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Physical Review A

Collisional angular-momentum mixing of Rydberg states of Na by He, Ne, and Ar

Thomas F. Gallagher, S. A. Edelstein, R. M. Hill

Published May 1, 1977• 144 citations
Publisher

Abstract

The collisional angular-momentum mixing of $n=5\ensuremath{-}15$ Na $d$ states with the $l>2$ states of the same $n$ has been studied using He, Ne, and Ar as collision partners. At rare-gas pressures of \ensuremath{\sim}1 Torr, the $l\ensuremath{\ge}2$ states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the $l\ensuremath{\ge}2$ states of the same $n$. Using \ensuremath{\sim}1 Torr of neon to collisionally mix the $l\ensuremath{\ge}2$ states, the average lifetime for $l\ensuremath{\ge}2$ was measured for each $n$ and compared to the theoretical prediction for hydrogen, with which it is in excellent agreement. The cross section for $l$ mixing by each of the gases is found to increase sharply from $n=5 \mathrm{to} 10$ and decrease above $n=10$. The magnitudes of the $l$-mixing cross sections are found to correlate with the low-energy scattering lengths of the collision partners.

DOI
10.1103/physreva.15.1945

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The collisional angular-momentum mixing of n=5\ensuremath−15n=5\ensuremath{-}15n=5\ensuremath−15 Na ddd states with the l>2l>2l>2 states of the same nnn has been studied using He, Ne, and Ar as collision partners. At rare-gas pressures of \ensuremath{\sim}1 Torr, the l\ensuremath≥2l\ensuremath{\ge}2l\ensuremath≥2 states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the l\ensuremath≥2l\ensuremath{\ge}2l\ensuremath≥2 states of the same nnn. Using \ensuremath{\sim}1 Torr of neon to collisionally mix the l\ensuremath≥2l\ensuremath{\ge}2l\ensuremath≥2 states, the average lifetime for l\ensuremath≥2l\ensuremath{\ge}2l\ensuremath≥2 was measured for each nnn and compared to the theoretical prediction for hydrogen, with which it is in excellent agreement. The cross section for lll mixing by each of the gases is found to increase sharply from n=5to10n=5 \mathrm{to} 10n=5to10 and decrease above n=10n=10n=10. The magnitudes of the lll-mixing cross sections are found to correlate with the low-energy scattering lengths of the collision partners.
Collisions with rare-gas atoms are observed to produce a lengthening of the lifetime of the highly excited ($n=5\ensuremath{-}10$) ddd states of Na. The effect is interpreted as collisional angular momentum mixing of the ddd state with l>2l>2l>2 states; thus the average lifetime of all states for which l> 2l>~2l> 2 is observed. The cross section for the process appears to increase as the geometrical cross section of the excited atom.
In Na, the energy gap $\ensuremath{\Delta}E$ between the nnn, ddd state and the nnn, l>2l>2l>2 states is ten times larger than $\ensuremath{\Delta}E$ between nnn, fff and the nnn, l>3l>3l>3 states. To investigate the effect of this difference on the ddd- and fff-state lll-mixing cross sections, ${\ensuremath{\sigma}}_{d}$ and ${\ensuremath{\sigma}}_{f}$, we have recently carried out experiments to measure ${\ensuremath{\sigma}}_{d\ensuremath{-}f}$, the lll-mixing cross sections for a microwave-induced mixture of ddd and fff states. Using the previously measured values of ${\ensuremath{\sigma}}_{d}$, we have derived values of ${\ensuremath{\sigma}}_{f}$ which have the same nnn dependence as ${\ensuremath{\sigma}}_{d}$. ${\ensuremath{\sigma}}_{f}$ is larger than ${\ensuremath{\sigma}}_{d}$ for Ne, but smaller for He and Ar. In addition, we have analyzed the final states after one collision with Ar using selective field ionization of the 17l17l17l states and have observed that after one collision all the lll states are equally populated indicating that there are no $\ensuremath{\Delta}l$ selection rules for the process. This confirms the earlier suggestion that lll mixing is caused by a short-range interaction.
A classical model for l mixing of Rydberg states in atomic collisions is described. The primary assumption of the model is that l changing occurs in a single hard-sphere collision between the Rydberg electron and the perturbing atom which is represented by the zero-energy scattering length L. Predictions of the model, which are in the form of cross sections as functions of principal quantum number n, are compared with data for l mixing of Na(nd) and Rb(nf) by rare-gas atoms. Agreement is, in most cases, quite good, comparable with that of other, more sophisticated, models. It is shown that, because the calculation must be carried out in the reference frame of the ion core, the energy deficit between low angular momentum states and the nearest hydrogenic manifold can be made up in a single collision between the Rydberg electron and the perturbing atom, an effect that is analogous to the gravitational slingshot effect used to alter the orbits of a spacecraft under the influence of the Sun's gravitational field. Comparison of data for l mixing by ground-state Rb atoms with model calculations in which L is treated as a free parameter leads to an estimate of 10 a.u. for the zero-energy scattering length of Rb.
Cross sections for the collisional lll mixing of Na(n2D)\mathrm{Na}(n^{2}D)Na(n2D) states from n=5to14n=5 \mathrm{to} 14n=5to14 by N2{\mathrm{N}}_{2}N2​ and CO have been measured by time-resolved laser fluorescence and calculated in a two-state approximation by assuming the perturbing gases are spherically symmetric. For both CO and N2{\mathrm{N}}_{2}N2​ the experimental cross sections rise sharply from n=5n=5n=5 to n=10n=10n=10 and remain constant for n>10n>10n>10. The theoretical calculations overestimate the experimental cross sections by a factor of 3 from n=10to12n=10 \mathrm{to} 12n=10to12, but are in good agreement for the smaller nnn values.
The collisional angular-momentum mixing of the Nand\mathrm{Na}\mathrm{nd}Nand Rydberg states into states of higher angular momentum with Xe as the collisional partner has been studied in zero field and in the presence of a small electric field. The collisional lll-mixing cross section in zero field has been measured for $9\ensuremath{\le}n\ensuremath{\le}23$ using a vapor-cell-fluorescence method and a crossed-beam technique with a selective-field-ionization (SFI) scheme as the state detector. Using the ∣ml∣|{m}_{l}|∣ml​∣ selectivity of the SFI, we have also investigated the final-∣ml∣|{m}_{l}|∣ml​∣-state distribution of the collisionally populated states of l>2l>2l>2. Our measurements suggest that the collisionally populated states have predominantly low ∣ml∣|{m}_{l}|∣ml​∣ values ($|{m}_{l}|\ensuremath{\le}2$). An application of a low electric field (\ensuremath{\sim} 50 V/cm) substantially reduces the collisional population of the low-∣ml∣|{m}_{l}|∣ml​∣ states, thus reducing the total cross section as well.