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The line width and half life are related to one another but that doesn't really answer the question.
The rate of spontaneous emission of photons is given here....sorry, you cannot view external links. To see them, please
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The natural width of a line, in the absence of particular situations (example: metastabile levels) is proportional to the square of the excited level's dipole moment and to the cube of the energy difference between the two levels at which the transition happens.