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Physical Review

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

J. Brossel, Francis Bitter

Published May 1, 1952• 373 citations
Publisher

Abstract

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 $^{3}P_{1}$ 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 $^{3}P_{1}$ 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 $g$-factor of the $^{3}P_{1}$ state for isotopes with zero spin, measured in terms of the proton $g$-factor, is 1.4838\ifmmode\pm\else\textpm\fi{}0.0004.

DOI
10.1103/physrev.86.308

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Depolarization of Resonance Radiation

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Depolarization and quenching of mercury resonance radiation are phenomena of quite different type. Depolarization is produced by two effects. With gases which quench by effecting the transition $^{3}P_{1}\ensuremath{\rightarrow}^{3}P_{0}$ upon collision with Hg\ensuremath{'} atoms, there exists a pronounced reverse transition $^{3}P_{0}\ensuremath{\rightarrow}^{3}P_{1}$ produced by collision with high speed molecules. Atoms which radiate without any collision emit polarized light under the conditions of the experiment. Those which become $^{3}P_{1}$ atoms after having existed as $^{3}P_{0}$ atoms have experienced a large number of collisions and have lost their orientation relative to the incident electric vector; accordingly they emit radiation polarized in random directions. The second depolarizing influence arises in collisions at distances exceeding the ordinary kinetic theory collision such as is described above, at which the distance is too great for a collision of the first or second type, but still small enough for the field of the gas atom to exert a perturbing influence on the orientation of the Hg\ensuremath{'} atom. Depolarization by ${\mathrm{H}}_{2}$ is an excellent example of the second influence while the first effect is sufficient to interpret the experimental data with the rare gases, the atomic fields of which decrease with a high power of the radial distance.

Physical Review•Sep 1, 1927•1 citation
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{10}^{\ensuremath{-}7}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.
In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.
Breit has derived formulae giving the polarization P(H)P(H)P(H) and the angle of maximum polarization $\ensuremath{\theta}$ of a resonance line showing hyperfine structure, as a function of a weak magnetic field applied in the direction of observation of the resonance radiation. The formulae give a means of estimating the effect of hyperfine structure on the calculation of the mean life $\ensuremath{\tau}$ of an excited atom from experiments on the magnetic depolarization and rotation of the plane of polarization of resonance radiation. The calculation has been carried through for the case of the resonance line of $\mathrm{Cd}(\ensuremath{\lambda}3261)$ and that of $\mathrm{Hg}(\ensuremath{\lambda}2537)$, and it is found that the differences between the value of $\ensuremath{\tau}$ calculated from hyperfine structure data and that calculated from $tan2\ensuremath{\theta}$ by the usual non-hyperfine structure method lie well within the experimental error. P(H)P0\frac{P(H)}{{P}_{0}}P0​P(H)​ is found to be practically the same whether hyperfine structure is taken into account or neglected. This is due to the fact that the greatest contribution of the polarization in these cases comes from the isotopes having no nuclear spin and the ggg-value for the upper state of these isotopes is larger than any other upper hyperfine structure state involved. The mean lives of the 73S17^{3}S_{1}73S1​ state of mercury have been recalculated from Richter's data on the polarization of stepwise radiation. The values of $\ensuremath{\tau}$ obtained by this method of calculation are 7.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ for $\ensuremath{\lambda}4047$, 1.69\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ for $\ensuremath{\lambda}4358$ and 1.53\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ for $\ensuremath{\lambda}5461$. A discussion of Richter's results is given.
A new technique of microwave spectroscopy is proposed for application to excited states of short lifetime. If atoms are excited by electron bombardment, closely-spaced energy levels may be unequally populated. The radiation emitted in decay to lower states may have an angular distribution and polarization character correlated with the direction of bombardment. When such atoms are acted on by radio-frequency fields, transitions may occur between excited states which cause an observable change in the pattern of decay radiation. An analysis is made of the possibility of applying such a method to a determination of the finestructure patterns (1snp)3PJ(J=0,1,2)(1snp)^{3}P_{J}(J=0, 1, 2)(1snp)3PJ​(J=0,1,2) of the helium atom. After a review of previous optical spectroscopic work and theory of this fine structure, an old unsolved mystery concerning the polarization of collision light is discussed. The theory of the Zeeman effect is worked out in a form applicable to the microwave experiments. Expected transition frequencies and rf matrix elements, intensity changes and shape of resonance curves, Stark effect and singlet-triplet mixing are also considered. An estimate is made of the signal to be expected in the experiment described in the following paper.
Calculations are made of the frequency, intensity, and polarization of the light emitted by an atom in a $^{2}P\ensuremath{-}^{2}S$ transition in a weak magnetic field having an oscillating component. Near resonance, or when the frequency of the oscillating component approaches the Larmor frequency of one of the two states involved in the radiation process, all of the quantities calculated are modified. Qualitatively similar results are to be expected for other transitions. Observations in very weak fields would be of particular interest because they would give information on nuclear spins as well as atomic ggg-factors. Under such conditions, the Zeemann components will in general not be resolvable. There will, however, be a change in the polarization of the edges of a spectral line at resonance. It is shown that very small changes in this polarization structure are theoretically detectable.
Abstract This work is an experimental study of the modulation which has been found in resonance radiation when the fluorescing vapour is subjected to static and radio-frequency magnetic fields, as in the double resonance experiment of Brossel & Bitter. The particular example chosen for study in this work also was the resonance line λ 2537 Å of mercury. The experimental observations are compared with the predictions of a theoretical treatment which has already been published. The phenomenon was studied under a variety of geometrical configurations. When the polarization of the exciting light allowed excitation to only one excited state (a component of a Zeeman multiplet), the depth of modulation was found to depend on the closeness to resonance of the frequency, ω0, of the radio-frequency field to the Larmor precessional frequency, ω = γH , in the static field H. When the polarization of the exciting light allowed excitation to more than one component of the multiplet, resonance effects were found in the depth of modulation and in the mean intensity of the fluorescent light at fields where the applied frequency was equal, not to the Larmor frequency alone, but to combinations of the Larmor frequency with the nutational frequency. From a quantum-mechanical point of view, these new phenomena are related to the interference effects which are found in resonance fluorescence when there is degeneracy between excited states: in the present case the degeneracy is induced by the radio-frequency field. The ease with which the geometrical conditions could be altered allowed the theory to be tested in considerable detail without quantitative assessment of the resonance line contours: nevertheless, a quantitative study was made of one particular feature. The predictions of the theory were confirmed at all points where they were tested.
Depolarization and quenching of mercury resonance radiation are phenomena of quite different type. Depolarization is produced by two effects. With gases which quench by effecting the transition $^{3}P_{1}\ensuremath{\rightarrow}^{3}P_{0}$ upon collision with Hg\ensuremath{'} atoms, there exists a pronounced reverse transition $^{3}P_{0}\ensuremath{\rightarrow}^{3}P_{1}$ produced by collision with high speed molecules. Atoms which radiate without any collision emit polarized light under the conditions of the experiment. Those which become 3P1^{3}P_{1}3P1​ atoms after having existed as 3P0^{3}P_{0}3P0​ atoms have experienced a large number of collisions and have lost their orientation relative to the incident electric vector; accordingly they emit radiation polarized in random directions. The second depolarizing influence arises in collisions at distances exceeding the ordinary kinetic theory collision such as is described above, at which the distance is too great for a collision of the first or second type, but still small enough for the field of the gas atom to exert a perturbing influence on the orientation of the Hg\ensuremath{'} atom. Depolarization by H2{\mathrm{H}}_{2}H2​ is an excellent example of the second influence while the first effect is sufficient to interpret the experimental data with the rare gases, the atomic fields of which decrease with a high power of the radial distance.