The lifetime, coherence narrowing, and collision broadening of the
72S21 excited state of atomic thallium has been studied by the technique of zero-field level-crossing spectroscopy. The lifetime of the
72S21 state is determined to be 7.55 (0.08) nsec. The full coherence-narrowing effect gave a branching ratio, from
F=0 of
72S21 to the ground state, of 43%. The cross section for thallium-thallium resonance-broadening collisions is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{5.38(0.49)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$
cm2. The effect of 426-torr helium on the thallium lifetime, coherence narrowing, and resonance broadening was also investigated. From the low-thallium-density region the cross section for helium depolarization of the thallium
72S state is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{H}\mathrm{e}}\ensuremath{\cong}\frac{7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}}{\overline{v}}$
cm2. There is also indication of a buildup of population in the metastable
62P23 thallium state. From the data, the cross section for the process $\mathrm{Tl}(6^{2}P_{\frac{3}{2}})\ensuremath{\rightarrow}\mathrm{Tl}(6^{2}P_{\frac{1}{2}})$ by helium collisions is $\ensuremath{\sigma}\ensuremath{\simeq}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$
cm2. The Tl branching ratio in the presence of helium is 39%. It was also found that the thallium-thallium resonance-broadening cross section is ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{4.04(0.32)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$
cm2 in the presence of 426 torr of helium. In the presence of 113 torr of He, the resonance-broadening cross section was found to be ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{T}\mathrm{l}}=\frac{5.22(0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}}{\overline{v}}$
cm2. In the case of Ar as the buffer gas, ${\ensuremath{\sigma}}_{\mathrm{T}\mathrm{l}\ensuremath{-}\mathrm{A}\mathrm{r}}=\frac{8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}}{\overline{v}}$
cm2.
A method is developed for calculating the cross section for line broadening in the limiting case in which important collisions may be considered to occur very rapidly with respect to the periods corresponding to the transitions in question. This method is essentially an extension of the familiar "sudden" approximation; reference is made throughout to the particular example of optical double resonance only for definiteness and because there are available experimental results for comparison with the theory. Assuming the impact model and considering the case when the energy levels in question are well resolved with respect to their width, an exact expression is found for resonant self-broadening in the usual weak rf field limit of interest in double resonance. For the case of very small oscillator strengths for the optical transition (intercombination lines), the resonant broadening becomes sufficiently small so that second-order, intermediate-state processes dominate, and approximations must be made to effect sums over intermediate states. Here the broadening is of the same sort as foreign gas broadening, and in many cases of interest, the approximations can be made in a sufficiently realistic manner to obtain useful expressions for the broadening. It is shown that the resonant cross section and this "second-order" cross section are not additive, but that the one which is larger dominates the total cross sections very strongly. Finally, we evaluate explicitly the self-broadening and foreign gas broadening (by the noble gases) of double resonance lines in the group II metals and the self-broadening in the optical spectrum of helium. In all cases our theoretical predictions are in good agreement with measurements which have been made.
A general theory of line broadening is used to study the effects of collisions on absorption line shapes when self-broadening is important. Special attention is focused on the role of processes in which an excited atom transfers its electronic excitation to an unexcited atom; it is this process which distinguishes self-broadening from foreign-gas broadening. Several forms for the absorption rate are presented corresponding to particular assumptions about the amplitudes associated with this phenomenon. For example, one approximation leads to a generalized Lorentz-Lorenz law in which the one-atom polarizability is replaced by one that accounts for line broadening. Finally, the importance of many-body effects in the calculation of the linewidth is briefly discussed to determine when simple impact theories are applicable.
A detailed calculation of the relaxation matrix of resonance atomic states by resonant collisions is carried out in the semiclassical impact theory. The validity of the different approximations is discussed. These results have been tested by observing self-broadening of level-crossing curves in high field and in zero field, in the
63P1 state in mercury. Observation of these signals at high pressures is very difficult with a pure isotope because of strong absorption and trapping of resonance light in the vapor; it is made very easy by observing level-crossing signals of one isotope in a very low concentration in the vapor of another isotope. Collisions between the different pairs of mercury isotopes have been thus systematically studied. Results are in excellent agreement (10%) with theory, both for the absolute value of cross sections and for the ratio of orientation broadening to alignment broadening.
The shapes of the thallium (Tl) 535- and 377.6-nm resonance lines broadened by 500-1500 Torr of noble gases have been measured at 743 K. The reported normalized emission intensities yield absorption coefficients in absolute units for all portions of the line. The shift and broadening of the Lorentzian-shaped line cores, the wavelengths of the transition to non-Lorentzian wings, wing shapes, and satellite positions, shapes, and intensities are reported. As an example, a pair of excited and ground-state interaction potentials are given for the Xe case to explain the shift, width, and intensities in all portions of the line wings.
General expressions are derived for the spectral line shapes of resonance absorption and scattering of coherent radiation in collision-broadened gases, taking into account effects of coherent excitation of two or more atoms (or molecules), as steady-state solutions of a hierarchy of master equations described in a previous publication (paper I). Coupling between the coherent motions of the atoms, provided by a Bethe-Salpeter---type effective interaction, in the binary-collision approximation, forms the essential mechanism for introducing cooperative coherent effects into the steady-state spectra. Explicit expressions are given for the effects of two-atom coherence in the binary-collision approximation, in which the Bloch-type dressed-atom self-energy superoperator is modified by the presence of collisions in which both atoms retain memory of their coherent propagation before the collision. The self-energies include the effects of resonance exchange symmetrization in self-broadening, and are renormalized by the coincidence of radiative transitions during the collisions. The impact (near-resonance) and the quasistatic (line-wing) limits of the applied-frequency detunings are discussed. In the quasistatic limit, coherent many-atom excitations become irrelevant; however, interactions of both collision partners with the radiation during the collision accounts for such phenomena as collision-induced absorption or radiative collisions. In the impact limit, the inclusion of the Bethe-Salpeter interactions allows for the appearance of two-atom resonances. Magnitude estimates of these effects are discussed. Effects of higher-rank (many-body) coherences are formally discussed with the help of a diagrammatic method, leading into implicit bootstrap equations that can be solved by iterative or other procedures.