Correlation effects in the theory of combined doppler and pressure broadening—I. Classical theory

A classical Fourier amplitude theory of combined Doppler and pressure broadening in the impact approximation is developed which treats phase changes changes due ti translation and collision on an equal basis. Radiator motion is accounted for properly by including speed dependence in the collision frequency and velocity dependence in the distribution function for phase shifts and final velocities as the result of a collision. The resulting theory is shown to be equivalent to a previous kinetic equation formulation of the problem. The one-perturber and classical analogue of the quantum one-interacting-level approximations are derived. In the latter case, a simple expression for the line shape in terms of speed dependent width and shift functions is obtained without approximation. Correlation effects are investigated by means of model speed dependent width and shift functions calculated for an inverse power interaction using straight line trajectories. The model shows no departure from a Voigt profile for the r^-3 interaction and for the r^-6 and r^-12 interactions the resulting profile is narrower in the core than the Voigt and in general asymmetric. Analysis of correlated profiles as Voigt profiles is shown under some conditions to lead to non-linear density dependence in the width and shifts resulting in extra- polation anomalies and to significant errors in temperatures inferred from Doppler widths. Results are compared with previous work.     

Intensities and widths of H2O lines between 1800 and 2100 cm-1

A non-linear, least-squares program was used to obtain the line intensities and widths of 91 air-broadened lines in the ν₂ rotation-vibration band of water vapor in the region from 1800 to 2100 cm^-1. The values obtained for the line intensities are, on the average, about 7% stronger than the Air Force Cambridge Research Laboratories (AFCRL) Atmospheric Absorption Line Parameters Compilation. The experimental values for the half widths of the H₂O lines are, on the average, 4% higher than the calculated AFCRL values. The measurements have confirmed the narrow widths of some high J transition lines measured by tunable diode laser spectroscopy.     

Ar+17和 Ar+16谱线的电子碰撞展宽

利用修改后伦敦理工大学的UCL扭曲波程序, 本文计算了自由电子与原子或离子的碰撞反应矩阵, 以此得到它的散射矩阵和碰撞强度.利用碰撞强度, 研究电子碰撞对辐射谱线影响.具体地, 以Ar⁺¹⁷和Ar⁺¹⁶的α线和β线为例, 计算了不同电子温度和密度下谱线的展宽和位移.     

Stark shift of the CI 2479 Å spectral line of carbon

The Stark shift of the CI 2479 Å emission line of atomic carbon is measured in a broad range of electron densities between ~6 × 10¹⁶ and ~4 × 10¹⁸ cm^–3. It is established that the shift is linear and its value is significantly lower than that predicted by theory. The line shape is found to be dominated by the Stark effect at Т = 32 kK and electron concentration N _e ≈ 3.9 × 10¹⁸ cm^–3. The electron-impact and ion widths of this contour are in good agreement with the Grim data, while its total shift to longer wavelengths is found to be half that calculated theoretically.     

Strengths and air-broadened widths of H2O lines in the 2950–3400 cm-1 region

Measurements of the strengths and air-broadened widths of 223 lines of water vapor have been made with high resolution in the region 2950–3400 cm^-1. The strength data of the lines in the 2ν₂ and ν₁ bands are analyzed to determine the band strengths and the coefficients of the F factors. The band strengths of the 2ν₂ and ν₁ bands were found to be 1.75±0.08 and 10.3±1.1 cm^-2 atm^-1 at 296 K, respectively. The selection rules of the lines observed in the ν₃ band are forbidden in the symmetric-rotor limit. The majority of the measured strengths of these lines differ from the calculated values because of different asymmetries in the upper and lower vibrational states. Also, Coriolis perturbations in several lines of the ν₁ and ν₃ bands were observed in the strength measurements. The direct method was applied to determine the air-broadened line widths. The results are compared to the computed values of Benedict and Kaplan. There is good agreement between this work and the computed results for line width values greater than 0.05 cm^-1 atm^-1. However, for line widths less than 0.05 cm^-1 atm^-1, the measured values are smaller than the computed widths. A value of 0.018 cm^-1 atm^-1 is given for the width of the line at 3378.071 cm^-1, whereas the calculated value is 0.032 cm^-1 atm.     

Chemical shifts in strontium compounds by X-ray spectroscopy

The positions of the X-ray K-absorption edge of strontium in various compounds and in aqueous solutions have been measured. With the help of modified Moseley diagram the wavelength of the X-ray K-absorption edge of Strontium in metal has been extrapolated. Chemical shifts of the K-absorption edge with respect to this extrapolated value have been presented. The fine structure has been observed on the high energy side of the main absorption edge both in Rubidium and Strontium compounds. Bond lengths for various compounds have been calculated from the maxima-minima separations. The chemical shifts of fluorescence Kα_1,2 lines with respect to their position in Sr²⁺ ion have also been studied. While the edge shift with respect to the edge in free ion is towards the low energy side, the line shift with respect to the line in free ion is towards the high energy side.     

Water absorption line, 931–961 nm: selected intensities,N2-collision-broadening coefficients,self-broadening coefficients,and pressure shifts in air

Intensities were measured for 97 lines of H₂O vapor between 932 and 961 nm. The lines were selected for their potential usefulness for remote laser measurements of H₂O vapor in the earth's atmosphere. The spectra were obtained with several different H₂O vapor abundances and N₂ broadening gas pressure; the spectral resolution was 0.046 cm^?1 FWHM. Measured H₂O line intensities range from 7 × 10^?25 to 7 × 10^?22 cm^?1/molecules/cm². H₂O self-broadening coefficients were measured for 13 of these strongest lines; the mean value was 0.5 cm^?1/atm. N₂-collision-broadening coefficients were measured for 73 lines, and the average was 0.11 cm^?1/atm HWHM. Pressure shifts in air were determined for a sample of six lines between 948 and 950 nm; these lines shift to lower frequency by an amount comparable to 0.1 of the collision-broadened widths measured in air or N₂. The measured intensities of mainly lines of the 300-000 band are much larger than expected from prior computations, in some cases by over ab order if magnitude. Coriolis interactions with the stronger 201-000 band appear to be the primary cause of the enhancement of these line intensities.     

Line shift and mixing in the ν4 and 2ν2 band of NH3 perturbed by H2 and Ar

Pressure induced line shift and line mixing parameters have been measured for 66 rovibrational lines in the ν₄ band and for 10 lines in the 2ν₂ band of NH₃ perturbed by H₂ and Ar at room temperature (T = 296 K). These lines with J values ranging from 2 to 10 are located in the spectral range 1450-1600 cm⁻¹. Experiments were made with a high-resolution Fourier transform spectrometer. The line shifts and line mixing parameters have been derived from the non-linear least-square multi-pressure fitting technique. The shift coefficients are compared with those calculated from the Robert-Bonamy formalism (RB). The results are generally in satisfactory agreement with the experimental data.     

可见光谱区水汽分子碰撞加宽的理论计算

根据能级的实验数据,采用最小二乘法拟合得到水汽分子(202),(122)和(004)振动态的Watson的Hamiltonian常数值。利用这些常数值和修正的量子傅里叶变换(QFT)(即QFT^*)方法,分别计算了水汽分子(202)带中已有实验数据的一些谱线的氮分子碰撞加宽线宽,以及(202),(122)和(004)带^eR(1,1)支谱线的氮分子碰撞加宽线宽、及线宽的温度依赖关系。与实验结果比较表明,利用拟合方法求得的Hamiltonian常数值是合理的,而且QF 关键词：     

Pressure broadening by argon in the hyperfine resolved P(10) and P(70) (17,1) transitions of I2 XΣ(0g)→BΠ(0u) using sub-Doppler laser saturation spectroscopy

The dependence of pressure broadening upon hyperfine component in the P(10) and P(70) lines of the (17,1) band of the I₂ X¹Σ(0_g⁺)→B³Π(0_u⁺) has been studied using laser saturation spectroscopy. By limiting absorption to the zero velocity group, Doppler broadening is removed, lineshapes with widths (FWHM) <9 MHz are detectable, and collision-induced broadening is measured at pressures of 0.2-1.2 Torr. The rates for broadening by argon are 8.3±0.3 and 10.7±0.4 MHz/Torr for the P(70) and P(10) lines, respectively. No significant variation in broadening rates is observed for the 15 hyperfine components of these even rotational lines. The effects of velocity cross-relaxation introduce a broad baseline into the spectra, which is strongly dependent on rotational state, pressure, and laser modulation frequency. The observed broadening rates correlate well with prior measurements and the polarizability of the collision partner.     

Low rotational transitions of the CF3H molecule: The pressure-induced shift and broadening

Using a microwave spectrometer with a radioacoustic signal detection, the absorption profiles in the multiplets of the low rotational transitions J’?J = 2?1, 3?2, 4?3, and 5?4 of the ¹²CF₃H molecule in the ground vibrational state at pressures of pure gaseous CF₃H from 0.1 to 1.3 Torr when all the K components of the multiplets merge into a single spectral line are studied. The parameters of the pressure-induced shift and broadening of the observed lines are determined by comparing the theoretically modeled absorption signal and the experimental spectrum. The model used takes into account weak lines corresponding to the excited vibrational states v₃ and v₆ of the ¹³CHF₃ molecule and the instrumental features of the spectrometer. The observed multiplet is simulated as an isolated Lorentzian line and as a sum of the profiles of the K components with known unshifted positions and known amplitude ratio. The shift and broadening parameters obtained in both cases are shown to agree well with each other. The dependences of the shift and broadening parameters on the quantum number J are analyzed and compared with the previously obtained data for the lines J’?J = 1?0 and 2?1.     

Broadening and shift of lines of the ν<Subscript>2</Subscript> + ν<Subscript>3</Subscript> band of water vapor induced by helium pressure

The broadening and shift coefficients of more than 100 absorption lines of the ν₂ + ν₃ band of water vapor that are induced by the pressure of helium are measured and calculated. The broadening and shift coefficients are obtained from analysis of the room-temperature absorption spectra of an H₂O-He mixture measured with a resolution of 0.007 cm^?1 on a Fourier spectrometer in a large range of helium pressures. The specific features in the rotational dependence of the line center shifts are determined, which, in contrast to the broadening induced by other gases, are mainly positive. The calculated coefficients of the line broadening and shift of line centers are determined by a semiclassical method. An unusual dependence of the shift coefficients is explained by the rotational dependence of the intermolecular isotropic interaction potential.     

Line parameters and shapes of high clusters: R branch of the ν3 band of CH4 in He mixtures

The IR absorption spectra of CH₄ in pure gas and in mixture with helium were studied in the region of ν₃ band at higher J line clusters R(17)-R(22). The frequencies and intensities of rotation-vibration lines were estimated from the experimental spectra at Doppler shape conditions. The line frequencies and intensities were calculated and used for the attribution of overlapped lines in clusters. The calculated line intensities are close to the experimental values. The calculated frequency structure of the higher J manifolds are somewhat wider than the observed one. The shapes of helium-broadened line clusters were compared with those calculated accounting for line mixing. The relaxation matrix W, which is necessary in shape calculations, was constructed using semiclassical collision rate constants. The calculated shapes are in satisfactory accordance with the measured ones.     

在等离子体中镁离子谱线MgⅡλ4481?的宽度和位移

本工作测量了MgIIλ4481?(3²D—4²F)在电子数密度为7×10¹⁶—3.1×10¹⁷电子数/cm³范围内的谱线轮廓和位移。采用振荡型电容放电作为光谱光源。在光源中引入水汽,由测量H_β谱线宽度来定电子数密度。观测结果指出,H_β的实验轮廓和Griem-Kolb-Shen的计算结果符合颇好。实验发现MgIIλ4481?谱线向紫方位移,并正比于微观电场的平方;由此定出一个经验上的二级斯塔克效应常数C₄=5.0×10^-14cm⁴/sec。该谱线的轮廓宽度和标准微观电场之间也有平方正比的关系。发现在本实验条件范围内,宽度和位移的比值γ/△保持为常数,其值为γ/△=10.4±0.6。由于谱项4²D的二级斯塔克效应的干扰而产生上能级4²F位移的理论计算虽能说明谱线位移和微观电场间的平方正比关系,但数值偏小于实验结果,指出还有电子贡献的部分。把光谱线的宽度和Lindholm理论公式及Griem等的近似公式作了比较;简单的估计指出,实验结果和后者符合较好。     

Line shifts in the ν2, 2ν2, and ν4 bands of NH3 perturbed by O2

Pressure-induced line shift coefficients have been measured for more than 200 rovibrational lines of NH₃ perturbed by O₂ at room temperature (T = 295 K) in some branches of the ν₂, 2ν₂, and ν₄ bands. These lines with J values ranging from 1 to 13 are located in the spectral range 800-1800 cm⁻¹. Experiments were made with a high-resolution Fourier transform spectrometer. The treatment of vibration-rotation lines includes interference effects caused by the overlapping of lines. The O₂ pressure-induced shift coefficients have been derived from the non-linear least-squares multi-pressure fitting technique. The results illustrate a vibrational dependence of line shifts with vibrational quantum number. Most of the measured shifts are negative in the ν₄ band. They are positive for the ν₂ and 2ν₂ bands. The measured shift coefficients are compared with previous measurements and with those calculated from a semiclassical theory based upon the Robert-Bonamy formalism extended to the case of symmetric top molecule with inversion motion. The predictions are generally in satisfactory agreement with the experimental data. Analyses of measured and predicted results illustrate that these shifts mainly originate from the isotropic part of the intermolecular potential.     

Predissociation of the Schumann-Runge bands of O2

The predissociation line broadening in the Schumann-Runge bands of O₂ is interpreted through an ab initio calculation of the pertinent repulsive potential energy curves and spin-orbit matrix elements. The ab initio results provide an overall qualitative picture of the predissociation which is further refined through a detailed comparison of calculated level shifts and widths with experimental data. The position of the dominant repulsive curve is also deduced by a deperturbation of the level shift in the second vibrational difference. The predissociation is dominated by the ⁵Π_u state crossing the $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ state around 1.875 Å with a spin-orbit matrix element of 65 cm^?1. The ¹Π_u and ³Π_u states have small spin-orbit matrix elements and play only minor roles in the predissociation. The calculated and experimental widths are in good agreement for low and high vibrational levels. The apparent experimental widths between v = 5 and 11 are shown to be inconsistent with the theoretical analysis, the difference probably being due to line blending.     

Shift measurements of Hα and Hβ lines in arc plasmas

Red shifts are reported for the H_α and H_β lines at electron densities of 10¹⁶–10¹⁷ cm^-3. The peak shift of the H_α line agrees with the ELC shift. For the H_β line, the dip shift exceeds the ELC shift systematically. The H_β dip shift is proportional to N_e/T.     

A line parameter list for the ν2 and ν4 bands of 12CH4 and 13CH4, extended to J′ = 25 and its application to planetary atmospheres

Line parameters (transition frequencies, line strengths, line widths, ground state energies and quantum identifications) for the ν₂ and ν₄ bands of ¹²CH₄ and ¹³CH₄ have been calculated for J'?25 using the simultaneous coupled fitting procedure of Gray and Robiette. Molecular constants for the ν₂ band of ¹³CH₄ were estimated from isotopic shifts from ¹²CH₄ values. Agreement with laboratory spectra, where available, is always well within 1 cm^-1 over the entire spectral range covered by the list. The most serious problem in comparison with laboratory data is the omission of lines belonging to “hot” bands in this spectral region. This list is valuable in remote sensing problems for sorting out lines of trace species from weak methane lines and for determining the atmospheric opacity in relatively transparent spectral regions. Applications of the parameter list are demonstrated for remote sounding of the Jovian atmosphere. The list is available on magnetic tape from the authors.     

CO2-broadened water in the pure rotation and ν2 fundamental regions

The CO₂-broadened water coefficients (half-widths, line shifts, and temperature dependence of the widths) are predicted using a fully complex Robert-Bonamy formulation for the 937 allowed and forbidden perpendicular type transitions of (000)-(000) between 200 and 900 cm⁻¹ in order to facilitate atmospheric remote sensing of Mars and Venus. In addition, empirical Lorentz line widths and pressure-induced frequency-shifts of CO₂-broadened H₂¹⁶O are obtained at room temperature for 257 perpendicular transitions of the (010)-(000) fundamental. For this, calibrated spectra recorded at 0.0054 cm⁻¹ resolution are measured assuming Voigt line shapes. For transitions between 1287 and 1988 cm⁻¹ with rotational quanta up to J = 13 and K_a = 6, the widths vary from 0.045 to 0.212 cm⁻¹ atm⁻¹ at 300 K; the pressure-shifts are quite large and range from −0.0386 to +0.0436 cm⁻¹ atm⁻¹. For the (010)-(000) band, the RMS and mean observed and calculated differences for CO₂-broadened H₂O half-widths are 12% and −1.9%, respectively, while the RMS and mean ratios of the observed and calculated pressure-induced shift coefficients are 1.6 and 0.79, respectively. For pairs of transitions involving K_a = 0 and 1, such as 2_0 2 ← 3_1 3 and 3_1 3 ← 2_0 2, both the calculated and observed pressure induced shifts in positions are opposite in sign and often similar in magnitude. The data are too limited to characterize vibrational dependencies of the widths, however.     

Stark-Effekt-Verbreiterung der Neon I-Übergänge mit schwacher Feldstärkeabhängigkeit (2p 5 3s-2p 5 3p)

The half widths of Stark-broadened Ne I spectral lines (2p ⁵ 3s-2p ⁵ 3p) were measured in wall stabilized arc plasmas (pressurep=1 atm, andp=3 atm) consisting of several gas components (Ar 68%, Ne 27%, He 3%, H₂ 2%). The theoretical half widths of two spectral lines (λ=6,266.50 Å,λ=6,163.59 Å) with known calculated broadening parameters according to Griem differ by a factor 1.8 to 1.9 from the measured widths. Within the errors of Griem's line broadening calculations of about 20% there was agreement between experimental and theoretical half widths regarding two other spectral lines (λ=5,881.90 Å,λ=5,852.49 Å). Calculated adiabatic widths are smaller than the widths according to Griem. Therefore in some cases the deviation of the adiabatic widths from the measured widths is smaller than the difference between Griem widths and experimental ones. Static quadratic coefficients of NeI transitions 2p ⁵ 3s-2p ⁵ 3p calculated from measured Stark-broadened lines showed wavelength displacements in the order of 0.005 Å referring to an electrical field of 100 kV/cm. The determined coefficients are 10² times smaller than those values measurable by known methods of emission spectroscopy.