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Broadening and Shifting of the Alkali-Metal Resonance Lines by Collisions with their Parent Monoatoms
M. Bouledroua1) and A. Dalgarno2)
(1) Laboratoire de Physique des Rayonnements, Badji Mokhtar University, Annaba, Algeria
(2) Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USA
The purpose of this work is the computation 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 [1, 2], these two quantities are given in terms
of the phase shifts ηl(E) 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 Landau and Lifshitz
[3] and Mott and Massey [4], show that:
• the cross sections σw and σs vary with the energy like 1/√E;
• w and d do not depend on the temperature;
• the long-range interactions have a big influence on w and d;
• the rate coefficients w/n and d/n 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.
References
[1] M. Baranger, Phys. Rev. 111, 481 (1958).
[2] J. Szudy and W.E. Baylis, J. Quant. Spectr. Radiat. Transfer 15, 641 (1975); Phys. Rep.
266, 127 (1996).
[3] L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Non-Relativistic Theory, (Pergamon
Press, Oxford, 1981).
[4] N.F. Mott and H.S.W. Massey, The Theory of Atomic Collisions, (Oxford University
Press, Oxford, 1965).
Remark:
THIS IS AN ORAL CONTRIBUTION
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