An experimental study of the collisional broadening of the Na-D lines by Ar and N2 perturbers in flames and vapor cells—II. The line wings

In this paper, we report on measurements of the fluorescence-excitation profile of the red Na-D₁ line wing from about 1 cm^?1 to 1100 cm^?1 and of the blue Na-D₂ line-wing from about 1 cm^?1 to 600 cm^?1, with respect to the corresponding line centre. We have also measured the fluorescence-excitation profile of the red Na-D₂ and blue Na-D₁ inner (overlapping) line wings from 1 cm^?1 with respect to the centre of each of the lines. All these wings were measured in several premixed, laminar, shielded H₂O₂Ar and H₂O₂N₂ flames at 1 atm (1400 K ? T ? 2300 K). We also measured these wings in a vapor cell containing Ar or N₂ perturbers (T ～ 480 K, p ～ 0.4 atm) in order to determine the influence of temperature on these wings. Using a tunable CW dye laser as excitation source, we determined the fluorescence-excitation profiles by measuring the total fluorescence intensity while tuning the laser wavelength. In order to specify the contributions that the different kinds of major flame perturbers (Ar, N₂, H₂O) make to the wings, we compared the wing profiles measured in various flames of different flame-gas compositions. In this comparison, the wing profiles were normalized with respect to the line-centre. We compared our measurements of far red Na-D₁ and blue Na-D₂ line-wings ($\text{Δσ ? 30}\text{cm}{}^{\mathrm{?1}}$) specified to Ar perturbers (at T = 500 K and T = 2000 K) with the results derived from quasi-static theory using available interaction potential data. In the case of Ar perturbers at T = 500 K, we observed a satellite at about 8 cm^?1 from the line-centre on the red Na-D₁ wing: this satellite was absent at T = 2000 K. The position of this red satellite was explained with the help of a set of “modified” potentials, which were constructed for interpreting the collisional Na-D broadening- and shift-rates deduced from our line-core observations and which were reported in Part I of this paper.     

Saturation of sodium fluorescence in a flame irradiated with a pulsed tunable dye laser

Theoretical and experimental saturation curves and associated saturation parameters for the Na-D doublet in an H₂-O₂-Ar flame at 1 atm (T=1700 K) are compared. These parameters are found to agree within the experimental error of 25%. An explanation based on the spatial and temporal distribution of the laser intensity is given for the deviating saturation curves reported by various authors. The shape of the fluorescence pulse is shown to depend on the O₂ concentration in the flame. A lower limit for the rate constant of the doublet mixing transition is estimated from the ratio of the saturated fluorescence intensities of the Na-D components and found to be 3x10⁸s^-1. Conclusions are drawn which restrict the use of saturated atomic fluorescence intensities as a measure for the total atomic number density in the flame.     

Power broadening of the Na-D lines in a flame—I. Time-dependent spectral and spatial properties of a flashlamp pumped dye laser

Prior to power broadening experiments on the Na-D lines in a flame (described in Part II), we investigated the time-dependent spectral and spatial properties of a flashlamp-pumped pulsed dye laser (pulse duration about 800 ns, FWHM), with Rhodamine-6G in methanol as dye liquid and an interference filter combined with a Fabry-Pérot etalon as bandwidth-restricting elements in the cavity. An experimental set-up is described that permits measurements of time-dependent spectra with a time-resolution of 10 ns and a spectral resolution of 2.5 × 10⁵. Results are given for different concentrations of the dye solution and for two different bandwidth settings of the laser. In general the spectral profiles at different moments during the pulse are well described by Gaussian curves. The spatial profiles at different moments during the pulse are best fitted by Lorentzian curves. At small concentrations of the dye solution, the time behaviour of the shift and the bandwidth are in (qualitative) agreement with theoretical predictions, i.e. a narrowing of the bandwidth and a shift to longer wavelengths of the line centre.     

Profil und Äquivalentbreite der Na-D 1-Linie als Funktion von Temperatur und Magnetfeld

Because of the anomalous Zeeman-effect and the Paschen-Back-effect of the hyperfinestructure and theL-S-decoupling, the line profil and also the equivalent width of resonance lines is greatly influenced by an external magnetic field. The decoupling effects in the fine- and the hyperfinestructure of the Na-D ₁-line as an example will be determined quantum-mechanically by a second order perturbation, and it will be shown, how the line contour and the equivalent width are varied by temperature, magnetic induction and optical depth. There are certain regions of temperature and optical depth, where the hyperfinestructure may be accounted for approximately by the so called method of quadratic momentum.     

Wing profile measurements of the Na-doublet lines in C2H2/O2/N2, H2/O2/N2 and H2/O2/Ar frames at 1 atm

Fluorescence-excitation (wing) profiles of the Na-D doublet lines were measured over a wavelength range extending from 0.3 to 200 Å from the line center for the red D₁ and blue D₂ wings and from 0.3 to 3 Å for the red D₂ and the blue D₁ wings, respectively. The line profiles were determined with the aid of a tunable CW dye-laser as a background source by measuring the total fluorescence intensity observed on detuning the laser wavelength. The flames were premixed, laminar, shielded flames at 1 atm, with temperatures ranging from 1860 to 2270 K; N₂ and Ar served as diluent gases. The line core and near-wing profiles (i.e. the region covering 0.3<Δλ<7 Å for the outer wings and 0.3<Δλ<3 Å for the inner ones) in all of the flames studied appeared to have the same frequency dependence, regardless of the nature and concentrations of the gases used. The blue D₂-line profile followed an unexpected (-2.2) law, while the other three profiles obeyed the theoretically expected (-2) law (the dispersion profile function). The line profile in the Δλ range between the impact and quasistatic regions was found to depend on the main perturbers involved. We found that the far blue D₂- and red D₁-wings in the Ar-diluted H₂/O₂ flame obeyed the (-$\text{5}\text{4}$) and (-$\text{3}\text{2}$) laws, respectively, as predicted by the quasi-static theory for the Lennard-Jones interaction. For the N₂-diluted C₂H₂/O₂ and H₂/O₂ flames, we did not find these wing dependences in the Δλ range investigated.     

Single-mode optical pumping and superradiant emission in D2O and CH3F

Superradiant FIR emission in both D₂O and CH₃F has been investigated using a tunable single-mode CO₂ TEA laser as optical pump, and results compared with multimode pumping. The frequency offset of the absorbing transitions has been measured and compared to other work. Estimates of the dipole transition moments were also obtained from saturation broadening data. Fine structure of the CH₃F (Q12, K) lines have been resolved and compared with theory. High quantum conversion efficiencies were observed for several lines in D₂O: 38% (99 μm), 20% (385 μm) and 12.5% (121 μm) and in CH₃F 21% (496 μm).     

The far-wing broadening of the Na D lines by K,Rb and Cs and the electrostatic interaction potentials of the NaK,NaRb and NaCs molecules

The far wings of the NaD lines broadened by K, Rb and Cs have been measured in absorption by scanning a single-mode dye laser across the lines and detecting the flourescence signal. The relative absorption coefficients for the NaRb and NaCs are normalized using the impact widths recently measured by Kamke et al. The found red asymmetries of the lines are surprising results when only the theoretical van der Waals interactions are taken into account. It is demonstrated that the addition of dipole-quadrupole forces is necessary to explain the experimental findings. Using the extended electrostatic interaction potentials the theoretical impact widths of the NaD lines by Rb were found to be in agreement with the experimental data of Kamke et al.     

Energy Transfer in an Optically Pumped D<Subscript>2</Subscript>O Gas THz Laser

We report on the mid-infrared (MIR) and terahertz (THz) wave spectra of D₂O gas pumped using a fundamental transverse mode transversely excited atmospheric CO₂ laser with an emission wavelength of 9.26 μm. We obtain MIR emission lines at center wavelengths of 9.262, 9.491, and 9.752 μm, which correspond to the vibrational-energy-level-transition lines of D₂O. We observe an intense THz stimulated Raman emission line of 385 μm and a weak cascade-transition line of 359 μm for transitions from rotational levels 4₂₂ to 4₁₃ and 4₁₃ to 4₀₄ in the first-excited vibration state of the D₂O molecule gas. We establish a four-energy-level system for modeling the laser kinetics of the dual-wavelength (385 and 359 μm) superradiation THz laser. For the optically pumped D₂O gas 385 μm THz laser, in considering the cavity effect and insertion loss of a THz cavity oscillator, an approximation treatment of the THz laser kinetics can be made based on a three-energy-level system.     

From free fields to AdS: The case of particles with spin

It is shown that one-loop diagrams with three external lines in the usual conformal field theory in D dimensions are equal to a finite sum of tree diagrams with one vertex in theory with the AdS _{D + 1} metric. Some terms of the dual Lagrangian that are responsible for interaction are calculated. Spin-0, spin-1/2, and spin-1 particles are considered.     

Measurement of isotope shifts,fine and hyperfine structure splittings of the lithium D lines

The lithium D lines were studied using a diode laser that was frequency modulated by an electro-optic modulator, to excite an atomic beam. The transmission of part of the laser beam through an etalon was monitored to correct for the nonlinearity of the laser scan. The results for the ^6,7Li 2 S _1/2 and 2 P _1/2 hyperfine splittings agree very well with the best existing data while those for the D1 isotope shift and ^6,7Li fine structure splittings disagree significantly from data obtained by a previous laser atomic beam experiment. Our result for the D1 isotope shift is very close to the latest value computed using Hylleraas variational theory. Received 8 April 2002 / Received in final form 26 June 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: wvw@yorku.ca     

Relativistic theory of atom-laser interactions at very high laser intensities

The high-frequency approximation of Kristi? and Mittleman is considered in detail as a basis for the relativistic theory of atom-laser interactions. The properties of the 3D potentials are discussed. Within a one-dimensional model similar to that employed by Kylstra, Ermolaev, and Joachain in ab initio calculations on the time-dependent Dirac equation, the electron mass-shift due to dressing by a superstrong laser field is investigated. In the full domain of the laser parameters, the frequency ω and the peak field strength ?₀, the 1D bound states exhibit remarkable features. The numerical calculations show the existence of a very wide intermediate range of the field strengths where, in the zeroth order of the high-frequency approximation, the binding is stabilized by the field.     

Critical properties of the biaxial Ising model with both the longitudinal crystal field and the transverse dilution crystal field

Within the effective field theory (EFT), the critical properties of the biaxial Ising model with both longitudinal crystal field and transverse dilution crystal field are investigated for a simple cubic lattice. The tricritical point (TCP) and its trajectory are discussed in T-D_x and T-D_z space. A new phenomenon of two TCPs is found in T-D_x space. There exists a second-order line between two first-order lines, separated by two TCPs. The change of dilution concentration leads to a complex relation of the trajectory of the TCP. The degenerate patterns at the ground state appear by changing the longitudinal crystal field. The range of the ordered phase for transition lines labelled as a positive or (negative) value of D_x/J becomes larger or (smaller) with the decrease of t_x in T-D_z space. Some results have not been revealed in previous works.     

High-resolution spectroscopy with and frequency stabilization of a cw dye laser

The hyperfine splittings of the Na D₁ and D₂ lines were investigated using a single mode cw dye laser. The light of the laser was scattered by the atoms of an atomic beam and the fluorescent light was observed as the frequency of the laser was tuned across the D lines. The Doppler width of the atomic beam was reduced to about 2.5 MHz so that the absorption width of the atoms of the beam was essentially determined by the natural width of the 3²P_1/2 and 3²P_3/2 levels, which is about 10 MHz. Since the linewidth observed for the hyperfine transitions was 30 MHz, most of the hyperfine components of the D₁ and D₂ lines could be resolved. In another experiment the frequency of the dye laser was locked to a hyperfine transition of the D₁ line. The observed variation of the output frequency of the dye laser was less than ±1.5 MHz. In addition, the intensity of the dye laser was controlled to about 10⁻³, using an electro-optically variable transmission filter.     

Improved deuterium bromide 1-0 band molecular constants from heterodyne frequency measurements

Heterodyne frequency measurements have been made on selected deuterium bromide 1-0 band transitions ranging from P(20) to R(17). Difference frequency beat notes between a tunablediode laser whose frequency was locked to the DBr absorption lines and a CO laser whose frequency was either locked or adjusted to a reference synthesized from CO₂ laser frequency standards were measured. The beat note frequency was then combined with the measured CO laser frequency to give the DBr frequency. For two of the measurements, frequency-doubled CO₂ laser radiation was substituted for the CO laser radiation. The measurements included electric quadrupole split triplets comprising the R(0) and P(1) transitions in the D⁷⁹Br isotope. New DBr constants have been determined, and a table of frequencies is presented for the calibration of spectrometers and tunable lasers in the wavenumber range 1600 to 1990 cm^?1. A table of far-infrared frequencies is also given for DBr covering the range from 50 to 206 cm^?1.     

Far-infrared two-photon intraband transitions in n-InSb

Two-photon cyclotron resonance and two-photon shallow donor transitions have been excited by a high power pulsed D₂O laser emitting λ = 119 μm and 66 μm laser lines at the same time. Transitions involving the absorption of two 119 μm photons or simultaneously one 119 μm and one 66 μm photon were observed. Two-photon selection rules are discussed by a rigorous treatment of the symmetry of the free electron Hamiltonian.     

Measurement of total decay rates of excited states in a deuterium plasma by laser-resonance fluorescence

In a deuterium plasma with an electron density of 2.8 × 10¹³ cm^-3 and an electron temperature of 1850 K, the n = 2 level is coupled to the n = 6 level by absorption of short-pulsed laser light. Due to inelastic and superelastic electron collisions, the enhanced n = 6 population density is distributed to its neighbouring levels, i.e., n = 5 and n = 7. The laser-resonance fluorescences of the Balmer lines D₅, D₆, and D₇ were measured with time resolution. The transient behaviour of the fluorescence is compared with numerical calculations, which are based on the rate equations for population densities of a system with 5 states. It is observed that the rate coefficients of Johnson cannot explain our experimental data. The coefficients of Vriens and Smeets compare favourably with the measurements within experimental errors.     

Transition moment,radiative lifetime,and quantum yield for dissociation of the 3Π0+u state of 81Br2

The electric dipole moment of the B → X transition of ⁸¹Br₂ has been calculated from the measured absorption of single vibration-rotation lines with a YAG laser at 558 nm to be |R_e|² = 0.12 D². The corresponding radiative lifetime is τ_rad = 20 μsec. Fluorescence decay times have been measured, as a function of pressure, with a narrowband, nitrogen pumped, dye laser, for vibrational levels v′ = 16, 19, 23. The quantum yield for predissociation at zero pressure is near unity.     

Peculiarities of the SEHRS spectrum of 4,4′-bipyridine molecule

The SEHRS spectrum of 4,4′-bipyridine is analyzed on the base of the Dipole-Quadrupole theory. It is demonstrated that there appear strong lines caused by vibrations transforming after the unit irreducible representation of the D₂ symmetry group, which is most probably describes the symmetry properties of the molecule. These lines are nearly forbidden for the molecule, adsorbed on rough metal surfaces. Appearance of these lines is associated with a strong quadrupole light–molecule interaction, which exists in this system. In addition, there are lines caused by contributions from both the vibrations transforming after the unit irreducible representation A and the representation B₁, which describes transformational properties of the d_z component of the dipole moment, which is perpendicular to the surface. This result is associated with the specific geometry of the molecule, when the indicated vibrations can be nearly degenerate and cannot be resolved by the SEHRS spectra analysis. Analysis of the SEHRS spectra for the possible geometry of the molecule with the D_2h symmetry group leads to similar results. This issue is in a full coincidence with the results of the SEHRS Dipole-Quadrupole theory.     

Saturation spectroscopy of hydrogen 1-011-011-01lines with a multi-mode cw dye laser

With an intense, broadband multi-mode cw dye laser collisional studies of H_α fine-structure resonances with saturated absorption are extended to He buffer gas pressures larger than 30 mbar (0°C). The broadening and shift of the two prominent H_α(2P?3D) transitions are measured in a (He+4% H) gas discharge. The absolute magnitude and the differences in the width of the lines are explained theoretically by different inelastic fine-structure transfer cross sections which can also be deduced from the pressure effect data. Nuclear polarization of hydrogen atoms by H_α optical pumping and polarization transfer to the H(1S) ground state via Ly-α decay and further applications of the multimode laser are discussed.     

Polarization spectroscopy of Rb and Cs

Theoretical calculation of ⁸⁵Rb and ¹³³Cs D₁ signals in polarization spectroscopy is presented by using the method of velocity-selective optical pumping in a four-level system. Since good agreement between theory and experiment has been found in Na D₁ polarized signals, the theoretical calculation can be also applied to Rb and Cs D₁ lines. Rb and Cs atoms have higher total angular momentum F in the hyperfine structures than Na atom and then the calculation is more complicated. The relative signal intensities in polarization spectroscopy are compared with those in saturation spectroscopy.