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Physical Review A

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

Ivan A. Sellin

Published Apr 1, 1971• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.3.1512

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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.
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.
A more extensive analysis of the effects of different assumptions about initial state populations is added to a previous paper on the coherent excitation of hydrogen fine structure by foils. It is found that the previously postulated alignment of angular momenta perpendicular to the beam direction is a sufficient but not necessary assumption; an alternative assumption that the broad lll-state distribution of the collision products has a maximum for ddd states also matches the experimental traces adequately. A method of obtaining initial state populations in a manner which suppresses the corrections required for cascade effects is discussed. The method avoids the errors of extrapolating decay-curve fits.
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.
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.
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.