This presentation describes my research on a hyperfine transition within the iron atom, using a laser setup for evaporating iron and measuring its spectrum.

1. Atomic beam production and spectroscopy on the
iron 3d64s2 5D4  3d64s4p 5D4 transition
Bachelors presentation by Joost Jan van Barneveld
Facilities Laser Centre Vrije Universiteit
Supervisors Prof. Dr. Wim Ubachs
Dr. Eric-Jan van Duijn

2. Overview
• Motivation – Why spectroscopy on Iron ?
• Atomic beam production and setup
• Theory of spectroscopy
• Results
– Resolving isotopes
• Discussion
– Resolving hyperfine splitting
• Conclusion
• Debate

3. Introduction
• Shifting constant results in
renewed interest in spectroscopy1,2
• Iron is a suitable element:
– High universal abundance
– High mass number, Z=56
 
• Ehf   Z g (S I ) 4 3

Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion
[1] PRL 96, 151101 (2006) – W. Ubachs et al - Indication of a Cosmological Variation of the Proton-Electron Mass Ratio Based on Laboratory Measurement and Reanalysis of H2 Spectra
[2] Nucl. Physics B 653 (2003) 256-278 - T. Dent, M. Fairbairn,

4. Beam production & setup
• Elements need to be in gas phase for LIF
spectroscopy
• Evaporated iron forms a gas
• Evaporation requires heat: 1808K
Thermogravimetric Measurement of the
Vapor Pressure of Iron from 1573 K to 1973 K
Frank T. Ferguson, Joseph A. Nuth, and Natasha M. Johnson
J. Chem. Eng. Data, 2004, 49 (3), 497-501 • DOI:
10.1021/je034152w
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

5. Beam production & setup
1. Fix the sample (iron curls)
2. Heat the sample
3. Contain the heat
4. Minimise speed distribution
(Doppler width)
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

6. Beam production & setup
Fixing the sample
• Sample holder needs to withstand the heat
• Tantalum sheet (.5mm) is suited
• Melting point 3269K
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

7. Beam production & setup
Heating the sample
• Hit the sample holder with inrared laser
light (Nd:YAG 1064 nm)
• Sample absorbs the light and heats up
• Hot object emits blackbody radiation
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

8. Beam production & setup
Containing the heat
• Reflect IR radiation back to sample
• Minimize conduction
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

9. Beam production & setup
Assemble an oven
• One vapour outlet
• Keep the window clean
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

10. Beam production & setup
Reduce doppler broadening
• Parallel velocity broadens the spectral line
• Pick out atoms with perpendicular velocity
• Doppler width estimated 19 MHz
Excitation laser
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

11. Beam production & setup
Eventual setup
• Frequency doubled tunable
Ti:S laser
• Atomic beam in vacuum:
2.3*10-7 mBar
• Observe fluorescence with
PMT
• Register wavelength with
ATOS LM007
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

12. Theory of spectroscopy
Overview – Zooming in on quantum mechanics
• Levels & Terms
• Isotope shifts
• Hyperfine splitting
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

13. Theory of spectroscopy
Levels & Terms
• Quantum numbers
– 3d64s2 5D4  3d64s4p 5D4
• Aufbau principle
– 2 electrons in every shell
– Distribution amongst shells
determines Terms
– Term symbols: 2s+1Lj
– Iron has 5D4 in the ground state
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

14. Theory of spectroscopy
Isotope Shifts
• Normal, Specific and Field shift
• Normal and specific shift
– Kinetic terms due to wobbling of the
nucleus
– Energy levels are influenced
– Effect:  MS   Z  Z   (M NMS  M SMS )
 
 Z  Z 
me 
M NMS 
mu
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

15. Theory of spectroscopy
Hyperfine splitting
• Caused by nuclear spin
• Charge circling the nuclear B-field
interacts as magnetic dipole
• New quantum number:
  
F I J
• Interaction energy:
A
E  F ( F  1)  J ( J  1)  I ( I  1)
2
g s gi me
• Splitting of levels A  Z 3 4 mec 2
3 Mp
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

16. Summary
• Evaporate iron to form a
beam
• Let the iron interact with the
excitation laser
• Quantum theory describes
this interaction
• Let’s analyse the
measurements !
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

17. Results Fraction Spin
54Fe 0.05845(35) 0
Isotopes 56Fe
57Fe
0.91754(36)
0.02119(10)
0
½
• Two isotopes easily 58Fe 0.00282(4) 0
found
• Intensity is directly
proportional to isotope
fraction
• Highest peaks
correspond to highest
fraction
• 57Fe and 58Fe remain
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

18. Results Fraction Spin
54Fe 0.05845(35) 0
56Fe 0.91754(36) 0
Isotopes 57Fe 0.02119(10) ½
•
58Fe
57Fe is split in four 0.00282(4) 0
– Summed relative intensities
should relate to isotope fraction
• 58Fe is very weak
– Should have the same
distance from 56Fe as 54Fe
 Z  Z 
 MS    ( M NMS  M SMS )
 Z  Z 
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

19. Peak Isotope Position Distance Width
1 54Fe -769 - 14.3
2 56Fe 0 769 14.3
3 57Fe 243 244 12.9
4 57Fe 455 212 18.2
5 57Fe 648 193 40.7
6 58Fe 735 86 32.1
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

20. Discussion
Hyperfine coupling constant
• E 
A
F ( F  1)  J ( J  1)  I ( I  1)
2
EA  Ecg  2  ( A2  A1 )
EB  Ecg  5 2 A2  2 A1
EC  Ecg  5 2  A1  2 A2
Ecg
ED  Ecg  5 2  ( A1  A2 )
 2 2 1  EA 
   A1   E 
 2 5 2 1  
  A2    B 
5 2 2 1   EC 
   E   

 5 2 5 2 1  ED 
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

21. Discussion
Hyperfine coupling constant
• Which peak corresponds to Ecg
which transition ?
– Longest arrow highest
frequency
– Clebsch-Gordan coefficients
• Can we be sure that A1 and A2
are both positive ?
– A1 should be positive*
 2 2 1  EA 
   A1   E 
 2 5 2 1  
 A  B
5 2 2   2   EC 
1 
  E   
 5 2 5 2 1  
 ED 
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion
[*] Physical Review V148 #1 1966 – “Hyperfine interactions and the magnetic fields due to core polarization in Fe”, W.J. Childs, L.S.
Goodman

22. Discussion
Hyperfine coupling constant Method A1 A2 Ecg
• Options for matrix algebra +,cgc -24 24 511
+,-Ta 43 47 445
– Omission of rows / least +,-Td 47 43 447
squares +,L. sq 45 45 455
– Clebsch gordan / Manual -, cgc -24 -24 511
peak assignment -, -Tb 47 43 424
– Sign of second coupling -, -Tc 43 47 424
constant -, l. sq 45 45 428
• None gives the expected
result  2 2 1  EA 
   A1   E 
 2 5 2 1  
 A  B
– Values are in the order of 5 2 2   2   EC 
1 
  E   
the literature values*  5 2 5 2 1  
 ED 
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion
[*] J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 5359–5365Optical isotope shifts in the iron atom - Bentony, Cochrane and Griffith

23. Conclusion
• Fe Atomic beam production is possible
– Oven can be improved to lengthen sample lifetime
• Isotope splitting has been resolved
• Hyperfine splitting has not been resolved
– One more peak is needed to solve the system exactly
– Excitation laser needs stability improvements
Introduction – Beam production – Spectroscopic Theory – Results – Discussion - Conclusion

24. Debate