Lifetimes and Polarizabilities icon

Lifetimes and Polarizabilities

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I. Introduction 3

A. Background 3

B. Purpose 4

C. Motivation 5

1. Lifetimes and Polarizabilities 5

2. New Level Search 10

D. Method 11

1. Lifetimes and Polarizabilities 11

2. New Level Search 14

II. Apparatus 17

A. The Vacuum System 17

B. The Oven 18

1. The Current Setup 18

2. Comments and Possible Improvements 20

C. The Laser System 21

D. The Interaction Region 21

E. The High Voltage System 23

F. Fluorescence Detection 24

G. Scattered Light Control 26

III. Data Collection/Analysis 27

A. Data Collection 27

B. Signal Modeling 29

C. Data fitting 30

IV. Theory 33

A. Overview 33

B. The Density Matrix 33

C. Evolution of the Matrix 35

D. The Absorption of Radiation. 36

E. The Quadratic Stark effect. 41

F. The Zeeman Effect. 45

G. Application of the Density Matrix to the Theory of Resonance Fluorescence 46

^ V. Results/Discussion 52

A. Presentation of Results 52

B. Comparison with other Experiments 56

1. Lifetimes 56

2. Polarizabilities 57

C. Comparison with Theory 58

1. Lifetime Calculations 58

2. Parametric Analysis 59

^ VI. Systematics 59

A. Overview 59

B. Lifetime and Polarizability Measurements 60

1. Radiation Trapping 60

2. Motion of Atoms in the Beam 65

3. PMT Afterpulses 67

4. PMT Linearity 69

5. Cascade Fluorescence 70

6. Zeeman Beats Induced by the Residual Magnetic Field 71

7. Hyperfine Beats 71

8. Hyperfine Stark Beats 72

9. Dependence of Decay Time on the Electric Field 72

10. Electric Field Inhomegeneity 73

C. Electric Field Measurement 75

1. Voltage Divider Calibration 75

2. Change of Electrode Gap Due to Vacuum 75

D. Reduced Quantum Beat Contrast 76

1. Error in Polarizer/Analyzer Orientation 76

2. Isotope Shift 76

3. PMT Response 77

4. AC Stark Shift and Saturation Effects 78

VII. Conclusion 78

A. Overview 78

B. Importance for the EDM search 79

1. Estimate of the Dipole Matrix Element 79

2. Estimate of the Enhancement Factor 79

C. New Level Search 82

1. Application to PNC/EDM 82

2. Ratio of Polarizabilites 82

VIII. Appendices 84

A. Software 84

1. Calculation of the Signal and Determination of Experimental Geometry 84

2. Data Collection 86

3. Data Analysis 86



Atomic spectroscopy is over a hundred years old. It has played an essential role in the development of our current view of nature, providing experimental data that led to the formulation of quantum mechanics. Later on, spectroscopic experiments were used to confirm the theory of quantum electrodynamics, and the existence of parity violation and electron-quark neutral currents. Today, atomic spectroscopy remains an important way of doing science, providing the means for searches for time-reversal violation and extensions to the Standard Model.

For the simplest elements, the basic spectroscopic task of establishing the energy level structure of each atom is largely complete. In the case of the more complex rare earth elements, such as samarium, however, many of the expected energy levels are missing from the tables, and only about a third of observed spectral lines have been identified [1]. Furthermore, additional information relating to many of the energy levels, such as lifetimes and tensor polarizabilities, are unknown.

The lowest energy configuration of samarium is (Xe)4f 66s2 (Fig. 1). The odd parity levels are known relatively well because they connect to the ground term by E1 transitions. Of the even parity levels, however, many levels are “missing,” even in the lowest terms. Lifetimes and electric polarizibilities have been measured for only a small number of the energy levels, and typically with poor accuracy.


In this work we have measured the lifetimes and electric polarizabilities of the low-lying odd parity levels of the 4f 66s6p term of the samarium atom (Fig. 1).

Follow-up work will include looking for unknown even parity levels of samarium. In particular, we would like to find levels of the 4f 66s2 5D term predicted by theory but never seen [2]. An earlier experiment [3] found three levels of this term and we will look for the two remaining levels.

Fig. 1. The low-lying configurations of atomic samarium. The rectangles indicate “bands” of closely spaced energy levels. The diagram also indicates the odd parity levels of interest for the lifetime and polarizability measurements, and the predicted positions of the “missing” even parity levels.

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