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Physical Review A

Influence of inelastic collisions on the width of optical lines involving Rydberg states

F. Gounand, Józef Szudy, M Hugon, B. Sayer, P. R. Fournier

Published Aug 1, 1982• 9 citations
Publisher

Abstract

It is shown that with use of some assumptions the cross sections for the broadening of optical lines originating from Rydberg levels can be interpreted with a simple model which takes into account the elastic and the quenching cross sections of the corresponding Rydberg states. The validity of the model is extensively discussed. Good agreement is observed in most cases between the values derived from the model and the available experimental data for the broadening and quenching cross sections of a wide set of Rb and Na Rydberg levels perturbed by noble gases. It is clearly demonstrated that inelastic processes can significantly affect the broadening cross sections even for large values of the principal quantum number $n$.

DOI
10.1103/physreva.26.831

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It is shown that with use of some assumptions the cross sections for the broadening of optical lines originating from Rydberg levels can be interpreted with a simple model which takes into account the elastic and the quenching cross sections of the corresponding Rydberg states. The validity of the model is extensively discussed. Good agreement is observed in most cases between the values derived from the model and the available experimental data for the broadening and quenching cross sections of a wide set of Rb and Na Rydberg levels perturbed by noble gases. It is clearly demonstrated that inelastic processes can significantly affect the broadening cross sections even for large values of the principal quantum number nnn.
The impact broadening rates of Rb ns Rydberg levels by He, Ar and Xe atoms measured by Weber and Niemax (1982) and by Ne and Kr atoms observed by Thompson et al. (1987) are quantitatively explained over the whole range of the principal quantum number n. As Rb ns Rydberg levels (quantum defect delta =3.13) are very close to the nearly hydrogenic high l levels, inelastic collisions make as important a contribution to the broadening rates as elastic collisions. The authors derive the cross sections for the elastic and inelastic using a combination of Kaulakys' (1984) and Lebedev and Marchenko's (1985) impact theories. Good agreement between the theoretical and experimental broadening rates is achieved over the whole range of n.
The theory of impact broadening of the isolated spectral lines of the Rydberg atomic series perturbed by neutral particles is developed within the framework of the impulse approximation. The analysis of the broadening process is based on the consideration of the inelastic nl to n' transitions between highly excited states of the Rydberg atom. The role of the potential and resonance scattering of the quasifree electron by a perturbing particle in the impact broadening of the Rydberg nl levels is investigated. It is shown that the general expressions for the broadening cross sections presented in this paper contain the results of asymptotic Alekseev and Sobel'man theory (1965) as special cases. Both elastic and inelastic scattering contributions of the perturber by the parent core of Rydberg atom to the broadening cross sections are also considered within the framework of the 'shake' model. The results obtained are used for a quantitative explanation of experimental data on the broadening of Rydberg atomic levels perturbed by alkali-metal atoms. The energies and widths of the 3 P resonances on the quasidiscrete levels of the negative K - and Rb - ions are determined.
The author obtains expressions for Rydberg level broadening and shift cross sections and rates suitable for elastic collisions of ground-state rare-gas atoms with Rydberg atoms. The semiclassical impact broadening theory is used. The interaction of a Rydberg atom with a rare-gas atom is approximated by the superposition of polarisation potentials and the Fermi pseudopotential. It is shown that similar expressions for the broadening and shift cross sections due to the perturber-Rydberg-electron interaction can be obtained in the JWKB approximation for the Rydberg-electron wavefunctions and for the square-well model potential. Consequently the shift and width of the Rydberg level are not very sensitive to the shape of the potential but only to its normalisation. Expressions for the shift and width in the square-well potential approximation suitable in the high-density limit of the perturbing atoms are obtained. Limits of the applicability of the expressions for the broadening and shift cross sections are discussed. Calculated broadening and shift rates agree well with experimental results for the broadening and shift of Rydberg levels with small, medium and large principal quantum numbers by all rare gases excepting neon.
The impact broadening of Na(nP1/2) (n=6-24), K(nP1/2) (n=8-24) and Rb(nP12/) (n=10-24) levels by noble-gas atoms, N2 molecules and alkali atoms in the ground state has been investigated. Broadening cross sections have been evaluated on the grounds of contributions coming from Rydberg-electron-perturber and ionic core-perturber scattering. Broadening cross sections for Cs(nD3/2)+Cs(6S) collisions for n=11-23 have also been calculated to compare with the experimental ones. Theoretically evaluated broadening cross sections for K(nP12/)+K(4S) and Cs(nD3/2)+Cs(6S) collisions appeared to be in good agreement with existing experimental data.
We have made comprehensive measurements of the noble-gas-induced (He, Ne, Ar, Kr, and Xe) broadening cross sections of the Na $3S\ensuremath{-}nS$ ($3S\ensuremath{-}nD$) transitions, from n=5to38n=5 \mathrm{to} 38n=5to38 (n=4to40n=4 \mathrm{to} 40n=4to40). These measurements were made using the trilevel-echo technique and are an extension and refinement of our earlier work. We find that the cross sections increase as the geometric cross section at low values of nnn, and then, at a value of nnn which depends on the particular noble gas, begin to decrease and eventually reach an asymptotic value at high nnn. The broadening cross sections for the nearly degenerate DDD states are significantly larger than those for the SSS states and clearly show the effect of lll-changing collisions. We also compare our measured SSS-state broadening cross sections with the cross sections calculated using the theory of Omont and find good qualitative agreement.