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Atoms in an excited state n chenges its state from n to n
spontaneously.
The number of transitions is proportional to the number of atoms
in the n state as

(2.133) 
where
represents the probability of transition
from n to n in unit time.
This coefficient is called Einstein's coefficient.
The lifetime of n level is related to this coefficient
as

(2.134) 
for this threelevel atom.
Kohji Tomisaka
20070708