Theoretical Analysis of the Hyperfine Structure of NaK

1
Theoretical Analysis of the Hyperfine Structure
of NaK

• Angela Wilkins
• Advisors Dr. Hickman of Lehigh U.
• Dr. Semak of UNC

2
Outline

• Molecular Spectroscopy
• Energy levels of NaK
• Angular Momentum Coupling
• Conclusions

3
Alkali Molecular Structure

• Each successive orbital has a higher energy and
  lower energy orbitals are filled first
• Alkali atoms have 1 valence electron
• NaK acts like a 2 electron molecule

3d
4p
(K)
4s
3p
(Na)
3s
2p
2s
1s
Energy
Electron orbitals of an atom
4

• Molecular Spectroscopy
• spectroscopy allows study of different
• energy levels

5
Experimental setup
Moveable Mirror
M- Mirror L- Lens
M
Dye Laser
L
L
Green Fluor. PMT
Red fluor. PMT
NaK Heat Pipe Oven
Ti-Sapphire Laser
M
M
6
Electronic State Notation

• 13D n2S1L
• Numeric label
• S-electron spin
• 2 electron molecules have parallel
• (S1, triplet) or anti-parallel (S0,
• singlet) spins
• L-orbital angular momentum along internuclear
  axis
• Whole integer numbers (L0 S, L1
  P, L2 D)

7
Different Electronic States
8
Energy Levels of a Diatomic Molecule
Electronic State (i.e. 13?) Vibrational levels
(v) Rotational levels (N) Fine Structure Hyperfine
Structure
9
Energy Levels of NaK

• Energy levels are labeled by the angular momentum
  quantum numbers R,L,S, and I.
• rotation of nuclei
• R is the nuclear orbital angular momentum
• L is the electronic orbital angular momentum
• S is the electron spin momentum
• I is the nuclear spin momentum

10
Fine Structure

• L precesses rapidly about the inter- nuclear
  axis, ? is a component of L.
• N?R
• JNS
• JN-S,, NS
• For the triplet NaK cases, S1,
• So J N-1, N, N1

Na
K
L
11
Fine Structure Levels

• N rotational angular momentum
• J total angular momentum (excluding the nuclear
  spin)

12
Hyperfine Structure (Includes Nuclear Spin)
N?R JNS FJI FJ-I,,JI For 13?
of NaK, I3/2 so F J-3/2, J-1/2, J1/2, J3/2
13
Hyperfine structure

• N rotational angular momentum
• J total angular momentum (excluding the nuclear
  spin)
• Ftotal angular momentum (including nuclear spin)

14
Experimental Data
N38
N15
N26
N45
As N becomes larger, the spacing between the
groups of peaks becomes less.
15
More Angular Momentum Coupling

• F NSI
• Case 1
  Case 2
• F NS I FN SI
• JNS GSI
• ? FJI ? FNG

Recall For 13? of NaK, S1 and I3/2
GS-I,,SI ? ? G1/2, 3/2, 5/2
16
Energy Levels for Limiting Cases
Case 1
Case 2
17
Model Hamiltonian for NaK (3?)

• H Hspin-orbit Hrotation Hhyperfine
  Hspin-rotation
• Hspin-orbit AvL?S
• Hrotation Bv (N(N1) - ?2 - Dv (N(N1) - ?2
  2
• Hhyperfine bI?S
• Hspin-rotation ? R?S
• The 12 energy levels are the eigenvalues of this
  Hamiltonian.
• We adjusted Av, b, and ? to fit the experimental
  energies.
• Case 1 Case 2
• BvN gtgt Av gtgt b BvN gtgt b
  gtgtAv

18
Intermediate Case
Case 1 limit
Case 2 limit
19
N15
20
N38
Case 1 limit
Case 2 limit
21
N86
Case 2 limit
Case 1 limit
22
Comparison of Experiment and Theory
N38 45
N86 87
N15
N26
Reduced Energy
Hyperfine coupling strength
Case 1 limit
Case 2 limit
23
Conclusions

• The intermediate angular momentum coupling cases
  explain data.
• The coupling scheme changes with N.
• Plan to work further and continue analysis on
  data at N values gt 86 to check agreement with
  limiting cases and include other electronic
  states.

24
Acknowledgements

• Dr A. Peet Hickman
• Dr Matthew Semak
• Dr. Huennekens
• Laurie Sibbach Catherine Deibel
• NSF for funding

25
Transition from LS to jj coupling
Light atoms tend to exhibit LS coupling, and
heavy atoms tend to exhibit jj coupling. The
transition from one to the other can be seen as
one goes down a column in the periodic
table. Diagram adapted from Condon and Shortley
26
Electron Transition