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Physical Review A

Breakdown of the impact approximation as seen in collision broadening at high densities of the (6p7s)P103 state of lead

Joshua B. Halpern, Ahmed Baghdadi, E. B. Saloman

Published Feb 1, 1974• 1 citation
Publisher

Abstract

The Hanle effect has been used to measure the resonant pressure broadening of the $(6p7s)^{3}P_{1}^{0}$ excited state of lead over a density range from ${10}^{14}$ to 4 \ifmmode\times\else\texttimes\fi{} ${10}^{16}$ atom/${\mathrm{cm}}^{3}$. Below ${10}^{16}$ atom/${\mathrm{cm}}^{3}$ the results agree with theories based on the impact approximation and the experimental results of Happer and Saloman. For densities above ${10}^{16}$ atom/${\mathrm{cm}}^{3}$ it is shown that the broadening should have the form $\overline{v}{\ensuremath{\sigma}}_{0}^{(L)}[N\ensuremath{-}\ensuremath{\beta}{N}^{2}]$, where $\overline{v}$ is the mean relative velocity of the atoms, ${\ensuremath{\sigma}}_{0}^{(L)}$ is the resonant-collision-broadening cross section for the L th multipole element of the excited-state density matrix, $N$ is the atomic density, and $\ensuremath{\beta}$ is a measure of the correlation of the atoms which represents the breakdown of the impact approximation. $\ensuremath{\beta}$ has been determined to be equal to 3.8(6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}18}$ ${\mathrm{cm}}^{3}$.

DOI
10.1103/physreva.9.668

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Orientation and alignment depolarization cross sections have been measured for the $(6{s}^{2}6p7s){^{3}P_{1}}^{\ensuremath{\circ}}$ excited state of lead. The cross sections are characteristic of resonance collision broadening; ${\ensuremath{\sigma}}_{\mathrm{al}}=7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm2{\mathrm{cm}}^{2}cm2 for ${v}_{\mathrm{rel}}=5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ cm/sec. The ratio of orientation broadening to alignment broadening was found to be $\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}=1.21(5)$. Expressions are derived for the signal shapes in Hanle-effect, optical-double-resonance, and light-beat experiments that show which components of the signals depend on orientation and alignment relaxation times, respectively.
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 63P16^{3}P_{1}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 change in the Hanle effect of the singlet resonance line of neutral barium has been studied over a wide range of density. The low density region has been used to confirm a lifetime of 8.37 ± 0.08 ns for the 6s6p1P1 level. We have determined the cross sections for the relaxation of the multipole moment of order 2 for collisions of the excited level with the ground level and with the metastable 6s5d1D2 level, and comparisons are made with the measured value of [Formula: see text] for the ground level with theoretical predictions.
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Collision broadening studies have been made of optical double resonance lines in cadmium. The results indicate that the collision frequency is velocity dependent, contrary to the usual theory of resonance self-broadening. This result supports the suggestion that the broadening results from interactions involving a number of intermediate states rather than only the initial and final states of the optical transition, because of the small oscillator strength (f=0.002f=0.002f=0.002) for transitions between the ${(5s)}^{2}^{1}S_{0}$ ground state and the excited state in question (5s5p)3P1(5s5p)^{3}P_{1}(5s5p)3P1​. The cross section in this case has a 1v‾1225\frac{1}{{{\overline{v}}_{12}}^{\frac{2}{5}}}v12​52​1​ velocity dependence, so the collision frequency varies as v‾1235{{\overline{v}}_{12}}^{\frac{3}{5}}v12​53​. Measurements show that under this assumption the self-broadening cross section for cadmium is ${\ensuremath{\sigma}}_{\mathrm{coll}}=(1.9\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\mathrm{cm}}^{2}/{{\overline{v}}_{12}}^{\frac{2}{5}},$ where v‾12{\overline{v}}_{12}v12​ is the average relative velocity in cm/sec. In the course of this work, the lifetime of the (5s,5p)3P1(5s, 5p)^{3}P_{1}(5s,5p)3P1​ state was redetermined and found to be (2.39\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec.
We have measured the broadening of Rb87{\mathrm{Rb}}^{87}Rb87 level-crossing signals due to collisions with Rb85{\mathrm{Rb}}^{85}Rb85. The depolarization or broadening rates for the 52P125^{2}P_{\frac{1}{2}}52P21​​ state orientation, the 52P325^{2}P_{\frac{3}{2}}52P23​​ state orientation and alignment, and the 52P325^{2}P_{\frac{3}{2}}52P23​​ state 58-G crossing were measured. Theoretical resonance-broadening depolarization rates for the electronic angular momentum, due to Carrington, Stacey, and Cooper, have been incorporated into calculations of the Hanle-effect signals in the presence of nuclear-spin coupling. The experimental broadening rates are corrected for a minor amount of coherence narrowing. The measured broadening rate for the three 52P325^{2}P_{\frac{3}{2}}52P23​​ state level-crossing signals are in 20% agreement with the theory. The measured 52P125^{2}P_{\frac{1}{2}}52P21​​ state broadening rate exceeds the theoretical by about a factor of 2. This discrepancy may be due to the action of the hyperfine interaction during these unusually long duration collisions. The natural lifetimes of the 52P325^{2}P_{\frac{3}{2}}52P23​​ and 52P125^{2}P_{\frac{1}{2}}52P21​​ states are determined from the low-density linewidth to be 27.0 \ifmmode\pm\else\textpm\fi{} 0.5 and 29.4 \ifmmode\pm\else\textpm\fi{} 0.7 nsec, respectively.