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Theoretical Analysis of the Hyperfine Structure of NaK

Theoretical Analysis of the Hyperfine Structure of NaK. Angela Wilkins Advisors : Dr. Hickman of Lehigh U. & Dr. Semak of UNC. Outline. Molecular Spectroscopy Energy levels of NaK Angular Momentum Coupling Conclusions.

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Theoretical Analysis of the Hyperfine Structure of NaK

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  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. 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 Alkali Molecular Structure 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 Internuclear separation (R) Na K

  5. Experimental setup Moveable Mirror M- Mirror L- Lens M Dye Laser L L GreenFluor. PMT Red fluor. PMT NaK Heat Pipe Oven Ti-Sapphire Laser M M

  6. Electronic State Notation 13D n2S+1L •Numeric label •S-electron spin: 2 electron molecules have parallel (S=1, triplet) or anti-parallel (S=0, singlet) spins •L-orbital angular momentum along internuclear axis: Whole integer numbers (L=0 S, L=1 P, L=2 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. K Na 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 J=N+S J=|N-S|,…, N+S For the triplet NaK cases, S=1, So J= N-1, N, N+1 Na K L

  11. J=16 J=15 J=14 N=17 N=16 N=15 J=17 J=16 J=15 J=18 J=17 J=16 Fine Structure Levels N = rotational angular momentum J = total angular momentum (excluding the nuclear spin)

  12. Hyperfine Structure (Includes Nuclear Spin) N=+R J=N+S F=J+I F=|J-I|,…,J+I For 13 of NaK, I=3/2 so F = J-3/2, J-1/2, J+1/2, J+3/2

  13. J=16 F=14.5 F=15.5 F=16.5 F=17.5 N=17 J=17 F=15.5 F=16.5 F=17.5 F=18.5 F=16.5 J=18 F=17.5 F=18.5 F=19.5 F=13.5 J=15 F=14.5 F=15.5 F=16.5 N=16 F=14.5 J=16 F=15.5 F=16.5 F=17.5 F=15.5 J=17 F=16.5 F=17.5 F=18.5 Hyperfine structure N = rotational angular momentum J = total angular momentum (excluding the nuclear spin) F=total angular momentum (including nuclear spin)

  14. N=86 Experimental Data N=38 N=15 N=26 N=45 As N becomes larger, the spacing between the groups of peaks becomes less.

  15. More Angular Momentum Coupling F= N+S+I Case 1Case 2 F= [N+S] + I F=N + [S+I] J=N+S G=S+I  F=J+I  F=N+G Recall: For 13 of NaK, S=1 and I=3/2 G=|S-I|,…,S+I   G=1/2, 3/2, 5/2

  16. F=15.5 F=14.5 F=16.5 F=14.5 F=15.5 F=16.5 F=15.5 F=16.5 F=15.5 F=17.5 F=17.5 F=18.5 F=17.5 F=16.5 F=16.5 F=18.5 F=18.5 F=19.5 F=17.5 F=17.5 G=5/2 N=17 G=3/2 G=1/2 J=16 F=13.5 F=17.5 N=17 J=17 F=18.5 F=18.5 J=18 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(N+1) - 2 ] - Dv[(N(N+1) - 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 >> Av >> b BvN >> b >>Av

  18. F=J+I F=N+G 2.0 J=N-1 G=5/2 1.0 J=N Relative Energy 0.0 G=3/2 J=N+1 G=1/2 -1.0 -2.0 Hyperfine coupling strength Intermediate Case Case 1 limit Case 2 limit

  19. F=J+I F=N+G 2.0 1.0 Relative Energy 0.0 -1.0 -2.0 Case 1 limit Case 2 limit Hyperfine coupling strength N=15

  20. F=J+I F=N+G 2.0 1.0 Relative Energy 0.0 -1.0 -2.0 Hyperfine coupling strength N=38 Case 1 limit Case 2 limit

  21. F=J+I F=N+G 2.0 1.0 Relative Energy 0.0 -1.0 -2.0 Hyperfine coupling strength N=86 Case 1 limit Case 2 limit

  22. Comparison of Experiment and Theory N=38 & 45 N=86 & 87 N=15 N=26 Reduced Energy Case 1 limit Hyperfine coupling strength 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 > 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

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