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Physical Review A

Broadening of the D Lines and the Relaxation of the Resonance Levels of Sodium Due to Collisions with Helium

E L Lewis, L. F. McNamara

Published Jun 1, 1972• 65 citations
Publisher

Abstract

Calculated potentials for the NaHe molecule are used to obtain collision-induced widths and shifts for the sodium $D$ lines together with cross sections for fine-structure transitions and the relaxation of the multipole polarizations of the resonance levels. The atomic collision is treated in an adiabatic approximation in which the colliding atoms form a molecular system which rotates during the collision. We find the resonance lines to be broadened equally and to be approximately 70% wider, and with associated shifts of an order of magnitude smaller, than expected on the basis of van der Waals forces. The dependence of the cross sections for relaxation of the multipole polarizations of the resonance levels on the molecular-coupling conditions and the rotation of the system during collision is discussed and indicates a limitation on the sum rule for these cross sections. Good over-all agreement with the existing experimental data is obtained.

DOI
10.1103/physreva.5.2643

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Calculated potentials for the NaHe molecule are used to obtain collision-induced widths and shifts for the sodium DDD lines together with cross sections for fine-structure transitions and the relaxation of the multipole polarizations of the resonance levels. The atomic collision is treated in an adiabatic approximation in which the colliding atoms form a molecular system which rotates during the collision. We find the resonance lines to be broadened equally and to be approximately 70% wider, and with associated shifts of an order of magnitude smaller, than expected on the basis of van der Waals forces. The dependence of the cross sections for relaxation of the multipole polarizations of the resonance levels on the molecular-coupling conditions and the rotation of the system during collision is discussed and indicates a limitation on the sum rule for these cross sections. Good over-all agreement with the existing experimental data is obtained.
Accurate values for the density shift and broadening of five isolated ${\mathrm{H}}_{\ensuremath{\alpha}}$ fine-structure transitions have been measured. Doppler-free polarization and double-quantum saturation spectroscopy with a cw dye laser are used in a He dc discharge with 1% H2{\mathrm{H}}_{2}H2​. The negative shifts and the huge broadening values are correctly predicted by an impact-approximation theory taking into account the large cross sections for fine-structure transfer (quenching) collisions and only Van der Waals interaction between H∗{\mathrm{H}}^{*}H∗ and He. Consequences of a comparison with the positive shift of the unresolved ${\mathrm{H}}_{\ensuremath{\alpha}}$ line and of the alkali-metal DDD lines in He buffer gas are discussed. For pressures below 0.1 Torr hfs decoupling collisions give rise to a positive shift of single ${\mathrm{H}}_{\ensuremath{\alpha}}$ fine-structure lines and to a collisional narrowing effect analogous to that observed in nuclear magnetic resonance.
In previous papers [1-3] we have reported experimental measurements of the relaxation rates of the k-multipole moments in the 4D level of sodium and the 3S-4D optical coherence. In the present paper we compare the experimental values with those obtained theoretically for different types of potentials. We show that the Van der Waals C6R -6 interaction is not sufficiently anisotropic to describe the relaxation of the k multipole moments. For Ar, Kr and Xe, much better results are obtained by taking into account the next term C8R-8 in the expansion of the long-range interaction. The potentials of Pascale and Vandeplanque [4] give very good results for helium. The results are also satisfactory for Ar, Kr and Xe, but the agreement could still be improved.
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.
The fluorescence intensities for the D lines in non-resonant excitation of the alkali-helium pairs under single-collision conditions were obtained from calculations of the optical collision spectra by the quantum coupled-channels method. The close relation of the non-adiabatic transition probability from a molecular level to an atomic state during the final stage of an optical collision and the spectral dependence of the relative fluorescence intensities is investigated. An analysis of the impact region in terms of line-broadening and fine-structure cross sections calculated separately for all systems confirms the factorisation approximation.
The fluorescence intensities for the D lines in non-resonant excitation of the alkali-helium pairs under single-collision conditions were obtained from calculations of the optical collision spectra by the quantum coupled-channels method. The close relation of the non-adiabatic transition probability from a molecular level to an atomic state during the final stage of an optical collision and the spectral dependence of the relative fluorescence intensities is investigated. An analysis of the impact region in terms of line-broadening and fine-structure cross sections calculated separately for all systems confirms the factorisation approximation.
A method is developed for calculating the cross section for line broadening in the limiting case in which important collisions may be considered to occur very rapidly with respect to the periods corresponding to the transitions in question. This method is essentially an extension of the familiar "sudden" approximation; reference is made throughout to the particular example of optical double resonance only for definiteness and because there are available experimental results for comparison with the theory. Assuming the impact model and considering the case when the energy levels in question are well resolved with respect to their width, an exact expression is found for resonant self-broadening in the usual weak rf field limit of interest in double resonance. For the case of very small oscillator strengths for the optical transition (intercombination lines), the resonant broadening becomes sufficiently small so that second-order, intermediate-state processes dominate, and approximations must be made to effect sums over intermediate states. Here the broadening is of the same sort as foreign gas broadening, and in many cases of interest, the approximations can be made in a sufficiently realistic manner to obtain useful expressions for the broadening. It is shown that the resonant cross section and this "second-order" cross section are not additive, but that the one which is larger dominates the total cross sections very strongly. Finally, we evaluate explicitly the self-broadening and foreign gas broadening (by the noble gases) of double resonance lines in the group II metals and the self-broadening in the optical spectrum of helium. In all cases our theoretical predictions are in good agreement with measurements which have been made.