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The Journal of Chemical Physics

Excitation transfer between fine structure levels: Angular dependence of the sensitized fluorescence

Lue‐Yung Chow Chiu

Published Mar 1, 1974• 1 citation
Publisher

Abstract

Excitation transfer is studied theoretically as an integral part of sensitized fluorescence, which is a third order time-dependent process, namely the excitation of the absorber atom, followed by the transfer of excitation from this atom to the receiver atom and finally the emission of sensitized fluorescence from the receiver atom. The phase correlation transmitted through such a third order process gives rise to the angular distribution of sensitized fluorescence which is shown to depend on the fine structure levels of both atoms. Long range electric dipole-dipole interaction is used as the mechanism for excitation transfer. Plane wave motion is assumed for the relative motion between two interacting atoms. A general formula is derived for the relative intensities (hence relative cross sections) of the sensitized fluorescence, involving different sets of fine structure levels. This cross-section ratio turns out to be angular dependent but nevertheless is shown to be expressible in a very simple form which can be readily calculated. The ratio calculation is illustrated for the case of K*(42P1/2,3/2) +Rb(52P1/2,3/2). Nuclear spin effect is also considered. For the weak coupling case, the nuclear spin is found to have no effect on the sensitized fluorescence.

DOI
10.1063/1.1681317

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Sensitized Fluorescence in Vapors of Alkali Atoms. XIII. 62P1/2−62P3/2 Excitation Transfer in Rubidium, Induced in Collisions with Noble Gas Atoms

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The cross sections for excitation transfer between the 62P fine-structure substates in rubidium, induced in collisions with noble gas atoms, have been determined in a series of sensitized fluorescence experiments. Mixtures of rubidium vapor and noble gases at pressures varying in the range 0–5 Torr were irradiated with each component of the second 2P rubidium doublet in turn and the following cross sections for 2P mixing were obtained from measurements of sensitised-to-resonance fluorescent intensity ratios. Rb–He: Q12(2P1/2 → 2P3/2) = 29.3 Å2; Q21(2P1/2 ← 2P3/2) = 19.0 Å2. Rb–Ne: Q12 = 10.3 Å2; Q21 = 6.4 Å2. Rb–Ar: Q12 = 24.0 Å2; Q21 = 14.9 Å2. Rb–Kr: Q12 = 23.2 Å2; Q21 = 14.6 Å2. Rb–Xe: Q12 = 43.9 Å2; Q21 = 27.7 Å2 In their dependence on the magnitude of the fine-structure splitting, the values are consistent with previously determined cross sections for mixing in the first and third 2P doublets of alkali atoms.

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Paul W. Pace, J. B. Atkinson

The method of sensitized fluorescence has been employed to investigate the [Formula: see text] excitation transfer processes in cesium induced in collisions with ground state cesium atoms. The cesium vapor density was kept sufficiently low to enable the cross sections for the mixing process to be determined under single collision conditions and to ensure that radiation trapping and quenching were negligible. A nitrogen laser pumped dye laser was used to excite the cesium atoms to each of the 72P levels in turn and measurements of the relative intensities of fluorescence yielded the following cross sections: [Formula: see text] These results are consistent with the empirical relationship between the magnitude of the cross sections and the fine structure splitting that has previously been determined for the alkalis.

Canadian Journal of Physics•Sep 1, 1974•16 citations
Excitation transfer is studied theoretically as an integral part of sensitized fluorescence, which is a third order time-dependent process, namely the excitation of the absorber atom, followed by the transfer of excitation from this atom to the receiver atom and finally the emission of sensitized fluorescence from the receiver atom. The phase correlation transmitted through such a third order process gives rise to the angular distribution of sensitized fluorescence which is shown to depend on the fine structure levels of both atoms. Long range electric dipole-dipole interaction is used as the mechanism for excitation transfer. Plane wave motion is assumed for the relative motion between two interacting atoms. A general formula is derived for the relative intensities (hence relative cross sections) of the sensitized fluorescence, involving different sets of fine structure levels. This cross-section ratio turns out to be angular dependent but nevertheless is shown to be expressible in a very simple form which can be readily calculated. The ratio calculation is illustrated for the case of K*(42P1/2,3/2) +Rb(52P1/2,3/2). Nuclear spin effect is also considered. For the weak coupling case, the nuclear spin is found to have no effect on the sensitized fluorescence.
Energy transfer and coherence transfer between two atoms of different species are studied theoretically. The electric dipole-dipole interaction is the mechanism considered for the excitation transfer. A generalized perturbation method for a damping system is used. A general formula is derived for the polarization of the sensitized fluorescence resulting from the excitation transfer. This polarization is shown to be dependent on the angular momenta of the two atoms, and to be independent of their relative velocity as well as of their difference in the energy of excitation. The polarizations are found to be nonzero in many cases which demonstrate the transfer of coherence through collision processes. A general and compact formula is also derived for the polarization of pure fluorescence where excitation exchange has not taken place. The polarization of the sensitized fluorescence is in general smaller than that of the pure fluorescence. This means that the coherence is transferred only partially. Finally, the magnetic field effect has been included. This field depolarization depends on the gj{g}_{j}gj​ values and the lifetimes of the excited states of both atoms. The general feature of the field dependence also differs considerably from that of the Hanle effect for resonance fluorescence.
The cross sections for the excitation energy transfer in the collisional processes Na*(3P 1 2/)+M(nS 1 2/) to or from Na*(3p 3 2/)+m(Ns 3 2/), m being ground-state Rb (n=5) or Cs (n=6) atom, have been measured by laser fluorescence method. With either of the two sodium 3P fine-structure states optically excited, the intensity ratio of the sensitized to direct fluorescence was measured. The polarization effects due to partially polarized and anisotropic direct fluorescence were investigated. The measured cross sections (T=530 K) for the sodium 3P fine-structure excitation transfer induced by collisions with Rb are: sigma ( 1 / 2 to 3 / 2 )=170 AA 2 , with an overall accuracy of 20%. The corresponding values in the Cs case are: sigma ( 1 / 2 to 3 / 2 )=140 AA 2 , sigma ( 3 / 2 to 1 / 2 )=83 AA 2 . The theoretical calculations reveal the decisive role of the dipole-quadrupole interaction. The obtained values are in satisfactory agreement with the experiment only if both the dipole-dipole and dipole-quadrupole interactions are taken into account, while the calculations involving the dipole-dipole term alone yield the cross section values which are as much as one order of magnitude lower than the experimentally observed ones.
The cross sections for excitation transfer between the 62P fine-structure substates in rubidium, induced in collisions with noble gas atoms, have been determined in a series of sensitized fluorescence experiments. Mixtures of rubidium vapor and noble gases at pressures varying in the range 0–5 Torr were irradiated with each component of the second 2P rubidium doublet in turn and the following cross sections for 2P mixing were obtained from measurements of sensitised-to-resonance fluorescent intensity ratios. Rb–He: Q12(2P1/2 → 2P3/2) = 29.3 Å2; Q21(2P1/2 ← 2P3/2) = 19.0 Å2. Rb–Ne: Q12 = 10.3 Å2; Q21 = 6.4 Å2. Rb–Ar: Q12 = 24.0 Å2; Q21 = 14.9 Å2. Rb–Kr: Q12 = 23.2 Å2; Q21 = 14.6 Å2. Rb–Xe: Q12 = 43.9 Å2; Q21 = 27.7 Å2 In their dependence on the magnitude of the fine-structure splitting, the values are consistent with previously determined cross sections for mixing in the first and third 2P doublets of alkali atoms.
Cross sections for inelastic transfer between the 82D3/2 and 82D5/2 fine-structure states in rubidium, induced in resonant collisions with ground-state Rb atoms, have been determined using an experimental method involving two-photon excitation of atomic fluorescence. Rubidium vapor in a fluorescence cell was irradiated with pulses of 641 nm radiation from a N2 laser-pumped dye-laser tuned to excite one of the 82D states. The resulting fluorescence included the direct component originating from the optically excited state and a sensitized component arising from the other fine-structure state populated by collisions. Relative intensities of the fluorescent components, determined by photon-counting techniques, yielded the cross sections for excitation transfer: Q(2D3/2 → 2D5/2) = 8.1 × 10−13 cm2; Q(2D3/2 ← 2D5/2) = 5.5 × 1013 cm2; as well as [Formula: see text], the effective quenching cross section. The excitation transfer cross sections which are considered accurate to within ±20% are in the ratio predicted by the principle of detailed balancing.
The cross sections for excitation transfer between the 62P fine structure levels of rubidium, induced in collisions with ground state rubidium atoms, have been measured using a nitrogen laser pumped dye laser as the optical excitation source in a fluorescence experiment. Rubidium vapor was irradiated with each component of the 2P rubidium doublet in turn, and measurements of the relative intensities of fluorescence yielded the following cross sections: [Formula: see text] These results are consistent with the empirical relationship between the magnitude of the cross sections and the fine structure splitting that has previously been established for the alkalis.
The method of sensitized fluorescence has been employed to investigate the [Formula: see text] excitation transfer processes in cesium induced in collisions with ground state cesium atoms. The cesium vapor density was kept sufficiently low to enable the cross sections for the mixing process to be determined under single collision conditions and to ensure that radiation trapping and quenching were negligible. A nitrogen laser pumped dye laser was used to excite the cesium atoms to each of the 72P levels in turn and measurements of the relative intensities of fluorescence yielded the following cross sections: [Formula: see text] These results are consistent with the empirical relationship between the magnitude of the cross sections and the fine structure splitting that has previously been determined for the alkalis.