In statistical mechanics, the excitation temperature (Tex) is defined for a population of particles via the Boltzmann factor. It satisfies
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[edit]
- ^ 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. Bibcode:2000ApJ...536..756D. doi:10.1086/308953.