spectrometer, and detect if there is strong blending of overlapping lines between these two ion stages as well as providing ionisation per photon ratios for both species. The new data is to be used for tungsten erosion/redeposition diagnostics. Methods : a significantly modified version of the GRASP0 atomic structure code in conjunction with DARC (Dirac Atomic R -matrix Code) are used to calculate the Einstein A coefficients and collisional rates used to generate a synthetic W II spectrum. The W II spectrum is compared against tungsten spectral emission experiments. Results : this study is used to model the spectrum of W ii, providing the predictive capability of identifying spectral lines from recent experiments. These results provide an integral part of impurity influx and redeposition determination, as the ionisation rates may be used to calculate S/XB ratios. [ABSTRACT FROM AUTHOR]

We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes' shift between forward and reverse transitions required by equilibrium with blackbody radiation. For Boltzmann statistics, the relative strengths of forward and reverse transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal chemical potentials of bands obey the Rydberg-Ritz combination principle. Each stimulated Einstein coefficient spectrum gives a frequency-dependent transition cross-section. Transition cross-sections obey causality and a detailed-balance condition with spontaneous emission, but do not directly obey generalized Einstein relations. Even with an energetic width much less than the photon energy, a predominantly absorptive forward transition with an energetic width much greater than the thermal energy can have such an extreme Stokes' shift that its reverse transition cross-section becomes predominantly absorptive rather than emissive., Competing Interests: Competing interests statement:The authors declare no competing interest.

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 b 1 Σ g + − X 3 Σ g , M s = 1 − 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 X 3 Σ g − state. The Einstein coefficients corresponding to vibronic v ′ − v ′ ′ bands 0–(2∼7), 1–(4∼7), 2–(6∼7), 3–7 of the b 1 Σ g + − X 3 Σ g , M s = 1 − 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 a 1 Δ g − X 3 Σ g , M s = 1 − is only defined by the orbital angular momentum term and the band intensity is not sufficient for observation. The electric-quadrupole a 1 Δ g − b 1 Σ g + and a 1 Δ g − X 3 Σ g , M s = 0 − 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 b 1 Σ g + − X 3 Σ g , Ms = 1 − sub-band arises from the spin current inside the zero-field split sublevels of the ground X 3 Σ g − state. Contributions of the a1Δg−1Πg and X 3 Σ g − − 3 ∏ g orbital transitions presented in the magnetic-dipole a1Δg- X 3 Σ g , Ms = 1 − transition are negligible. [ABSTRACT FROM AUTHOR]

Accurate knowledge of transition dipole moment matrix elements is crucial since important parameters associated with the interaction of light with matter, such as emission and absorption line intensities, lifetimes and Einstein coefficients, depend on these matrix elements.We report here an experimental study of the Na2 51Σ+g ↔ A1Σ+ u and 61Σ+g↔ A1Σ+ u electronic transition dipole moments and their dependence on internuclear distance. We have measured absolute transition dipole matrix elements for ro-vibrational transitions of the Na2 51Σ+g↔ A1Σ+ u and 61Σ+g↔ A1Σ+ u electronic transitions using Autler-Townes and optical-optical double resonance spectroscopy, and we compare the results to ab initio theoretical values [A. Sanli et al., J. Chem. Phys. 143, 104304 (2015)]. [ABSTRACT FROM AUTHOR]

[Display omitted] • The proximity of the 4d10 5p1 (2Po) and 4d9 5s2 (2D) excited states of silver and the presence of spin–orbit coupling makes the study of excited states of silver-containing molecules challenging. • Low-lying electronic states of AgH have been calculated using the multireference configuration interaction method incorporating scalar relativistic effects and spin–orbit coupling corrections. • Potential energy curves and spectroscopic constants were obtained for 24 individual Ω states, with an accurate description of the excited states of AgH after spin–orbit corrections. • Several excited states observed in the ultraviolet absorption spectra of AgH and AgD have been relabeled using the new ab initio data. Potential energy curves have been calculated for the low-lying electronic states of AgH, correlating to the 4d10 5s1 (2S), 4d10 5p1 (2Po), 4d9 5s2 (2D), and 4d10 6s1 (2S) states of atomic silver, using the MRCI method with scalar relativistic and spin–orbit corrections. Spectroscopic constants were obtained for 24 individual Ω states, and several excited states of AgH observed in the ultraviolet absorption spectra, i.e., the C1Π, B1Σ+, b3Δ 1 , and D1Π states, were relabeled based on the new ab initio data. The calculated Einstein A coefficients indicated that almost all electronic transitions with ΔΩ = 0, ±1 are allowed. [ABSTRACT FROM AUTHOR]

The intriguing law of anomalous numbers, also named Benford's law, states that the significant digits of data follow a logarithmic distribution favoring the smallest values. In this work, we test the compliance with this law of the atomic databases developed at the National Institute of Standards and Technology (NIST) focusing on line energies, oscillator strengths, Einstein coefficients and radiative opacities. The considered databases are the Atomic Spectra Database (ASD) and the NIST-LANL (Los Alamos National Laboratory) Lanthanide/Actinide Opacity Database. The present study is not limited to the first digit and the case of multipole lines is also considered. The fact that the law is verified with a high accuracy means that the occurrence of digits reflects the constraints induced, in a given angular-momentum coupling, by the selection rules for atomic processes. As a consequence, Benford's law may be of great interest to detect inconsistencies in atomic databases. • Benford's laws of first and first two digits is tested on NIST atomic and opacity databases. • Deviations from Benford's law are explained. • Importance of application of Benford's law to atomic databases is discussed. [ABSTRACT FROM AUTHOR]

Dicarbon species are of particular interest within the physical chemistry community. However, contrary to neutral C 2 , the theory of electronic structure and spectra concerning C 2 − ions is not well-established. To address this gap in information, high-level multireference configuration interaction (MRCI) calculations have been performed, and new potential energy curves for fourteen low-lying states of C 2 − are reported. The best estimate for the ground dissociation energy is 64,720 cm−1 at the MRCI+Q/AV5Z level of theory. The first excited state, A 2 Π u , lies at 3,836 cm−1 (R e = 2.4829 a 0 and ω e = 1649 cm−1). The infrared A 2 Π u − X 2 Σ g + transition has Einstein coefficients of the order of 103–104 s−1. The lifetime of the A 2 Π u state is given in microseconds. For the B 2 Σ u + state, it was calculated τ 0 ≈ 78 ns in good accord with the experimental value of 77 ± 8 ns. The a 4 Σ u + state is placed at an excitation energy of 32,369 cm−1, much higher than expected by experimentalists (19,448 cm−1). The spin-forbidden transitions a 4 Σ u + − X 2 Σ g + are strong enough to be detected experimentally (A 04 ≈ 3 × 106 s−1). The 1 4 Π g − a 4 Σ u + transitions are more concentrated in the IR region. The radiative lifetime of 1 4 Π g is computed to be 12 μ s. There is no doubt that the current data considerably enhance our understanding of the spectroscopy of C 2 −. • Accurate PECs for 14 low-lying states of C2- are obtained using MRCI calculations. • a 4 Σ u + → X 2 Σ g + , 1 2 Π g → A 2 Π u , and 2 2 Π g → A 2 Π u transitions are strong. • Radiative lifetimes of the a 4 Σ u + , 1 2 Π g , 2 2 Π g states are of the order of nanoseconds. • The 1 4 Π g → a 4 Σ u + , 1 2 Π g → 1 4 Π g , and 1 4 Δ u → 1 4 Π g transitions are in the infrared region. [ABSTRACT FROM AUTHOR]

• The potential energy curve of electronic states have been estimated for the (2) 3 Π − X 3 Π transition of GeC molecule using RKR method. • The radiative transition parameters have been estimated for the (2) 3 Π − X 3 Π transition of GeC molecule. • The effective vibrational temperature helps to ascertain the presence of GeC molecule in sunspot atmosphere. In this work, the experimental potential energy curves for (2) 3 Π and X 3 Π electronic states of GeC molecule have been constructed by using Rydberg-Klein-Rees (RKR) method. The radiative transition parameters viz., Franck-Condon (FC) factor, r-centroid, electronic transition moment, band strength, relative band strength, Einstein coefficients, radiative lifetime and oscillator strength for the (2) 3 Π − X 3 Π system of GeC molecule have been estimated for the experimentally observed vibrational levels from Rydberg-Klein-Rees (RKR) potential and the estimated values are tabulated. The estimated effective vibrational temperature found as 5628 K for the (2) 3 Π − X 3 Π system of GeC molecule. The radiative transition parameters and effective vibrational temperature are evident that the possible presence of GeC molecule in solar and sunspots atmosphere. Further, these parameters are employed in rationalizations of astrochemical and astrophysical observations. [ABSTRACT FROM AUTHOR]

The sodium monoxide radical (NaO) is observed in night-glow in the Earth's mesosphere and likely has astronomical importance. This study concerns the optical transitions within the ground X 2Π state and to the very low-lying (T e ≈ 2000 cm−1) excited A 2Σ+ state. A line list consisting of rovibronic term values, allowed electric dipole transitions, Einstein coefficients, and partition functions for varying temperature are produced using a variational solution of the coupled-channel Schrödinger equations using the program duo. multi-reference configuration interaction (MRCI) ab initio calculations characterizing the potential energy curves of the two states, spin-orbit and L -uncoupling non-adiabatic matrix elements, as well as permanent and transition dipole moments were integral in the formation of the final deperturbation model. Ab initio potential energy curves are represented in the analytical Extended Morse Oscillator form and refined, along with the spin-orbit and L -uncoupling functions, by least-squares fitting to the available spectroscopic data. The input experimental data consisted of pure rotational transitions within the fine-structure components of the X 2Π state for v ″ ∈ [0, 3] vibrational levels as well as the rovibronic A 2Σ+(v ′ = 0) ← X 2Π(v ″ = 0) transitions, both with limited coverage over rotational excitation. The lack of data detailing the vibrational structure of the X and A states points to the need for further experimental study of higher excited levels, which would provide a more robust spectroscopic model. The NaO NaOUCMe line list is available via www.exomol.com and the CDS data base. [ABSTRACT FROM AUTHOR]

Quantitative in situ elemental analyses of the impure deposited layer on the plasma-facing components (PFCs) of magnetically confined fusion devices such as EAST are crucial and challenging. Laser-induced breakdown spectroscopy (LIBS) is one of the most promising methods. In this study, we present an improved quantitative analytic algorithm for the deposited layers (in vacuum) of both major and minor elements via one-point calibration laser-induced breakdown spectroscopy (OPC-LIBS). OPC-LIBS is a variation of the calibration-free LIBS approach involving one matrix-matched standard sample with a known composition that effectively corrects the errors, caused by the uncertainty of Einstein's coefficient and inaccurate efficiency of the spectrum acquisition system of the CF-LIBS method. We found that the OPC-LIBS method is more accurate for the determination of composition of a series of Al–W–Mo coatings (EAST-like deposits) compared to the conventional CF-LIBS approach at 10−5 mbar to simulate the pressure condition of a fusion vessel. In the case of OPC-LIBS measurement, the relative error of major elements such as Al (85.65–95.51 at%) was below 2%, and the relative error of trace elements W (2.32–9.56 at%) was within 35% and Mo (2.17–11.66 at%) was within 20%. Finally, our results verify the ability of quantitative analysis by using the OPC method in a high-vacuum environment and film samples. [ABSTRACT FROM AUTHOR]

A field effect transistor having the active area made of monolayer graphene is simulated by a drift-diffusion model coupled with the Poisson equation. The adopted geometry, already proposed in (Nastasi and Romano in IEEE Trans. Electron. Devices 68:4729–4734, 2021, https://doi.org/10.1109/TED.2021.3096492), gives a good current-ON/current-OFF ratio as it is evident in the simulations. In this paper, we compare the numerical simulations of the standard (non-degenerate) drift-diffusion model, that includes the Einstein diffusion coefficient, with the degenerate case. [ABSTRACT FROM AUTHOR]

Despite many years of research into Raman phenomena, the problem of how to include both spontaneous and stimulated Raman scattering into a unified set of partial differential equations persists. The issue is solved by formulating the quantum dynamics in the Heisenberg picture with a rigorous accounting for both time- and normal-ordering of the operators. It is shown how this can be done in a simple, straightforward way. Firstly, the technique is applied to a two-level Raman system, and comparison of analytical and numerical results verifies the approach. A connection to a fully time-dependent Langevin operator method is made for the spontaneous initiation of stimulated Raman scattering. Secondly, the technique is demonstrated for the much-studied two-level atom both in vacuum and in a lossy dielectric medium. It is shown to be fully consistent with accepted theories: using the rotating wave approximation, the Einstein A coefficient for the rate of spontaneous emission from a two-level atom can be derived in a manner parallel to the Weisskopf–Wigner approximation. The Lamb frequency shift is also calculated. It is shown throughout that field operators corresponding to spontaneous radiative terms do not commute with atomic/molecular operators. The approach may prove useful in many areas, including modeling the propagation of next-generation high-energy, high-intensity ultrafast laser pulses as well as spontaneous radiative processes in lossy media. [ABSTRACT FROM AUTHOR]

The electronic spectra of neutral NpO and NpO2 as well as of their mono- (NpO+, NpO2+) and dications (NpO2+, NpO22+) were studied using multiconfigurational relativistic quantum chemical calculations at the complete active space self-consistent field/CASPT2 level of theory taking into account spin-orbit coupling. The active space included 16 orbitals: all the 7s, 6d, and 5f orbitals of neptunium together with selected orbitals of oxygen. The vertical excitation energies on the ground state geometries have been computed up to ca. 35 000 cm-1. The gas-phase electronic spectra were evaluated on the basis of the computed Einstein coefficients at 298 K and 3000 K. The computed vertical transition energies show good agreement with previous condensed-phase results on NpO2+ and NpO22+. [ABSTRACT FROM AUTHOR]

The electronic spectra of neutral NpO and NpO2 as well as of their mono- (NpO+, NpO2+) and dications (NpO2+, NpO22+) were studied using multiconfigurational relativistic quantum chemical calculations at the complete active space self-consistent field/CASPT2 level of theory taking into account spin-orbit coupling. The active space included 16 orbitals: all the 7s, 6d, and 5f orbitals of neptunium together with selected orbitals of oxygen. The vertical excitation energies on the ground state geometries have been computed up to ca. 35 000 cm-1. The gas-phase electronic spectra were evaluated on the basis of the computed Einstein coefficients at 298 K and 3000 K. The computed vertical transition energies show good agreement with previous condensed-phase results on NpO2+ and NpO22+. [ABSTRACT FROM AUTHOR]

The visible spectrum of H+ is studied using high-sensitivity action spectroscopy in a cryogenic radiofrequency multipole trap. Advances are made to measure the weak ro-vibrational transitions from the lowest rotational states of H+ up to high excitation energies providing visible line intensities and, after normalisation to an infrared calibration line, the corresponding Einstein B coefficients. Ab initio predictions for the Einstein B coefficients are obtained from a highly precise dipole moment surface of H+ and found to be in excellent agreement, even in the region where states have been classified as chaotic. [ABSTRACT FROM AUTHOR]

Coupled lattice Boltzmann and discrete element methods were employed to investigate the rheological properties of oblate spheroid suspensions in a Newtonian fluid. The volume fraction of the particles is varied along with the particle aspect ratio. As the particle shape is varied from sphere to oblate, we observe an increase in the relative viscosity as well as an increase in the particle contacts and the contact distance. The more oblate particles in denser suspensions are observed to reorient systematically subject to the shear flow. We recast the viscosity data using the Krieger–Dougherty formula and report the modified Einstein coefficients. [ABSTRACT FROM AUTHOR]

The aggregate in an asphalt mixture is coated with mastic consisting of bitumen (dilute phase) and filler (particulates phase). The interaction of bitumen and filler and packing of filler plays an important role in the properties of mastics. The micromechanics models from composite rheology can be used to predict the stiffening effect of a suspension. In this research, the stiffening effect of fillers was investigated based on the rheology of mastic. The frequency sweep tests in a dynamic shear rheometer at different temperatures were performed within a linear viscoelastic range to construct the master curves. The volume fractions were expressed as compositional volumes of filler in mastic. The particle shape and surface texture are determined through microscopy. We used six micromechanics-based models to predict the stiffening potential of fillers in mastics. The models include Maron–Pierce, Lewis Nielsen, Mooney, Krieger–Dougherty, Chong, Robinson, and Hashin Models. The results show that the same volume content of filler has a different effective volume. The fillers increase the stiffening effect of the composite, especially at high temperatures. The behaviour of fillers with similar effective volume and packing is identical. The filler type affects the stiffening of mastics. Micromechanics modelling results show that most models show an accurate stiffening effect at lower concentrations with the exception of the Chong Model. The Maron–Pierce Model under-estimates the stiffening potential for granite mastic at higher concentrations beyond the 30% filler content fraction. The value of maximum packing fraction (ϕm) and Einstien coefficient (KE) in the Mooney model are significantly different from other models for limestone and granite, respectively. The line of equality graph shows good agreement of measured and predicted stiffness. It is difficult to precisely model the mastic data with any single model due to the presence of complex stiffening effects beyond volume filling. [ABSTRACT FROM AUTHOR]

Spectropolarimetric measurements of gamma-ray burst (GRB) optical afterglows contain polarization information for both continuum and absorption lines. Based on the Zeeman effect, an absorption line in a strong magnetic field is polarized and split into a triplet. In this paper, we solve the polarization radiative transfer equations of the absorption lines, and obtain the degree of linear polarization of the absorption lines as a function of the optical depth. In order to effectively measure the degree of linear polarization for the absorption lines, a magnetic field strength of at least 103 G is required. The metal elements that produce the polarized absorption lines should be sufficiently abundant and have large oscillation strengths or Einstein absorption coefficients. We encourage both polarization measurements and high-dispersion observations of the absorption lines in order to detect the triplet structure in early GRB optical afterglows. [ABSTRACT FROM AUTHOR]