Excitation temperature

Short description: Concept in statistical mechanics

In statistical mechanics, the excitation temperature (Tex) is defined for a population of particles via the Boltzmann factor. It satisfies

[math]\displaystyle{ \frac{n_{\rm u}}{n_{\rm l}} = \frac{g_{\rm u}}{g_{\rm l}} \exp{ \left(-\frac{\Delta E}{k T_{\rm ex}} \right) }, }[/math]

where

* nu is the number of particles in an upper (e.g. excited) state;
* gu is the statistical weight of those upper-state particles;
* nl is the number of particles in a lower (e.g. ground) state;
* gl is the statistical weight of those lower-state particles;
* exp is the exponential function;
* k is the Boltzmann constant;
* ΔE is the difference in energy between the upper and lower states.

Thus the excitation temperature is the temperature at which we would expect to find a system with this ratio of level populations. However it has no actual physical meaning except when in local thermodynamic equilibrium. The excitation temperature can even be negative for a system with inverted levels (such as a maser).

In observations of the 21 cm line of hydrogen, the apparent value of the excitation temperature is often called the "spin temperature".[1]

## References

1. ↑ Dickey, J. M.; Mebold, U.; Stanimirovic, S.; Staveley‐Smith, L. (2000). "Cold Atomic Gas in the Small Magellanic Cloud". The Astrophysical Journal 536 (2): 756. doi:10.1086/308953. Bibcode: 2000ApJ...536..756D.

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