Hyperfine splitting page

This page is an attempt to collect information and links pertaining especially to hyperfine splitting in the microwave frequency range.

Some atoms have multiple entries when multiple transitions may be of use for timing purposes. So far only microwave and not optical frequencies have been considered.

Isotope	I	Groundstate	Transition	v	Ref.
$^{1} H$	$\frac{1}{2}$	$S_{1 / 2}$	(F=1, m=0) -> (F=0, m=0)	1.420405751768(2) GHz	H-1 1970
$^{1} H$	$\frac{1}{2}$	$S_{1 / 2}$	(F=1, m=0) -> (F=0, m=0)	1.4204057517662(30) GHz	H-1 1973
$^{2} H$	1	$S_{1 / 2}$	(F=1, m=0) -> (F=0, m=0)	327.3843525222(17) MHz	H-2 1972
$^{3} H$	$\frac{1}{2}$	$S_{1 / 2}$	(F=1, m=0) -> (F=0, m=0)	1.5167014708087(71) GHz	H-3 1967
$^{3} He$	$\frac{1}{2}$	$S_{1 / 2}$		8.665649867(10) GHz
$^{6} Li$	1	$S_{1 / 2}$		228.2052590(30) MHz
$^{7} Li$	$\frac{3}{2}$	$S_{1 / 2}$		803.5040866(10) MHz
$^{9} Be +$	$\frac{3}{2}$	$S_{1 / 2}$		1.250017678096(8) GHz
$^{21} Na$	$\frac{3}{2}$	$S_{1 / 2}$	(F=2, m=0) -> (F=1, m=0)	1.906471880(200) GHz	Na-21 1997, Na-21 1998
$^{23} Na$	$\frac{3}{2}$	$S_{1 / 2}$	(F=2, m=0) -> (F=1, m=0)	1.7716261288(10) GHz	Na-23 2003
$^{24} Mg$	0	$S_{0}$	3P0,mj=0 -> 3P1,mj=0	601.2771583(2) GHz
$^{24} Mg$	0	$S_{0}$	3P1,mj=0 -> 3P2,mj=0	1.22057 THz
$^{25} Mg +$	$\frac{5}{2}$	$S_{1 / 2}$		1.788763128(162) GHz
$^{37} K$	$\frac{3}{2}$	$S_{1 / 2}$		240.3 MHz	K-38 1997
$^{38} K$	$3$	$S_{1 / 2}$		1.4153 GHz	K-38 1997
$^{39} K$	$\frac{3}{2}$	$S_{1 / 2}$		461.7197202(14) MHz
$^{40} K$	4	$S_{1 / 2}$		1.286 GHz	K-40 2005
$^{41} K$	$\frac{3}{2}$	$S_{1 / 2}$		254.0138720(20) MHz
$^{40} Ca$	0	$S_{0}$	3P0,mj=0 -> 3P1,mj=0	1.5636 THz
$^{40} Ca$	0	$S_{0}$	3P1,mj=0 -> 3P2,mj=0	3.1742 THz
$^{63} Cu$	$\frac{3}{2}$	$S_{1 / 2}$		11.73583(1) GHz
$^{65} Cu$	$\frac{3}{2}$	$S_{1 / 2}$		12.56881(1) GHz
$^{85} Rb$	$\frac{5}{2}$	$S_{1 / 2}$		3.035732440(3) GHz	Rb-85 1976
$^{87} Rb$	$\frac{3}{2}$	$S_{1 / 2}$	(F=2, m=0) -> (F=1, m=0)	6.834682610904324(4)(7) GHz	Rb-87 2003
$^{107} Ag$	$\frac{1}{2}$	$S_{1 / 2}$		1.712512111(18) GHz
$^{109} Ag$	$\frac{1}{2}$	$S_{1 / 2}$		1.976932075(7) GHz
$^{111} Cd +$	$\frac{1}{2}$	$S_{1 / 2}$		14.57 (20) GHz
$^{113} Cd +$	$\frac{1}{2}$	$S_{1 / 2}$		15.24 (20) GHz
$^{133} Cs$	$\frac{7}{2}$	$S_{1 / 2}$	(F=4, m=0) -> (F=3, m=0)	9.192631770 GHz
$^{133} Ba +$	$\frac{1}{2}$	$S_{1 / 2}$		9.92545355459(10) GHz
$^{135} Ba +$	$\frac{3}{2}$	$S_{1 / 2}$	(F=2, m=0) -> (F=1, m=0)	7.18334023490(0.57) GHz	Ba-135+ 1983
$^{137} Ba +$	$\frac{3}{2}$	$S_{1 / 2}$		8.03774166769(36) GHz
$^{171} Yb +$	$\frac{1}{2}$	$S_{1 / 2}$		12.642812118466(2) GHz
$^{173} Tb +$	$\frac{5}{2}$	$S_{1 / 2}$		10.49172023955(9) GHz
$^{197} Au$	$\frac{3}{2}$	$S_{1 / 2}$		6.099321840(130) GHz
$^{199} Hg +$	$\frac{1}{2}$	$S_{1 / 2}$		40.5073479968416(4) GHz
$^{199} Hg +$	$\frac{1}{2}$	$S_{1 / 2}$		40.50734799684159(14)(41) GHz	Hg-199+ 1998
$^{201} Hg +$	$\frac{3}{2}$	$S_{1 / 2}$		29.94(15) GHz
$^{203} Tl$	$\frac{1}{2}$	$P_{1 / 2}$		21.106 GHz
$^{205} Tl$	$\frac{1}{2}$	$P_{1 / 2}$		21.3108339461(5) GHz
$^{210} Fr$	6			4.0451(11) GHz	Fr-210 2003

Notations

Ground state notation

For a groundstate notation of $n^{s} L_{j}$

n

Principal quantum number, integer number 1, 2, 3 ...

L

Orbital letter, indicating oribtal number being an integer of 0, 1, 2, ... as given by

0 \leq l \leq n - 1

L	l
S	0
P	1
D	2
F	3
G	4
H	5

s

j

Total angular momentum.

j = l +- s

References

H-1 1965: N. F. Ramsay, "The Atomic Hydrogen Maser", Metrologia 1965
H-1 1970: H. Hellwig, R.C. Vessot, M.W. Levine, P.W. Zitzewitz, D.W. Allan and D.J. Glaze, "Measurement of the Unperturbed Hydrogen Hyperfine Transition Frequency", IEEE T. Instrum. Meas. 19 p200-209
H-1 1973: L Essen, R W Donaldson, E G Hope, M J Bangham, "Hydrogen Maser Work at the National Physical Laboratory", Metrologia July 1973
H-2 1972: D. J. Wineland and N. F. Ramsey, "Atomic Deuterium Maser", Physical Review February 1972
H-3 1967: B. S. Mathur, S. B. Crampton, D. Kleppner and N. F. Ramsey, "Hyperfine Separation of Tritium", Physical Review June 1967
Na-21 1997: M. A. Rowe, S. J. Freedman, B. K. Fujikawa, G. Gwinner, S.-Q. Shang, P. A. Vetter, "A Hyperfine Measurement in Laser Trapped Radioactive Na-21", NSD Na-21 1997
Na-21 1998: S. J. Freedman, B. K. Fujikawa, M. A. Rowe, N. Scielczo, P. A. Vetter, "Laser Trapped Radioactive Na-21", NSD Na-21 1998
Na-23 2003: D. Steck, "Sodium D Line Data", October 2003 (originally May 2000)
K-38 1997: Robert S. Williamson, "Magneto-optical trapping of potassium isotopes", PhD at University of Wisconsin-Madison 1997
K-40 2005: I. D. Leroux, "Manipulation of Ultra-Cold Atoms Using Radio-Frequency and Microwave Radiation", University of Toronto April 2005
Rb-85 1976: M. Tetu, R. Fortin, J. Y. Savard, "A New Determination of the Rb 85 Unperturbed Hyperfine Transition Frequency", IEEE Transactions on Instrumentation and Measurements, Vol. IM25, No. 4, pp. 477-480, December 1976
RB-87 1999: S. Bize, Y. Sortais, M. S. Santos, C. Mandache, A. Clairon, C. Salomon, "High-accuracy measurement of the Rb-87 ground-state hyperfine splitting in an atomic fountain", Europhysics Letters 45 pp. 558-564, 1999
RB-87 2003: H. Marion, F. Pereira, D. Santos, M. Abgrall, S. Zhang, Y. Sortais, S. Bize, I. Maksimovic, D. Calonico, J. Gruenert, C. Mandache, P. Lemonade, G. Santarelli, P. Laurent, A. Clairon, C. Salomon, "High-accuracy measurement of the Rb-87 ground-state hyperfine splitting in an atomic fountain", Europhysics Letters 45 pp. 558-564, 1999
Ba-135+ 1983: W. Becker, G. Werth, "Precise determination of the ground state hyperfine splitting of Ba-135+", Zeitschrift fur Physik A Hadrons and Nuclei 1983
Hg-199+ 1998: D.J. Berkeland, J.D. Miller, J.C. Bergquist, W.M. Itano, and D.J. Wineland, "Laser-Cooled Mercury Ion Frequency Standard", Phys. Rev. Lett. 80, 2089-2092 1998
Fr-210 2003: S. A. M. Aubin, "High Efficiency Francium Trap for Precision Spectroscopy", State University of New York August 2003

Magnus Danielson <cfmd at bredband dot net>