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Journal of Physics B Atomic Molecular and Optical Physics

Far-wing profile of photoabsorption spectra of Na(3s–3p) atoms perturbed by helium

Kamel Alioua, Moncef Bouledroua, Abdul-Rahman Allouche, Monique Aubert-Frécon

Published Aug 26, 2008• 17 citations
Publisher

Abstract

The far wings of the sodium spectra arising from the collisional broadening of the D lines by ground helium atoms are investigated theoretically. The required X2Σ+, A2Π and B2Σ+ potential-energy curves and transition dipole moments have been generated from ab initio CASSCF-MRCI calculations to determine, within the framework of the semiclassical and full quantum-mechanical approaches, the temperature-dependent photoabsorption spectra. The profile is dominated by the free–free transitions at all temperatures ranging from 500 K to 3000 K and the computations show the existence of a satellite structure in the blue wing attributed to the X → B transitions. The satellites occur around the wavelength position 520 nm when the calculations are performed classically and around 528 nm when they are performed quantum mechanically. The results are in good accordance with those produced by other theoretical and experimental works.

DOI
10.1088/0953-4075/41/17/175102

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The far wings of the sodium spectra arising from the collisional broadening of the D lines by ground helium atoms are investigated theoretically. The required X2Σ+, A2Π and B2Σ+ potential-energy curves and transition dipole moments have been generated from ab initio CASSCF-MRCI calculations to determine, within the framework of the semiclassical and full quantum-mechanical approaches, the temperature-dependent photoabsorption spectra. The profile is dominated by the free–free transitions at all temperatures ranging from 500 K to 3000 K and the computations show the existence of a satellite structure in the blue wing attributed to the X → B transitions. The satellites occur around the wavelength position 520 nm when the calculations are performed classically and around 528 nm when they are performed quantum mechanically. The results are in good accordance with those produced by other theoretical and experimental works.
This work reports pressure-broadening line-wing and line-core of the lithium Li (2 p ← 2 s) resonance line perturbed by ground sodium Na (3s) atoms. In far-wing regions, the calculations are performed quantum-mechanically and are intended to examine the photoabsorption coefficients at diverse temperatures. The results show the existence of three satellites, in the blue wing near the wavelengths 470 nm and in the red wing around 862 nm and 1070 nm. For the line-core region, by adopting the simplified Baranger model, the line-width and line-shift rates are determined, and their variation law with temperature is examined. No published data were found to compare these results with.
We present a detailed theoretical investigation of the sodium-helium interaction and report results of quantum close-coupled calculations for the pressure-broadened widths and shifts of the sodium D lines and the 819.48 nm line over the temperature range 70-500 K, and for the total and fine-structure cross sections in the 3p 2 P level. We also present the first theoretical investigation of the hyperfine pressure shifts using a semiclassical scattering formalism and report results for the hyperfine transition in the 3s 2 S 1/2 ground state over the temperature range 70-1000 K. Finally, we calculate the refractive index of helium for sodium matter waves with velocities up to 2000 m s -1 . Several of the calculations were performed using two versions of the adiabatic molecular potentials of Peach (Peach G 1996 unpublished) and the results compared with those obtained using the l -dependent pseudo-potentials of Pascale (Pascale J 1985 XIII Summer School on Quantum Optics ed J Fiutak and J Mizerski pp 39-91) and Peach (Peach G 1996 unpublished). Detailed comparisons with other theoretical calculations and experimental results are also made.
Recent advances in experimental spectroscopy offer the promise of yielding much detailed information about molecular potentials and collisional interactions from a study of the light emitted or absorbed in the far wings of atomic lines. However, readily manipulable, accurate theoretical expressions and methods are needed to extract such knowledge. Straightforward formulas, based on the distorted-wave approximation, for the normalized emission intensity in the far wing of a pumped atomic line are given here. By normalizing theoretical spectra with respect to the strength of the atomic line, one obtains a convenient form for the analysis of experimental differential spectra that are reported in nonarbitrary units. Theoretical and experimental spectra are numerically consistent in the test case of the blue-wing satellite (\ensuremath{\sim}7610 A\r{}) of the Rb D2{D}_{2}D2​ line (7800 A\r{}) broadened by Xe perturbers.
The purpose of this work is the evaluation of the linewidth w and lineshift d of the sodium resonance line 3p − → 3s when the excited atoms are evolving in their parent gas. Assuming the Baranger impact approximation, these two quantities are given in terms of the phase shifts of the ground Na(3s) + Na(3s) and the excited Na(3p)+Na(3s) states. The quantal calculations and the semi-classical method, developed by Mott and Massey and Landau and Lifshitz, show that the cross sections σ and λ vary with the energy like E−1/2, the width w and the shift d do not depend on the temperature, the long-range interactions have a big influence on w and d, and the rate coefficients depend on the dispersion coefficients like w/n ≈ +7.298 × 10−8C3(Σ) and d/n ≈ +8.893 × 10−9C3(Σ). The study also shows that the sodium results can be extended to the other alkali-metal atoms (Li, K, Rb, Cs, and Fr) by a simple scaling. Keywords: potential energy curve, broadening cross section, rate coefficient, linewidth, lineshift, dispersion coefficient
Experimental ratios for branching into the fine-structure levels of the Na 3p multiplet, as a consequence of an optical collision with He, Ne, Ar, Kr, or Xe, are reported. The process studied is Na(3s 2S1/2^{2}S_{1/2}2S1/2​)+scrR+nh\ensuremath{\nu}\ensuremath{\rightarrow} Na(3p 2Pj^{2}P_{j}2Pj​)+scrR+(n-1)h\ensuremath{\nu} , where scrR represents a rare-gas atom and where the laser frequency \ensuremath{\nu} is tuned in the wings of the Na resonance transitions. The branching ratios are defined as I(D1)/I(D2) where I(D1) and I(D2) are measured intensities of the atomic Na D1 and D2 lines. The ratios are determined for detunings ranging from about 650 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the blue wing to 170 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the red wing of the Na 3p multiplet. The branching is found to be strongly detuning dependent in the vicinity of the NaAr, NaKr, and NaXe near-red-wing satellites. The blue-wing branching ratios show a detuning-dependent approach to a recoil, or sudden statistical, limit of 0.5, irrespective of the rare gas. Fine-structure changing cross sections have also been measured for resonant excitation of the Na 3p 2Pj^{2}P_{j}2Pj​ state; the results are consistent with cross sections obtained from wing excitation.
Measurements are presented for the blue-wing satellite bands of the Rb first resonance line (780 nm) emitted in the presence of the noble gases Ne, Ar, Kr, and Xe. The continuum intensity per spectral interval and perturber density is expressed as a fraction of the total Rb (780 nm) fluorescence from optically thin vapor. Over the \ensuremath{\sim}1018{10}^{18}1018-1019{10}^{19}1019 cm3{\mathrm{cm}}^{3}cm3 density range investigated this normalized satellite-peak intensity is found to scale linearly with perturber density and approximately exponentially in $\frac{\ensuremath{-}1}{T},T$ being the absolute temperature. In the classically forbidden region beyond the satellite peak the intensity drops exponentially with frequency for Xe perturbers, but departs from exponential behavior in the Ar and Kr data. We observe undulations in the spectra between line center and the satellite. This is expected due to the possibility of interference between contributions to the transition probability at two internuclear separations, the separations at which the difference potential equals the photon energy.