1
Measured Zeeman Photodetachment Transition
Strengths
A. K. Langworthy, D. M. Pendergrast, J. N.
Yukich, Davidson College, Davidson, North Carolina
Abstract
We have probed the relative weight of the first
Zeeman transition in photodetachment from O- and
S- at the 2P3/2 ? 3P2 detachment threshold, using
laser light polarized perpendicular to a 1-T
field. We find a non-zero transition strength at
the first threshold, a clear discrepancy with
previously published theory based on LS coupling
in the ion and the atom. Our results agree,
however, with other work published on detachment
from Se-.
Background
Detachment in Magnetic Fields
Ion trap apparatus, showing UHV vacuum, 2.0
Tesla electromagnet and magnet power supply.
Optical apparatus, showing diode laser MOPA
in foreground and wavemeter electro-optics.

• X- photon ? X e-
• Considered as ½ of an electron-atom collision.
• Minimum energy needed to detach is called the
• electron affinity, analogous to photoelectric
  effect.
• Electron detaches as plane wave into continuum.

Example Data

• Departing electron executes cyclotron motion in
  field.
• Motion in plane perpendicular to B is quantized
  to
• Landau levels separated by cyclotron ?
  eB/me.
• For typical B 1.0 Tesla, ? 30 GHz, period
  36 ps.
• Electron revisits atomic core once every
  cyclotron period.
• Motion along axis of field is continuous,
  non-quantized.
• Quantized Landau levels add structure to
  detachment
• cross section. Structure results from electron
  wave
• function interfering with itself as it revisits
  core.

Magnetic Structure of S S-

• To the left we see the magnetic structure of S
  and S-at a magnetic field of roughly 1 Tesla.
• The S and S- states are split by the Zeeman
  effect. Thefirst Zeeman transition is 2P3/2
  mJ -3/2 ? 3P2 mJ-2

Motivation
Detachment scan showing ratio of S- ions
surviving laser illumination near the 2P3/2 ?
3P2 threshold (electron affinity). The first
Zeeman threshold is responsible for the initial
sharpincrease in detachment probability.

• Previous results, notably by Elmquist et al 4,
  have shown a clear departure from the
  conventionally accepted theory of Blumberg,
  Itano, and Larson1-2 hereafter referred to as
  BIL. While BIL theory has produced good
  agreements with a number of experimental
  results, in certain cases it does not.
• As O- and S- are isoelectronic with the Se-
  species used for the results of Elmquist et al,
  we want to know how well the first Zeeman
  threshold agrees with BIL theory for O- and S-
  detachment.
• The experiments done by Elmquist et al were done
  at a very high magnetic field. Our experiment is
  partially an attempt to determine if the
  disagreement with BIL theory is manifested at a
  lower field strength.
• Spectroscopic measurements are influenced by
  knowledge of Zeeman transition strengths.
  Therefore, knowledge of how the Zeeman levels
  behave experimentally for O- and S- will aid in
  properly analyzing future experiments.

 
Conclusions

• By fitting BIL theory to the data with
  adjustable parameters, we find for both ion
  species a non-zero strength for the first
  Zeeman transition, consistent with that of Ref.
  4. BIL theory predicts zero transition
  strength for this threshold.
• Although the first Zeeman threshold is not
  visually resolvable in our data, our results show
  that the discrepancy with the BIL theory is
  numerically resolvable even at the lower magnetic
  fields used in our experiment.
• Our results strongly suggest that the
  discrepancy discovered by Elmquist et al 4 for
  Se- was not somehow an artifact of the high
  magnetic field used, or of the ion trap used, or
  unique to the Se- ion.
• The observed discrepancies suggest an underlying
  failure of the BIL theory with regard to relative
  strengths of the Zeeman transitions.

Experimental Technique

• Ions produced by dissociative attachment from a
  carrier gas, using hot tungsten filament.
• Ions trapped and stored in Penning ion trap (see
  figures below), with B 1.0 Tesla.3
• Relative detachment cross section probed with
  highly-tunable, single-mode laser. For O-, an
  amplified diode laser at 850nm is used. For S-,
  a ring dye laser tuned to 598nm with a
  birefringent filter and solid etalons is used.
  
• Least-squares fitting of the BIL theory to the
  data, using adjustable parameters, determines the
  strength of Zeeman transitions.

Active Layer
Future Work

• Evaporative cooling of trapped ion population
  by precise control of the cooling of the ion
  sample, theory dictates that we can improve
  the spectroscopic resolution of Landau and Zeeman
  levels. This work is already underway at the
  time of this writing.
• Replace hot tungsten filament with cold
  field-emission electron source to reduce further
  the trapped ion
• population temperature.
• Possible analysis of other ion species.

Apparatus
References

•  
• W. A. M. Blumberg, R. M. Jopson, and D. J.
  Larson, Phys. Rev. Lett. 40, 1320 (1978).
• W. A. M. Blumberg, W. M. Itano, and D. J. Larson,
  Phys. Rev. A 19, 139 (1979).
• D. J. Larson and R. C. Stoneman, Phys Rev. A 31,
  2210 (1985).
• R. E. Elmquist, C. J. Edge, G. D. Fletcher, and
  D. J. Larson, Phys. Rev. Lett. 58, 333 (1987).
• H. F. Krause, Phys. Rev. Lett. 64, 1725 (1990).
• H. Wong, A. R. P. Rau, and C. H. Greene, Phys.
  Rev. A 37, 2393 (1988).
• I. I. Fabrikant, Phys. Rev. A 43, 258 (1991).
• O. H. Crawford, Phys. Rev. A 37 2432 (1988).
• L. D. Landau and E. M. Lifshitz, Quantum
  Mechanics Non-relativistic Theory
  (Addison-Wesley, 1991).
• I. Y. Kiyan and D. J. Larson, Phys. Rev. Lett.
  73, 943 (1994).
• J. N. Yukich, C. T. Butler, and D. J. Larson,
  Phys. Rev. A 55, R3303 (1997).
• D. M. Pendergrast and J. N. Yukich, Phys. Rev. A
  67, 062721 (2003).
• N. B. Mansour, C. J. Edge, and D. J. Larson,
  Nuclear Instrum. and Methods in Physics Res. B31,
  313 (1988).
• E. P. Wigner, Phys. Rev. 73, 1002 (1948).
• L. G. Christophorou, Electron-Molecule
  Interactions and Their Applications, vol. 1
  (Academic Press, 1984).
• A. K. Langworthy, D. M. Pendergrast, and J. N.
  Yukich, Phys. Rev. A 69, 025401 (2004)
•  

• Overall equipment layout
• Single-mode tunable laser used in experiments.
• Beam output from laser split to Fabry-Perot
  spectrum analyzer and
• traveling Michelson-interferometer wavemeter.
• Computer controlled shutter gives precise beam
  control into trap, while a photodiode measures
  light flux to compensate for beam variation.

• Penning ion trap system
• Trap consists of three hyperbolic electrodes
  coaxial with B field.
• Biased trap endcaps form nearly-harmonic axial
  potential well.
• Heterodyne detection system measures relative
  trapped ion
• population before and after laser
  illumination.

Acknowledgements

• This work has been supported by
• Research Corporation
• Davidson College
• ACS Petroleum Research Fund
• We would like to thank R.C. Stoneman for
  providing some of the S- data for this work.