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Physical Review Letters

Zero-Field Quantum Beats in Lyman- β Radiation from Beam-Foil-Excited Hydrogen Atoms

Donald J. Lynch, C. W. Drake, M. J. Alguard, Clifford E. Fairchild

Published May 17, 1971• 21 citations
Publisher

Abstract

Zero-field quantum beats were observed in $\mathrm{L}\mathrm{y}\ensuremath{-}\ensuremath{\beta}$ emission (1026 \AA{}) from hydrogen atoms formed by beam-foil excitation, and the energy dependence of the magnetic-substate cross sections for $n=3$, $l=1$ states was determined for beam energies in the range from 230 to 500 keV/atom.

DOI
10.1103/physrevlett.26.1211

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Zero-field quantum beats were observed in Ly\ensuremath−\ensuremathβ\mathrm{L}\mathrm{y}\ensuremath{-}\ensuremath{\beta}Ly\ensuremath−\ensuremathβ emission (1026 \AA{}) from hydrogen atoms formed by beam-foil excitation, and the energy dependence of the magnetic-substate cross sections for n=3n=3n=3, l=1l=1l=1 states was determined for beam energies in the range from 230 to 500 keV/atom.
Intensity beats in the emission of $\mathrm{L}{\mathrm{y}}_{\ensuremath{\alpha}}$ from beam-foil excited hydrogen in various static electromagnetic field configurations have been studied. The observed beat frequencies agree with the calculated values, which are independent of the field directions. The beat amplitudes, however, show significant dependence on the field directions relative to the beam. The theory for emission of light from the decay of coherently excited states is applied in the sudden perturbation limit. Agreement with experiment can only be obtained under the assumption that the foil excitation generates initial coherent wave functions ${\ensuremath{\Psi}}_{\mathrm{I},\mathrm{I}\mathrm{I}}=\ensuremath{\alpha}|p,\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2}〉+\ensuremath{\beta}|s,\frac{1}{2},\ensuremath{\mp}\frac{1}{2}〉$, where ∣l,j,mj〉|l,j,{m}_{j}〉∣l,j,mj​〉 notation and the beam as quantization axis are used. The ratio $\frac{\ensuremath{\alpha}}{\ensuremath{\beta}}$ is then determined, which gives the ratio of the excitation cross section of the ppp to that of the sss states as $\frac{{\ensuremath{\sigma}}_{p}}{{\ensuremath{\sigma}}_{s}}>~4\ifmmode\pm\else\textpm\fi{}1$ at a beam energy of 200 (keV) per atom.
We have developed an experimental method for determining the initial density matrix of the foil-excited atoms. The excited hydrogen (n=2)(n=2)(n=2) atoms pass through a region of a variable electric field ($\ensuremath{-}200\mathrm{k}\mathrm{V}/\mathrm{m}$ to +200kV/m+200\mathrm{k}\mathrm{V}/\mathrm{m}+200kV/m), and the intensity of the Lyman-\ensuremath{\alpha} line (121.6 nm) emitted in a free space downstream is observed. By using a vacuum ultraviolet polarizer, the dependence of the intensities of the polarized components on the electric field, including the field-dependent quantum beats, was measured and it was numerically fitted to a calculation. Thus all the initial density matrix elements were determined in a single measurement. It was found that, in the energy range 100--180 keV, just after the excitation, the electron cloud has higher density in the front side of the ion and the electron probability current is backwards.
The creation of ML{M}_{L}ML​ alignment due to the foil excitation process is demonstrated with the observation of zero-field quantum beats in He $3^{3}P\ensuremath{-}2^{3}S$ 3880-\AA{}, hydrogen ${\mathrm{H}}_{\ensuremath{\alpha}}$, and hydrogen ${\mathrm{H}}_{\ensuremath{\beta}}$ emission.
An expression is given for the Stark-induced beat signal in the Lyman-$\ensuremath{\alpha}$ radiation from hydrogen atoms in a beam-foil experiment. This expression includes possible contributions to the beat signal from coherent excitation of SSS and PPP states in the beam-foil process. For the case where the electric field is applied parallel to the beam, the coherentexcitation contributions can be separated experimentally from those resulting purely from coherence produced by the electric field, by simply reversing the direction of the electric field.
Within the limits set by our experimental apparatus, large-amplitude zero-field oscillations of H fine-structure amplitudes treated in a recent letter of Macek were not observed in polarization---versus---flight-path measurements on ${\mathrm{H}}_{\ensuremath{\beta}}$, ${\mathrm{H}}_{\ensuremath{\gamma}}$, and ${\mathrm{Ly}}_{\ensuremath{\alpha}}$ emissions from suddenly excited H atoms (50- and 150-keV incident protons). Random initial phases for orbital and magnetic substates and approximately equal magnetic substate populations are indicated, in contrast to binary electron capture in gases. A successful test of the theoretical polarization of 2s2s2s Stark quench radiation was also made.