Sunday, April 17, 2016

[wuekezop] Hyperfine structure of ground state cesium

Neutral (i.e., non-ionized) cesium (caesium, cæsium) has 55 electrons, including a single electron in its outermost shell (valence shell).  Having a single outermost electron is characteristic of alkali metals, and hydrogen.

In the ground state, this outermost electron occupies the 6s orbital.  There is (exactly) one hyperfine transition possible for this 6s ground state electron: between spin up and spin down.  There is no hyperfine structure for the electrons in the inner shells because they are all paired (1 spin up pairing with 1 spin down) in completely filled shells.  Therefore, there is exactly one hyperfine transition for ground state cesium.  (The motivation for this post was, cesium atomic clocks are said to be regulated by the hyperfine transition of ground state cesium; however, which hyperfine transition?)

For ground state cesuim, the total electron angular momentum J has magnitude 1/2.  The total nuclear angular momentum I has magnitude 7/2.  The total atomic angular momentum F can take magnitudes F = 3 and F = 4.  Transitioning between these two F states (equivalently J = 1/2 and J = -1/2) induces the hyperfine structure.  F = 4 is the higher energy state.  The difference in the two energy levels corresponds to radiation with frequency exactly 9192631770 Hz, providing the definition of the second.

The speed of light is also an exact number by definition, so the wavelength (lambda = c/f) can be expressed as an exact rational number: 21413747/656616555 meters.  This might be the only wavelength that makes sense to be expressed as an exact rational number.  The frequency factors as 2 * 3 * 3 * 5 * 7 * 7 * 47 * 44351.  The speed of light (in m/s) factors as 2 * 7 * 73 * 293339.  The greatest common factor is 14.  Had humanity settled on different base units for time and length many years ago, these numbers would be different.

The wavelength happens to be a human-scale length: about 3 cm or 1.25 inches.

Incidentally, starting from the ground state with its electron in the 6s orbital, the most common excited state pushes the electron to the 6p orbital, yielding the high intensity spectral cesium D lines.  The 4f and 5d orbitals (and others) are harder to get to.  There are two possible excited 6p states, corresponding to J = 1/2 and J = 3/2 (yielding 2 D lines).  In the latter, F can be 2, 3, 4, or 5 so there are many hyperfine transitions between them.

References from which this post was written:

Cesium D Line Data, Daniel Steck

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