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Physical Review A

Relative Orbital and Magnetic Substate Amplitudes in Single-Foil Excitation of Fast Hydrogen Atoms

I. A. Sellin, John A. Biggerstaff, P. M. Griffin

Published Aug 1, 1970• 37 citations
Publisher

Abstract

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 $2s$ Stark quench radiation was also made.

DOI
10.1103/physreva.2.423

Related papers

Comment on Relative Magnetic Substate Amplitudes in Foil Excitation of Fast Hydrogen Atoms

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If the particle-foil interaction potential governing production of H atoms coherently excited by passage through thin foils obeys the $\mathrm{LS}$ coupling scheme applied by Macek (conservation of $z$ components of total orbital and spin angular momenta of the entire particle-foil system, and incoherence of final states of foil constituents), the ad hoc assumption that random phases prevail among the hydrogenic magnetic substate amplitudes invoked in the interpretation of certain recent experiments is avoided. Arguments concerning relative phases of states of different orbital angular momentum are unaffected.

Physical Review A•Apr 1, 1971•1 citation

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Zero-Field Intensity Oscillations Following Impulsive Excitation of Hydrogen

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In a beam-foil experiment, we have observed zero-field oscillations of approximately 25% in the intensity of ${\mathrm{H}}_{\ensuremath{\beta}}$ radiation polarized parallel to the beam. An unmodulated decay is observed when a signal proportional to the total intensity is examined. Our observations substantiate Macek's theory of coherent decay from fine-structure levels.

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

Donald J. Lynch, C. W. Drake, M. J. Alguard +1 more

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.

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Stark-Induced Quantum Beats in H L Y α Emission

H. J. Andrä

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 $|l,j,{m}_{j}〉$ 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 $p$ to that of the $s$ 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.

Physical Review A•Dec 1, 1970•42 citations
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 H\ensuremathβ{\mathrm{H}}_{\ensuremath{\beta}}H\ensuremathβ​, H\ensuremathγ{\mathrm{H}}_{\ensuremath{\gamma}}H\ensuremathγ​, and Ly\ensuremathα{\mathrm{Ly}}_{\ensuremath{\alpha}}Ly\ensuremathα​ 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.
If the particle-foil interaction potential governing production of H atoms coherently excited by passage through thin foils obeys the LS\mathrm{LS}LS coupling scheme applied by Macek (conservation of zzz components of total orbital and spin angular momenta of the entire particle-foil system, and incoherence of final states of foil constituents), the ad hoc assumption that random phases prevail among the hydrogenic magnetic substate amplitudes invoked in the interpretation of certain recent experiments is avoided. Arguments concerning relative phases of states of different orbital angular momentum are unaffected.
Protons with velocities ranging from 3.2 \ifmmode\times\else\texttimes\fi{} 108{10}^{8}108 to 6.3 \ifmmode\times\else\texttimes\fi{} 108{10}^{8}108 cm/sec were passed through a carbon foil producing excited hydrogen atoms which decayed in flight after emergence. With the foil in magnetic fields from 2 to 25 G, the lines ${\mathrm{H}}_{\ensuremath{\alpha}}$ through ${\mathrm{H}}_{\ensuremath{\epsilon}}$ showed periodic intensity fluctuations due to Stark mixings of fine-structure levels caused by motional electric fields (6-158 V/cm). An extension of the Bethe-Lamb theory of Stark quenching provides good agreement between a small number of theoretically dominant frequencies and the measured fluctuation frequencies. Apparent discrepancies between theory and experiment noted by other experimenters are shown to be removed by our calculations except in one measurement on ${\mathrm{Ly}}_{\ensuremath{\alpha}}$. The necessity of using double foils postulated in the previous work is discussed. Our analysis suggests the preferential alignment of the final-state angular momenta perpendicular to the beam direction. Reasons for this alignment are given.
Hydrogen atoms are excited into high Rydberg states following fast proton impact on a thin carbon foil. The effects of various electromagnetic fields on these atoms are observed by measuring the integral ionization yield in an additional constant electric field. These experiments reveal oscillations in that yield, regularly spaced as a function of electric field. A model is outlined that quantitatively describes the observed field dependence. This new phenomenon indicates selective excitation of the Stark substates.
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=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.