Lorentzian Width Research Articles

Vibrational mode mixing in terminal acetylenes: High-resolution infrared laser study of isolated J states

Mode–mode vibrational coupling in the acetylinic CH stretch at 3330 cm−1 of 1-butyne and 1-pentyne is studied via high-resolution, direct absorption infrared spectroscopy. As in our previous study of propyne, mixing of the CH stretch vibration carrying oscillator strength (the bright state) with the bath of multiquantum combination states (the dark, or background, states) manifests itself in the spectrum via fragmentation of the isolated bright state transitions into clusters of closely spaced spectral lines in a ∼0.01 cm−1 window about the zeroth order acetylinic CH stretch position. In the 1-butyne spectrum, we find an experimental density of mixed states of 114±30 states/cm−1 compared to a direct state count prediction of 90 total states/cm−1, and thus quantitatively determine that all possible states appear in the spectrum. The 1-butyne line spacing distribution suggests the Wigner distribution expected for a quantum mechanically ergodic system. Analysis of the mode mixing as a function of J′ shows that anharmonic terms in the potential, rather than Coriolis effects, contribute most strongly to the coupling. The acetylinic CH stretch spectrum of 1-pentyne (2400 states/cm−1) reveals only broad rovibrational transitions with ∼0.01 cm−1 Lorentzian width, even at our 10−4 cm−1 resolution. J′ independent, anharmonic coupling with a minimum of 1/3 of all states must be invoked to reproduce the observed broadening. In contrast, the 1-pentype methyl CH stretch spectrum shows broadening greater than five times larger than that observed at the acetylinic end. Via Fourier transform methods, the spectra for both 1-butyne and 1-pentyne indicate vibrational energy localization in the CH stretch for ∼500 ps. However, for the methyl CH stretch, energy redistribution takes place in <40 ps, clearly indicating the presence of mode specific, nonRRKM vibrational relaxation pathways.

Classical theory for real-time femtosecond probing of the NaI* photodissociation

Femtosecond pump-probe experiments [Rosker et al., Chem. Phys. Lett. 146, 175 (1988)] on the dissociation of NaI* are modelled classically to obtain the absorption transients as a function of the pump and probe wavelengths. The initial ground state, the optically pumped predissociating state, and the third surface that is coupled by the probe pulse are explicitly included. The classical model can almost quantitatively explain all the features of the experimental results. The oscillations in the transients are shown to be due to molecules trapped in the adiabatic well, with most of the intensity coming from the covalent region of the well before the crossing point rx. The rising troughs in the transients are due to successive leaks out of the well into the covalent region after the crossing point rx, leading to dissociation. The difference in the absorption transient between on-resonance 589 nm probing as compared to off-resonance 612 nm and 580 nm probing is shown to arise from the difference in Lorentzian absorption widths between the trapped (500 cm−1) and dissociating (100 cm−1) covalent molecules, with the transition dipole moment to the third surface having about the same magnitude over the range of the covalent potential.

Measurements of argon broadened Lorentz width and pressure-induced line shift coefficients in the ν_4 band of ^12CH_4

Room temperature argon broadened halfwidth and pressure-induced line shift coefficients have been determined for 118 transitions in the nu(4) band of (12)CH(4) from analysis of high resolution laboratory absorption spectra recorded with the McMath Fourier transform spectrometer operated on Kitt Peak by the National Solar Observatory. Transitions up to J''= 12 have been measured using a nonlinear least-squares spectral fitting procedure. The variation of the measured halfwidth coefficients with symmetry type and rotational quantum number is very similar to that measured previously for N(2) and air broadening, but the absolute values of the argon broadening coefficients are all smaller. On average, the ratio of the argon broadened halfwidth coefficient to the corresponding N(2) broadened halfwidth coefficient is 0.877 +/- 0.017 (2sigma). More than 95% of the pressure-induced shifts are negative with values ranging from -0.0081 to +0.0055 cm(-1) atm(-1). The pressure shifts in argon are nearly equal to corresponding values measured previously in N(2) and air.

Doppler-free laser-induced fluorescence of oxygen atoms in an atmospheric-pressure flame

Doppler-free laser-induced fluorescence of oxygen atoms has been measured in the burnt gases of an atmospheric-pressure flame, where the Doppler and collisional widths are similar. The 3p(3)P level was excited using counterpropagating beams at 226 nm. Upper-state fine-structure splitting could be partially resolved, and a collisionally broadened Lorentzian width of 0.42 cm(-1) was measured. This corresponds to a broadening cross section of 10(-13) cm(2), which is larger than that expected for collisional quenching alone.

Hilbert-space formulation of Feshbach-Fano methods for atomic and molecular photoionization: Optimal choice of zeroth-order states in shape-resonance channels

An explicit Hilbert-space formulation is provided of Feshbach-Fano methods for ionization continua employing a novel zeroth-order state particularly well suited to shape-resonance profiles. The resulting photoionization cross sections are of Lorentzian form, with shifts and widths that are generally slowly varying functions of the energy. Fano q and ϱ parameters are avoided entirely in the development. Applications to a model problem having broad and narrow shape resonances indicate that precise crosssectional values can be obtained in this way from Stieltjes calculations employing L 2 pseudo spectra that have energy spacings considerably greater than the resonance width. The advantages of the zeroth-order state introduced here in applications to molecular ionization continua are also indicated.

Spectral hole burning in the inhomogeneous ν 3 absorption profile in CH 3F isolated in mixed Ar:Kr matrices

Using two diode lasers, homogeneous spectral holes are burned and recorded in the inhomogeneous ν 3 absorption profile of CH 3F isolated in mixed Ar:Kr matrices. The Lorentzian hole width, fwhm, is (9.1±0.5) × 10 −3 cm −1 at 5 K and narrows to (5.6±1) × 10 −3 cm −1 at 9.35 K. The hole refilling time at 5 K is ≈ 10 s. The hole width is ascribed to dephasing by localized librational modes, the refilling to thermal reorientation of the molecule in the trap site.

Universal functions for estimating total vibration-rotation band absorptance—III. asymmetric tops

The method of universal functions (MUF) for estimating total band absorptances and their derivatives, for nonoverlapping lines of vibration-rotation bands of linear molecules and spherical and symmetric tops, 1,2 is extended to asymmetric top bands. The universal functions for symmetric tops are employed. The accuracy of MUF is within a few percent for the 010-000 and 001-000 bands of H 2O and O 3 and Lorentz line shapes at temperatures of 175–325 K. A simple technique for obtaining an effective Lorentz width for all of the band lines is proposed for application to MUF.

Shakeup in soft-x-ray emission. II. Plasmon satellites and x-ray photoemission spectroscopy.

We report the first observation of a plasmon satellite in the K emission spectrum of diamond. The previously identified plasmon satellites of Al and graphite are also presented, and data is compared with an oscillator model applicable to soft-x-ray emission and photoemission. The graphite satellite is shown to exhibit an anomalous location with respect to the parent emission. We report for the Al ${L}_{\mathrm{I}}$-${L}_{\mathrm{I}\mathrm{I},\mathrm{I}\mathrm{I}\mathrm{I}}$ core-core transitions a spin-orbit splitting of 0.42\ifmmode\pm\else\textpm\fi{}0.02 eV with a Lorentzian width of 0.67\ifmmode\pm\else\textpm\fi{}0.02 eV. The oscillator model applied to x-ray photoemission predicts a shift of the plasmon satellite with respect to the zero loss line as the final-electron kinetic energy is varied.

Measurements of air-broadened and nitrogen-broadened Lorentz width coefficients and pressure shift coefficients in the ν_4 and ν_2 bands of 12CH_4

Air-broadened and N(2)-broadened halfwidth and pressure shift coefficients of 294 transitions in the nu(4) and nu(2) bands of (12)CH(4) have been measured from laboratory absorption spectra recorded at room temperature with the Fourier transform spectrometer in the McMath solar telescope facility of the National Solar Observatory. Total pressures of up to 551 Torr were employed with absorption paths of 5-150 cm, CH(4) volume mixing ratios of 2.6% or less, and resolutions of 0.005 and 0.01 cm(-1). A nonlinear least-squares spectral fitting technique has been utilized in the analysis of the twenty-five measured spectra. Lines up to J' = 18 in the nu(4) band and J' = 15 in the nu(2) band have been analyzed.

Spin fluctuation in an Fe65Ni35 Invar alloy

The spin-spin correlation function I(q,t) has been measured on a polycrystalline sample of Fe65Ni35 above the Curie temperature by means of neutron spin-echo spectroscopy. The results are interpreted in terms of multiple Lorentzian energy widths ħTq, that are characteristic of this magnetically inhomogeneous system.

N-shell core-level widths for the elements 74W to 83Bi.

The Lorentzian lifetime widths of the 4d and 4f levels in the sixth-period elements W74 to Bi83 have been measured using photoelectron spectroscopy. A compilation of 4f-level widths from the literature is also made. The general trend of the 4f-level widths is well reproduced by McGuires calculations, although the absolute widths seem to be underestimated. The 4d5/2-level width shows a remarkable constancy over the whole series of elements and it varies only between 3.6 and 4.0 eV for all the investigated elements. The determined 4d level widths are well reproduced by recent calculations by Ohno and Wendin. Special attention has been paid to lifetime broadenings which are characteristic for the solid phase. Such broadenings are observed for the 4d3/2 level due to N4N5O45 Coster-Kronig processes. In the 4f shell a small Coster-Kronig broadening is also observed in the beginning of the series. © 1987 The American Physical Society. (Less)

Rietveld refinement of Debye–Scherrer synchrotron X-ray data from Al2O3

The application of the Rietveld refinement technique to synchrotron X-ray data collected from a capillary sample of Al2O3 in Debye–Scherrer geometry is described. The data were obtained at the Cornell High Energy Synchrotron Source (CHESS) with an Si(111) double-crystal monochromator and a Ge(111) crystal analyzer. Fits to a number of well resolved individual peaks demonstrate that the peak shapes are very well described by the pseudo-Voigt function, which is a simple approximation to the convolution of Gaussian and Lorentzian functions. The variation of the Gaussian and Lorentzian half widths, ΓG and ΓL, with Bragg angle can be approximated quite closely by the functions V tan θ and X/cos θ which represent the contributions from instrumental resolution and particle-size broadening respectively. Rietveld refinement based on this model yields generally satisfactory results. The refined values of V and X are consistent with the expected vertical divergence (≃0.1 mrad) and the nominal particle size (≃ 0.3μm). In particular, the use of a capillary specimen virtually eliminates preferred orientation effects, which are highly significant in flat-plate samples of this material.

Measurement of the broadening and asymmetry of the calcium resonance line (422.7 nm)

The broadening parameters of the calcium resonance line (422.7 nm) perturbed by rare gases have been obtained by laser fluorescence so as to be free of instrumental broadening. The data have been fitted directly to a more sophisticated lineshape which was found to describe the data to a much higher degree of accuracy than the usual Voigt profile. This modified lineshape (the asymmetric speed-dependent Voigt profile ASDVP) includes the effect of finite collision time and of correlations between pressure broadening and emitter speed. The values obtained for broadening by the rare gases He, Ne, Ar, Kr and Xe are as follows: 24.4, 14.9, 27.8, 28.9 and 33.7*10-24 mK m3 (full Lorentzian widths). The collision time asymmetry parameter, b, has also been measured for each of these gases, and the following values obtained: +1.04, +0.3, -0.7, -1.35 and -2.24*10-4 mK-1. A negative value indicates greater intensity in the red wing.

?=2537 � line from a low-pressure mercury discharge lamp emission profile and line absorption by a gas containing a mercury vapor

By measuring the emission-line intensity of Hgi λ=2537 A (63 P→61 S) from a low-pressure mercurcury lamp, we have determined the dependence of the upper-level population on the discharge current and the mercury vapor density. From the radial profile of the intensity the spatial distribution function of the population has been determined to be the zero-th order decay mode for the trapped radiation. Line absorption by mercury vapor in a cell has been measured with various mercury densities and Lorentzian widths. The results are consistent with the upper-level population distribution as determined above. On the basis of these findings we calculate the emission-line profile and its change during the absorption in the absorption cell. The amount of absorption at an arbitrary depth of the absorption cell is calculated, and the optimum cold-spot temperature of the lamp of 40–50°C is suggested for the maximum absorption under the typical condition of the photo-CVD experiment.

The lineshapes of infrared-microwave two-photon transitions in the ν2 band of 15NH3

Abstract The lineshapes of the ssR (4, 2), ssQ (6, 4), and aaP (2, 1) transitions in the ν 2 band of 15 NH 3 were recorded at several pressures by means of a computer-coupled infrared laser microwave two-photon spectrometer. The lowest pressure lineshapes were Gaussian to high precision with Doppler widths within 0.1% of the calculated values. Plots of Lorentz widths vs. pressure obtained by assuming the lineshapes to be Voigt profiles gave negative intercepts. The data were reanalyzed under the assumptions of the soft-collision and hard-collision models of collisional narrowing. The resulting pressure-broadening parameters are 16.6, 18.1, and 16.5 MHz/Torr for the ssR (4, 2), ssQ (6, 4), and aaP (2, 1) transitions, respectively. These values are comparable to pressure-broadening parameters for inversion transitions in the ground state, but they are significantly larger than corresponding values for inversion transitions in the v 2 = 1 state. This comparison is explained as being the result of a larger contribution from adiabatic reorientation and/or phase-changing collisions to the pressure-broadening of the infrared transitions than to the inversion transitions in either state. The limiting low-pressure values of the center frequencies of the transitions are reported and the pressure shifts in the center frequencies are given. Collisional-narrowing parameters for the three transitions are estimated.

低圧水銀灯２５３７Å発光線と水銀蒸気によるその吸収 プロファイルと吸収効率

For Hg I λ2537 Å (63P→61S) line emitted from a low-pressure mercury lamp, we have determined the relative population in the upper level as a function of discharge current and mercury density. From the radial profile of the emission-line intensity, the spatial distribution function of the upper-revel population has been determined to be the zero-th order decay mode for the trapped radiation. Line absorption has been measured by a mercury vapor in a cell with various mercury densities and Lorentzian widths. The results are consistent with the upper-levl-population distribution as determined above. On the basis of these findings we calculate the emission-line profile and its change in the absorption cell. The amount of absorption at an arbitrary depth of the absorption cell is calculated, and the optium cold-spot temperature of the lamp of 40-50°C is suggested for the maximum absorption under the typical condition of the photo-CVD experiment.

Pulling by Neighbouring Transitions and its Effects on the Performance of Caesium-Beam Frequency Standards

Pulling by the wings of neighbouring field-dependent lines is usually taken into account in accuracy evaluation of caesium-beam frequency standards. Its magnitude is commonly calculated from the observed asymmetry of the neighbouring lines using a well-known formula in which the shape of all the Rabi lines is approximated with Lorentzian profiles of the same width.In this paper it is shown that use of these approximations yields in most cases grossly underestimated results for the pulling, and that the real shape of the Rabi wings must be computed in order to match experimental data.Line shapes far from Lorentzian and different widths for the different lines are obtained if the real rf field profile and the actual velocity distributions for each state are used. Unexpectedly high values are found in this way, which indicate this kind of frequency pulling as possibly the biggest single cause of inaccuracy in commercial caesium beams and a bias to be re-evaluated in primary laboratory standards.Theoretical computations show good agreement with experimental data and suggest that the well-known average frequency difference of about +1 × 10-12 which is shown by the ensemble of all short commercial standards with respect to long primary tubes may be traced to Rabi pulling. The effect turns out to be dependent on modulation type and parameters. Dependence on rf power is also studied, which may be the primary cause of temperature sensitivity and flicker noise in short tubes, and the roles of source temperature and beam optics variations in relation to long-term drift are indicated.

Pionic and muonic X-ray measurements on light isotopes

New data on strong interaction effects in the pionic atoms of 3He, 16O, 18O and Cl are presented. Energies and lorentzian widths of the 1s and partly of the 2p levels have been determined from the X-ray spectra. For the first time significant isotope effects could be observed in the 1s level width. Absolute and relative intensities are presented for K and L X-ray transitions respectively trom pionic and muonic spectra. Thus by fitting cascade parameters p-state absorption probabilities could be determined even for the lightest isotopes. The results are compared with those of others and with recent theoretical calculations. The nuclear γ-ray of the transition 5 2 + → 3 2 − in 13C was determined to be 169.356 ± 0.020 keV.

Self-broadening at low densities in the spectrum of neon

Self-broadening of the transitions at 585.2, 659.9 and 667.8 nm in neutral neon has been studied in emission by means of a scanning Fabry-Perot interferometer. These lines all connect to the strong resonance level (2p53s1P1), and the broadening is dominated by the resonance interaction. The source was a weak discharge run at pressures up to 10 Torr and cooled with liquid nitrogen (77K) or melting ice (273K). Data were recorded and analysed digitally; most spectral profiles were found to be well represented by the Voigt function, though evidence of slight profile distortion, attributed to excitation mechanisms, was found for all three lines under certain conditions of temperature and pressure. The Lorentzian widths varied linearly with pressure. All experiments were carried out with the natural mixture of isotopes and a sample enriched in 20Ne and no significant differences in the broadening were observed. When allowance was made for profile distortion the collisional broadening was found to be independent of the spectral line and of the temperature to within experimental error, in accordance with the prediction of theory for the case of pure resonance broadening. The measured broadening constants were 6.13(16) at 77K and 6.19(28) at 273K, to be compared with the theoretical value of 6.28(25), in all units of 10-20 cm-1 cm3 per atom. The Lorentzian width of lambda 585.2 nm extrapolated to zero pressure at 77K was found to exceed the radiation width of the line, in agreement with earlier workers, but only by 0.7(5) mK which is small enough to be attributed to excitation mechanisms. lambda 585.2 nm shows a small shift to longer wavelength with increasing pressure at both temperatures; this is attributed to higher order terms in the interaction potential.

Dynamic screening energy shifts and collision broadening of 2 p → 1s transitions in 2 MeV/amu H- and He-like Ne, Mg and S ions

The spectra of K X-rays emitted by 2 MeV/amu Ne, Mg, and S ions in a thick carbon target were measured with a curved-crystal spectrometer. Energy shifts of the hydrogen-like ion 2 2P→1 2S and the helium-like ion 2 1P→1 1Stransition were determined by means of energy calibrations obtained from thin target spectra, for which X-ray emission occured almost entirely in vacuum. The spectra were fitted with a least-squares program employing Voigt functions to extract accurate peak centroids and, in the thick target cases, Lorentzian widths. The energy shifts were compared to those determined previously for S ions and found to be much smaller than expected on the basis of a dynamic screening model. The Lorentzian widths were found to increase slowly with decreasing projectile Z, and those for the 2P transition were ∼50% smaller than those for the 1P transition.