Abstract

We have measured the radiative lifetimes of the 4S, 4D, 4F, 5S, 5P, 5D, and 5F states in singly ionized helium using the high-energy atomic-beam technique. The measured values of the lifetimes are in excellent agreement with those calculated for hydrogenic atoms. Extensions of the experimental technique to the measurement of excitation cross sections and fine-structure splittings are discussed.

© 1967 Optical Society of America

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References

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  1. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Academic Press, Inc., New York, 1957).
    [Crossref]
  2. L. R. Maxwell, Phys. Rev. 38, 1664 (1931).
    [Crossref]
  3. Note added in proof. We have recently become aware of another measurement of the lifetime of the 4S state giving the result (1.36±0.20)×10−8 sec. [L. L. Hatfield, thesis, University of Arkansas (1967)].
    [Crossref]
  4. L. Kay, Phys. Letters 5, 36 (1963); Proc. Phys. Soc. (London) 85, 163 (1965).
    [Crossref]
  5. S. Bashkin, Nucl. Instr. & Methods 28, 88 (1964); S. Bashkin, L. Heroux, and J. Shaw, Phys. Letters 13, 229 (1964); A. S. Goodman and D. T. Donahue, Phys. Rev. 141, 1 (1966); W. S. Bickel and S. Bashkin, Phys. Letters 20, 488 (1966); S. Bashkin, D. Fink, P. R. Malmberg, A. B. Meinel, and S. G. Tilford, J. Opt. Soc. Am. 56, 1064 (1966); W. S. Bickel and A. S. Goodman, Phys. Rev. 148, 1 (1966).
  6. The foils are obtained from the Yissum Research and Development Company, Hebrew University, Jerusalem, Israel.
  7. Survey work using an Astro Mechanics f/2 Meinel spectrograph, borrowed from the U. S. A. F. Aerospace Research Laboratory, had indicated that the spectral lines studied could be sufficiently isolated by moderately narrow-band interference filters (with the half-width of the passband on the order of 70 Å).
  8. Straight-forward photon-counting techniques would have yielded a pulse rate too rapid for certain of the scalers available to us and for a projected on-line computerized data-acquisition and analysis system.
  9. The uniqueness of the minimum in ∑ R2, which we find, can be questioned. To the best of our knowledge, there is no proof that any fitting procedure yields a unique fit to a sum of exponentials. The initial values of the lifetime used in our iterative program differed from run to run and were within about ±30% of the calculated values.
    [Crossref]
  10. F. L. Roesler and J. E. Mack, Phys. Rev. 135, 57 (1964).
  11. G. F. Drukarev, The Theory of Electron-Atom Collisions (Academic Press Inc., New York, 1965).
    [Crossref]
  12. S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965).
    [Crossref]
  13. See, e.g., R. T. Robiscoe and B. L. Cousens, Phys. Rev. Letters 17, 69 (1966) and references therein.
    [Crossref]
  14. Another variation of the high-energy atomic-beam technique, which makes use of Stark mixing in a static electric field, has been used by C. Y. Fan, M. Garcia-Munoz, and I. A. Sellin, Phys. Rev. Letters 15, 15 (1965), to measure the Lamb shift in Li iii.

1966 (1)

See, e.g., R. T. Robiscoe and B. L. Cousens, Phys. Rev. Letters 17, 69 (1966) and references therein.
[Crossref]

1965 (2)

Another variation of the high-energy atomic-beam technique, which makes use of Stark mixing in a static electric field, has been used by C. Y. Fan, M. Garcia-Munoz, and I. A. Sellin, Phys. Rev. Letters 15, 15 (1965), to measure the Lamb shift in Li iii.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965).
[Crossref]

1964 (2)

S. Bashkin, Nucl. Instr. & Methods 28, 88 (1964); S. Bashkin, L. Heroux, and J. Shaw, Phys. Letters 13, 229 (1964); A. S. Goodman and D. T. Donahue, Phys. Rev. 141, 1 (1966); W. S. Bickel and S. Bashkin, Phys. Letters 20, 488 (1966); S. Bashkin, D. Fink, P. R. Malmberg, A. B. Meinel, and S. G. Tilford, J. Opt. Soc. Am. 56, 1064 (1966); W. S. Bickel and A. S. Goodman, Phys. Rev. 148, 1 (1966).

F. L. Roesler and J. E. Mack, Phys. Rev. 135, 57 (1964).

1963 (1)

L. Kay, Phys. Letters 5, 36 (1963); Proc. Phys. Soc. (London) 85, 163 (1965).
[Crossref]

1931 (1)

L. R. Maxwell, Phys. Rev. 38, 1664 (1931).
[Crossref]

Bashkin, S.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965).
[Crossref]

S. Bashkin, Nucl. Instr. & Methods 28, 88 (1964); S. Bashkin, L. Heroux, and J. Shaw, Phys. Letters 13, 229 (1964); A. S. Goodman and D. T. Donahue, Phys. Rev. 141, 1 (1966); W. S. Bickel and S. Bashkin, Phys. Letters 20, 488 (1966); S. Bashkin, D. Fink, P. R. Malmberg, A. B. Meinel, and S. G. Tilford, J. Opt. Soc. Am. 56, 1064 (1966); W. S. Bickel and A. S. Goodman, Phys. Rev. 148, 1 (1966).

Bethe, H. A.

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Academic Press, Inc., New York, 1957).
[Crossref]

Bickel, W. S.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965).
[Crossref]

Cousens, B. L.

See, e.g., R. T. Robiscoe and B. L. Cousens, Phys. Rev. Letters 17, 69 (1966) and references therein.
[Crossref]

Drukarev, G. F.

G. F. Drukarev, The Theory of Electron-Atom Collisions (Academic Press Inc., New York, 1965).
[Crossref]

Fan, C. Y.

Another variation of the high-energy atomic-beam technique, which makes use of Stark mixing in a static electric field, has been used by C. Y. Fan, M. Garcia-Munoz, and I. A. Sellin, Phys. Rev. Letters 15, 15 (1965), to measure the Lamb shift in Li iii.

Fink, D.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965).
[Crossref]

Garcia-Munoz, M.

Another variation of the high-energy atomic-beam technique, which makes use of Stark mixing in a static electric field, has been used by C. Y. Fan, M. Garcia-Munoz, and I. A. Sellin, Phys. Rev. Letters 15, 15 (1965), to measure the Lamb shift in Li iii.

Hatfield, L. L.

Note added in proof. We have recently become aware of another measurement of the lifetime of the 4S state giving the result (1.36±0.20)×10−8 sec. [L. L. Hatfield, thesis, University of Arkansas (1967)].
[Crossref]

Kay, L.

L. Kay, Phys. Letters 5, 36 (1963); Proc. Phys. Soc. (London) 85, 163 (1965).
[Crossref]

Mack, J. E.

F. L. Roesler and J. E. Mack, Phys. Rev. 135, 57 (1964).

Maxwell, L. R.

L. R. Maxwell, Phys. Rev. 38, 1664 (1931).
[Crossref]

Robiscoe, R. T.

See, e.g., R. T. Robiscoe and B. L. Cousens, Phys. Rev. Letters 17, 69 (1966) and references therein.
[Crossref]

Roesler, F. L.

F. L. Roesler and J. E. Mack, Phys. Rev. 135, 57 (1964).

Salpeter, E. E.

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Academic Press, Inc., New York, 1957).
[Crossref]

Sellin, I. A.

Another variation of the high-energy atomic-beam technique, which makes use of Stark mixing in a static electric field, has been used by C. Y. Fan, M. Garcia-Munoz, and I. A. Sellin, Phys. Rev. Letters 15, 15 (1965), to measure the Lamb shift in Li iii.

Wangsness, R. K.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965).
[Crossref]

Nucl. Instr. & Methods (1)

S. Bashkin, Nucl. Instr. & Methods 28, 88 (1964); S. Bashkin, L. Heroux, and J. Shaw, Phys. Letters 13, 229 (1964); A. S. Goodman and D. T. Donahue, Phys. Rev. 141, 1 (1966); W. S. Bickel and S. Bashkin, Phys. Letters 20, 488 (1966); S. Bashkin, D. Fink, P. R. Malmberg, A. B. Meinel, and S. G. Tilford, J. Opt. Soc. Am. 56, 1064 (1966); W. S. Bickel and A. S. Goodman, Phys. Rev. 148, 1 (1966).

Phys. Letters (1)

L. Kay, Phys. Letters 5, 36 (1963); Proc. Phys. Soc. (London) 85, 163 (1965).
[Crossref]

Phys. Rev. (2)

L. R. Maxwell, Phys. Rev. 38, 1664 (1931).
[Crossref]

F. L. Roesler and J. E. Mack, Phys. Rev. 135, 57 (1964).

Phys. Rev. Letters (3)

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965).
[Crossref]

See, e.g., R. T. Robiscoe and B. L. Cousens, Phys. Rev. Letters 17, 69 (1966) and references therein.
[Crossref]

Another variation of the high-energy atomic-beam technique, which makes use of Stark mixing in a static electric field, has been used by C. Y. Fan, M. Garcia-Munoz, and I. A. Sellin, Phys. Rev. Letters 15, 15 (1965), to measure the Lamb shift in Li iii.

Other (7)

G. F. Drukarev, The Theory of Electron-Atom Collisions (Academic Press Inc., New York, 1965).
[Crossref]

Note added in proof. We have recently become aware of another measurement of the lifetime of the 4S state giving the result (1.36±0.20)×10−8 sec. [L. L. Hatfield, thesis, University of Arkansas (1967)].
[Crossref]

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Academic Press, Inc., New York, 1957).
[Crossref]

The foils are obtained from the Yissum Research and Development Company, Hebrew University, Jerusalem, Israel.

Survey work using an Astro Mechanics f/2 Meinel spectrograph, borrowed from the U. S. A. F. Aerospace Research Laboratory, had indicated that the spectral lines studied could be sufficiently isolated by moderately narrow-band interference filters (with the half-width of the passband on the order of 70 Å).

Straight-forward photon-counting techniques would have yielded a pulse rate too rapid for certain of the scalers available to us and for a projected on-line computerized data-acquisition and analysis system.

The uniqueness of the minimum in ∑ R2, which we find, can be questioned. To the best of our knowledge, there is no proof that any fitting procedure yields a unique fit to a sum of exponentials. The initial values of the lifetime used in our iterative program differed from run to run and were within about ±30% of the calculated values.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

The layout of the experiment indicating the accelerator, the velocity-selection magnet, the moving foil, the interference filter and photomultiplier detection system, the Faraday cup, and the detection circuitry. Both the spectral line intensity and the beam intensity are integrated in a digital mode. The scalers are gated simultaneously by pulses from the foil drive mechanism.

Fig. 2
Fig. 2

Results of a run examining the 4686 Å (n = 4 to n = 3) transition. I is the ratio of the corrected photomultiplier signal to the beam-intensity signal. Solid points represent the experimental data and the solid straight lines indicate the contributions to the curve from the 4S, 4D, and 4F states. The 4P state apparently decays to an undetectable level in the first 2 cm after the foil. Extension of the various contributions back to the approximate foil position is indicated by the dashed lines.

Fig. 3
Fig. 3

Results of a run examining the 3203 Å (n = 5 to n = 3) transition. I is the ratio of the corrected photomultiplier signal to the beam-intensity signal. Solid points represent the experimental data and the solid straight lines indicate the contributions to the curve from the 5S, 5P, 5D, and 5F states. Extension of the various contributions back to the approximate foil position is indicated by the dashed lines.

Fig. 4
Fig. 4

Examples of variational analyses of the “best fit” values of two parameters. ∑ R2 is the sum of the squares of the residuals. The solid line represents N, the experimentally expected value of ∑ R2. The dashed line represents variations around the best-fit value of the 4S lifetime in a particular run; the dotted line represents variations around the best-fit value of the 4P lifetime in the same run. The 4S lifetime is said to be determined to ±3% and the 4P lifetime is said to be undetermined. (In this run the 4P amplitude was less than 0.5% of the total signal 2 cm downstream from the foil.)

Fig. 5
Fig. 5

An example of the effect of varying the lifetimes used in the fitting program. The figure is an expanded view of a segment of an n = 4 decay curve. I is the ratio of the corrected photomultiplier signal to the beam-intensity signal. Data points are shown with their appropriate error bars. The solid line indicates the decay curve generated by the “best fit” values found by the fitting program. The dashed curve indicates the decay curve generated by increasing the lifetime of the 4D state by 10% over the “best fit” value.

Tables (1)

Tables Icon

Table I Summary of the lifetime measurements in He ii.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

i D R i 2 = i D ( j n A j e - t i / τ j - S i ) 2 ,
n i = 0 A i e - t / τ i d t = A i τ i ,