Resolving Zeeman Transitions of the Negative Sulfur Ion Using Photodetachment Spectroscopy

J.E. Wells, Davidson College, Davidson, North Carolina

Abstract

Photodetachment from the negative sulfur ion in a magnetic field is a well studied phenomenon at the 2 P 3/2 → 3 P 2 transition, known as the electron affinity. It is modeled using the Blumberg, Itano, Larson (BIL) Theory. The goal of this work is to apply the BIL theory’s prediction to the less studied 2 P 1/2 → 3 P 2 transition. A Penning ion trap was used to trap the ions and photodetachment was achieved using a continuous wave tunable dye laser. For the first time, structure due to the magnetic field in the detachment cross-section was observed at this transition. For the first time at any transition using a 1.0-T magnetic field, evidence of individual Zeeman levels was observed.

Results Background

• The negative sulfur ion has 2 bound states: 2 P 3/2 and 2 P 1/2 • The ground state of the neutral sulfur atom is part of an inverted triplet: 3 P 2 3 P 1 , 3 P 0 . (lowest state), A plot showing the fraction of ions surviving detachment as a function of photon energy. Notice that the fraction of ions surviving does not simply decrease with photon energy as it would in the absence of a magnetic field. Instead there is structure caused by a combination of the Zeeman transitions and the quantized orbits of the freed electron. The black arrows show the locations of the Zeeman transitions suggested by the data. The table below compares the Zeeman transitions measured in the experiment to the theoretical values.

Transition 1 2 3 4 Experimental

Frequency (cm-1)

Spacing 16269.46

16269.70

16269.89

16270.13

.24

.19

.24

Theoretical

Frequency (cm-1)

Spacing 16269.60

16269.83

16269.99

16270.22

.23

.16

.23

Experimental Theoretical

Frequency (cm-1)

-0.14

-0.13

-0.10

-0.09

Zeeman Effect

•In the absence of a magnetic field, the energy levels which make up the 2 P 1/2 and 3 P 2 states are degenerate.

•In the presence of an external magnetic field the 2 P 1/2 and 3 P 2 states split into 4 and 5 levels respectively. •Instead of a single transition there are several transitions between these states. Which transitions are allowed is determined by conservation of momentum.

σ σ σ σ σ σ σ σ π π π π Polarization ½ ½ ½ ½ - ½ - ½ - ½ - ½ Initial Z Component of Angular Momentum of Ion ½ ½ - ½ - ½

Active Layer

2 1 0 -1 1 0 -1 -2 1 0 0 -1 Final Z Component of Angular Momentum of Neutral Atom Initial Z Component of Angular Momentum of Electron - ½ ½ - ½ ½ - ½ ½ - ½ ½ - ½ ½ - ½ ½ Shift for n=0 cyclotron state (cm -1 ) 0.545

0.778

0.156

0.389

1.245

1.479

-0.156

0.078

0.856

1.090

-0.545

-0.311

Apparatus

•The ions are held in a Penning ion trap in an ultra high vacuum (UHV) ~10 -8 Torr. • A continuous-wave ring dye laser, with kiton red dye as a lasing medium, is used to provide photons for photodetachment. Light with π polarization was used in this investigation.

•The fraction of ions surviving detachment can be measured by using a radio frequency (RF) potential to cause the ion ensemble to oscillate in the trap. This generates a current which can be measure and compared to the pre-detachment current magnitude to find the fraction surviving.

• A photodiode allows the same amount of light of to be used for each run This plot shows another data set which covers a much larger range of photon energies. It shows evidence of 8 Zeeman transitions, which are compared to theoretical values in the table below. 8 9 10 11 12 1 2 3 4 5 6 7 Transition Experimental Frequency (cm -1 ) 16269.64

16269.83

16270.06

16270.31

16270.57

16270.99

16271.27

16271.47

Spacing 0.19

0.23

0.25

0.26

0.28

0.20

Theoretical Frequency (cm-1) 16269.60

16269.83

16269.99

16270.22

16270.53

16270.76

16270.92

16271.15

16271.46

16271.70

16271.85

16272.09

Spacing 0.23

0.16

0.23

0.31

0.23

0.16

0.23

0.31

0.24

0.15

0.24

Experimental-Theoretical Frequency (cm-1) 0.04

0.00

0.07

0.09

0.04

0.07

0.12

0.01

Conclusions

•These data show the first time that any structure has ever been observed at this transition for negative sulfur ions or any isoelectronic species. •The Zeeman transitions found in this investigation are in fairly good agreement with the theoretical values. •These data also represent the first time that individual Zeeman transitions have been observed at a 1.0-T magnetic field.

References

[1] C. Blondel, W. Chaibi, C. Delsart, and C. Drag, J. Phys. B. 39, 1409 (2006).

[2] C. Blondel, C. Delsart, C. Valli, S. Yiou, M.R. Godefroid and S. Van Eck, Phys. Rev. A. 64, 052504 (2001).

[3] P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

[4] W. A. M. Blumberg, “Laser Photodetachment Spectroscopy of Negative Ions in a Magnetic Field” (PhD Thesis, Harvard University, 1979).

[5] W. A. M. Blumberg, R. M. Jopson, and D. J. Larson, Phys. Rev. Lett. 40, 1320 (1978).

[6] W. A. M. Blumberg, W. M. Itano, and D. J. Larson, Phys. Rev. A. 19, 139 (1979).

[7] C. W. Clark, Phys. Rev. A. 28, 83 (1983).

[8] H. G. Dehmelt and F. L. Walls, Phys. Rev. Lett. 21, 127 (1968).

[9] D. J. Griffiths, Introduction to Quantum Mechanics 2nd Ed (Pearson Education, Upper Saddle River, NJ, 2005). [10] C. Heinemann, W. Koch, G. G. Lindner and D. Reinen, Phys. Rev. A. 52, 1024 (1995).

[11] G. Herzberg, Atomic Spectra and Atomic Structure (Dover Publications, New York, 1945). [12] A. K. Langworthy, D. M. Pendergrast, and J. N. Yukich, Phys. Rev. A. 69, 025401 (2004). [13] D. J. Larson and R. Stoneman, J. de Physique. 43, C285 (1982).

[14] D. J. Larson and R. Stoneman, Phys. Rev. A. 31, 2210 (1985).

[15] D. M. Pendergrast and J. N. Yukich, Phys. Rev. A. 67, 062721 (2003).

[16] B. M. Smirnov, Physics of Atoms and Ions (Springer, New York, 2003). [17] E. P. Wigner, Phys. Rev. 73, 1002 (1948).

[18] J. N. Yukich, “Electron Wave Packets and Ramsey Interference in a Magnetic Field” (PhD Thesis, University of Virginia, 1996). [19] J. N. Yukich, C. T. Butler, and D. J. Larson, Phys. Rev. A. 55, 3303 (1997).

[20] J. N. Yukich, T. Kramer, and C. Bracher, Phys. Rev. A. 68, 033412 (2003).

Acknowledgements

Thanks to Dr. John Yukich and the Davidson Physics Department