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Physical Review

Resonant Broadening of Double-Resonance and Level-Crossing Signals: Application to the P13 State in Mercury

A. Omont, J. Meunier

Published May 5, 1968• 78 citations
Publisher

Abstract

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 $6^{3}P_{1}$ 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.

DOI
10.1103/physrev.169.92

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Resonant Collision Broadening of the (6s26p7s)P13∘ State in Lead

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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; ${\ensuremath{\sigma}}_{\mathrm{al}}=7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ ${\mathrm{cm}}^{2}$ 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.

Physical Review•Aug 5, 1967•68 citations

Experimental Evidence of the Inversion of Angular Momentum During the Transfer of Excitation by Resonant Collisions in the 6P13 State of Mercury

B. Dodsworth, A. Omont

The zero-field level-crossing signal of even isotopes of natural Hg excited by resonant collisions from directly excited ${\mathrm{Hg}}^{198}$ atoms has been observed with circularly polarized light. The signal is proportional to the atomic "orientation" (mean value of the angular momentum of the excited atoms). The sense of this orientation is reversed when the excitation is transferred by collisions from ${\mathrm{Hg}}^{198}$ to other isotopes, as predicted by the theory.

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A New "Double Resonance" Method for Investigating Atomic Energy Levels. Application to Hg P 1 3

J. Brossel, Francis Bitter

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We have measured the broadening of ${\mathrm{Rb}}^{87}$ level-crossing signals due to collisions with ${\mathrm{Rb}}^{85}$. The depolarization or broadening rates for the $5^{2}P_{\frac{1}{2}}$ state orientation, the $5^{2}P_{\frac{3}{2}}$ state orientation and alignment, and the $5^{2}P_{\frac{3}{2}}$ 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 $5^{2}P_{\frac{3}{2}}$ state level-crossing signals are in 20% agreement with the theory. The measured $5^{2}P_{\frac{1}{2}}$ 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 $5^{2}P_{\frac{3}{2}}$ and $5^{2}P_{\frac{1}{2}}$ 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.

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Experimental Determination of the De-excitation Cross Section for the 6P13 State of Mercury by Thallium

B. C. Hudson, B. Curnutte

The de-excitation or quenching cross section of thallium for the $6^{3}P_{1}$ state of mercury has been obtained over a range of temperatures of 800 to 900\ifmmode^\circ\else\textdegree\fi{}C. Comparison of the resonance fluorescence from a mercury-thallium vapor mixture with the resonance fluorescence from a pure mercury vapor at the same number density, as determined by line absorption, allows the calculation of the de-excitation cross section. The present data together with Garrett's value of the lifetime of the $6^{3}P_{1}$ state of mercury and existing data on the vapor pressures of mercury and thallium were used to obtain values of the de-excitation cross section. Values of the cross section range from 108\ifmmode\pm\else\textpm\fi{}41 ${\mathrm{\AA{}}}^{2}$ at 800\ifmmode^\circ\else\textdegree\fi{}C to 80\ifmmode\pm\else\textpm\fi{}19 ${\mathrm{\AA{}}}^{2}$ at 900\ifmmode^\circ\else\textdegree\fi{}C. The corresponding quenching-rate coefficients varied from (5.1\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ ${\mathrm{cm}}^{3}$/sec at 800\ifmmode^\circ\else\textdegree\fi{}C to (4.0\ifmmode\pm\else\textpm\fi{}0.9)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ ${\mathrm{cm}}^{3}$/sec at 900\ifmmode^\circ\else\textdegree\fi{}C.

Physical Review•Aug 5, 1966•6 citations
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.
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.
The zero-field level-crossing signal of even isotopes of natural Hg excited by resonant collisions from directly excited Hg198{\mathrm{Hg}}^{198}Hg198 atoms has been observed with circularly polarized light. The signal is proportional to the atomic "orientation" (mean value of the angular momentum of the excited atoms). The sense of this orientation is reversed when the excitation is transferred by collisions from Hg198{\mathrm{Hg}}^{198}Hg198 to other isotopes, as predicted by the theory.
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.
Excitation of atoms in a vapor by polarized light produces unequal population of the magnetic sublevels of the excited state. The emitted optical resonance radiation is therefore partly polarized. The application of radiofrequency or microwave fields at a magnetic resonance frequency will induce transitions between sublevels of the excited state. The degree of polarization of the emitted optical resonance radiation is altered when the magnetic resonance condition is fulfilled. As suggested by Brossel and Kastler, this effect may be used to reveal the structure of the energy level. A detailed theory applicable to, and experiments on the 3P1^{3}P_{1}3P1​ state of all the isotopes of mercury are reported. The results obtained indicate that double resonance phenomena constitute a valuable new tool for investigating the structure of atomic energy levels. The mean life of the 3P1^{3}P_{1}3P1​ state is shown by observations on the resonance line widths to be 1.55\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ sec for all the isotopes. The ggg-factor of the 3P1^{3}P_{1}3P1​ state for isotopes with zero spin, measured in terms of the proton ggg-factor, is 1.4838\ifmmode\pm\else\textpm\fi{}0.0004.
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.
The de-excitation or quenching cross section of thallium for the 63P16^{3}P_{1}63P1​ state of mercury has been obtained over a range of temperatures of 800 to 900\ifmmode^\circ\else\textdegree\fi{}C. Comparison of the resonance fluorescence from a mercury-thallium vapor mixture with the resonance fluorescence from a pure mercury vapor at the same number density, as determined by line absorption, allows the calculation of the de-excitation cross section. The present data together with Garrett's value of the lifetime of the 63P16^{3}P_{1}63P1​ state of mercury and existing data on the vapor pressures of mercury and thallium were used to obtain values of the de-excitation cross section. Values of the cross section range from 108\ifmmode\pm\else\textpm\fi{}41 A˚2{\mathrm{\AA{}}}^{2}A˚2 at 800\ifmmode^\circ\else\textdegree\fi{}C to 80\ifmmode\pm\else\textpm\fi{}19 A˚2{\mathrm{\AA{}}}^{2}A˚2 at 900\ifmmode^\circ\else\textdegree\fi{}C. The corresponding quenching-rate coefficients varied from (5.1\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ cm3{\mathrm{cm}}^{3}cm3/sec at 800\ifmmode^\circ\else\textdegree\fi{}C to (4.0\ifmmode\pm\else\textpm\fi{}0.9)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ cm3{\mathrm{cm}}^{3}cm3/sec at 900\ifmmode^\circ\else\textdegree\fi{}C.