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Physical Review A

Collisional angular-momentum mixing of highly excited Na(nD2) states by N2 and CO

Thomas F. Gallagher, R. E. Olson, William E. Cooke, S. A. Edelstein, R. M. Hill

Published Jul 1, 1977• 35 citations
Publisher

Abstract

Cross sections for the collisional $l$ mixing of $\mathrm{Na}(n^{2}D)$ states from $n=5 \mathrm{to} 14$ by ${\mathrm{N}}_{2}$ 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 ${\mathrm{N}}_{2}$ the experimental cross sections rise sharply from $n=5$ to $n=10$ and remain constant for $n>10$. The theoretical calculations overestimate the experimental cross sections by a factor of 3 from $n=10 \mathrm{to} 12$, but are in good agreement for the smaller $n$ values.

DOI
10.1103/physreva.16.441

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We report the first study of molecular-perturber-induced broadening of forbidden ground-to-Rydberg-state transitions. The ${\mathrm{N}}_{2}$- and CO-induced-broadening cross sections for the $3S\ensuremath{-}\mathrm{nS} (\mathrm{nD})$ transitions of sodium have been measured for values of $n$, the principal quantum number of the upper state, ranging from 4 to 41. These measurements, performed using the trilevel echo technique, were accomplished at sodium and perturber densities of ${10}^{\ensuremath{-}6}$ and 1 torr, respectively. The broadening rates, observed in the present experiment, differ in some respects from those observed previously with noble-gas perturbers. These differences, which presumably arise because of the presence of accessible internal degrees of freedom in the ${\mathrm{N}}_{2}$ and CO perturbers (and in the case of CO also because of its permanent electric-dipole moment), are most clearly displayed in $3S\ensuremath{-}\mathrm{nS}$ transitions. Previous work has shown that with noble-gas perturbers the $3S\ensuremath{-}\mathrm{nS}$ broadening cross sections display a dramatic increase at low values of $n$; they then decline at intermediate values of $n$, and at high $n$ they approach a limiting value. In the present experiment we find that the initial increase in $3S\ensuremath{-}\mathrm{nS}$ broadening cross sections with $n$ is relatively small and more gradual. For high $n$, the broadening cross sections become approximately constant. As is the case with noble-gas perturbers, the broadening of $3S\ensuremath{-}\mathrm{nD}$ transitions is generally larger than the broadening of the corresponding $3S\ensuremath{-}\mathrm{nS}$ transitions. With CO as a perturber, an unexplained irreproducibility in the broadening cross sections of high-$n$ $3S\ensuremath{-}\mathrm{nD}$ transitions is observed. One explanation has to do with the CO-induced frequency shifts being unusually large and exceeding the spectral width of our excitation lasers.

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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 $n=5\ensuremath{-}15$ 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 $l\ensuremath{\ge}2$ states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the $l\ensuremath{\ge}2$ states of the same nnn. 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 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.
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.
The collisional deactivation of the Na 5s5s5s and 4p4p4p states by collisions with N2{\mathrm{N}}_{2}N2​ molecules has been studied using the method of laser-induced fluorescence. The total cross sections for the depopulation of the 5s5s5s and 4p4p4p states are 86(8) and 43(4) A˚2{\mathrm{\AA{}}}^{2}A˚2, respectively. The cross sections for the specific collisional transfers $5s\ensuremath{\rightarrow}4p$, $5s\ensuremath{\rightarrow}3d$, and $4p\ensuremath{\rightarrow}3d$ are 32(8), 10(2), and 19(3) A˚2{\mathrm{\AA{}}}^{2}A˚2, respectively.
The total depopulation cross sections by N2{\mathrm{N}}_{2}N2​ of high rubidium Rydberg states, $\mathrm{Rb}(\mathrm{ns}) (n=25\ensuremath{-}46)$ and $\mathrm{Rb}(\mathrm{nd}) (n=23\ensuremath{-}44)$, have been measured using time-resolved field ionization technique and compared to previous results obtained on the quenching of Rb(nl)\mathrm{Rb}(\mathrm{nl})Rb(nl) by CO. It is shown that the Rb(nl)\mathrm{Rb}(\mathrm{nl})Rb(nl) depopulation by N2{\mathrm{N}}_{2}N2​ is much less efficient than the Rb(nl)\mathrm{Rb}(\mathrm{nl})Rb(nl) depopulation by CO and leads mainly to the quasielastic process of angular momentum mixing via the short-range interaction between the quasifree Rydberg-state electron and the molecule. It is clearly demonstrated that the presence of a permanent dipole in CO changes the collisional processes drastically. The agreement between experimental and theoretical predictions based on the impulse approximation is quite satisfactory.
Collisional transfers induced in the n=6--13 Li Rydberg states by H2{\mathrm{H}}_{2}H2​, N2{\mathrm{N}}_{2}N2​, and CO molecules have been experimentally studied in a heat-pipe oven. The l-mixing cross sections have been deduced from the fast component of the population relaxations following pulsed laser excitation. The order of magnitude of these cross sections (103{10}^{3}103 A˚2{\r{}}^{2}˚2) is well predicted by the existing theories. For large n, the cross sections stay approximately constant. This can be partly explained by the influence of inelastic processes such as n changing. In the particular case of H2{\mathrm{H}}_{2}H2​, n-changing collisions have been identified by the fluorescence starting from the n'=n\ifmmode\pm\else\textpm\fi{}1, n-2 levels. Cross sections of the order of 10 A˚2{\r{}}^{2}˚2 have been measured. The systematic study of the n-changing cross sections as a function of the transferred energy shows some evidence of resonance phenomena corresponding to an energy exchange between the Rydberg electron and the molecular rotation. This effect is also observed when H2{\mathrm{H}}_{2}H2​ is replaced by D2{\mathrm{D}}_{2}D2​. These resonances are well described by the theory of Petitjean and Gounand based on the e-quadrupolar interaction.
We report the first study of molecular-perturber-induced broadening of forbidden ground-to-Rydberg-state transitions. The N2{\mathrm{N}}_{2}N2​- and CO-induced-broadening cross sections for the $3S\ensuremath{-}\mathrm{nS} (\mathrm{nD})$ transitions of sodium have been measured for values of nnn, the principal quantum number of the upper state, ranging from 4 to 41. These measurements, performed using the trilevel echo technique, were accomplished at sodium and perturber densities of ${10}^{\ensuremath{-}6}$ and 1 torr, respectively. The broadening rates, observed in the present experiment, differ in some respects from those observed previously with noble-gas perturbers. These differences, which presumably arise because of the presence of accessible internal degrees of freedom in the N2{\mathrm{N}}_{2}N2​ and CO perturbers (and in the case of CO also because of its permanent electric-dipole moment), are most clearly displayed in $3S\ensuremath{-}\mathrm{nS}$ transitions. Previous work has shown that with noble-gas perturbers the $3S\ensuremath{-}\mathrm{nS}$ broadening cross sections display a dramatic increase at low values of nnn; they then decline at intermediate values of nnn, and at high nnn they approach a limiting value. In the present experiment we find that the initial increase in $3S\ensuremath{-}\mathrm{nS}$ broadening cross sections with nnn is relatively small and more gradual. For high nnn, the broadening cross sections become approximately constant. As is the case with noble-gas perturbers, the broadening of $3S\ensuremath{-}\mathrm{nD}$ transitions is generally larger than the broadening of the corresponding $3S\ensuremath{-}\mathrm{nS}$ transitions. With CO as a perturber, an unexplained irreproducibility in the broadening cross sections of high-nnn $3S\ensuremath{-}\mathrm{nD}$ transitions is observed. One explanation has to do with the CO-induced frequency shifts being unusually large and exceeding the spectral width of our excitation lasers.