6-3
Hydrogen-like (or alkali)
atoms
Hyperfine structure of 87Rb, with nuclear spin I=3/2, n0=DW/h=6,834,682,605 Hz and X=[(-mJ/J) +(mI/I)]H0/DW calibrated in units of 2.44 x 103 Oe.
S
N
Nuclear
spin and
dipole
Electron
spin and
dipole
N
Closed
electronic
shell
Electron
S
3
2
1
-1
-2
-3
2
3
4
X
MF =
  2
  1
  0
-1
MF =
-2
-1
0
1
F=2
F=1
DW
Nucleus
    Electron
Hydrogen-Like Atoms
   All commercial atomic frequency standards are based on hyperfine transitions of one of three hydrogen-like atoms, rubidium, cesium and hydrogen.
   The energy levels of an atom are generally classified according to their physical origin.  For example, the principal levels of an atom are associated with the radius of the "orbit" of an electron about the nucleus.  These levels have the largest atomic energy separations.  The principal energy levels are subdivided as a result of the quantization of the angular momentum of the atom.  The angular momentum due to the motion of a particle, such as an electron, is called orbital angular momentum.  Even when their motion is such that there is no orbital angular momentum, atomic particles may possess an intrinsic angular momentum or spin and a proportional intrinsic magnetic moment. The principal levels are first divided according to the shape of the electron "orbits."  Still finer division occurs as a consequence of the particular orientation of the electron's spin and the spin of the nucleus.
   The photons emitted when atoms change states among the principal energy levels are usually in the infrared and higher energy regions of the electromagnetic spectrum.  The frequencies of these energetic photons are too high for practical electronic devices. Atomic frequency standards are feasible because of the splitting of the ground state of the atom.  Next lower, in terms of energy, is the fine structure of the atom, which results from the interaction of the spin of the electron with the magnetic field due to the motion of the electron through the nuclear electric field.  This structure is thousands of times smaller than the separation of the principal energy levels.  Laboratory atomic frequency standards based on fine structure in calcium and magnesium have been built, but the fundamental frequencies of the atomic transitions are higher than 600 GHz, which is difficult to synthesize.
   A finer energy splitting than the spin-orbit coupling is produced by the interaction of the electron and nuclear spins; this is called the hyperfine structure.  The ground state of a hydrogen-like atom (e.g., H, Li, Na, K, Rb, Cs, and singly ionized Be) has a single unpaired electron in a symmetric orbit.  In this case, there is no orbital angular momentum and no fine structure.  The energy splitting due to the intrinsic magnetic moments of the electron and the nucleus can be a million times smaller than the separation of the principal energy levels.  The transition frequencies are convenient: 1.4 GHz for hydrogen, 6.8 GHz for rubidium, and 9.2 GHz for cesium.