In articles regarding models of atoms' ionization by a laser electric field, the ionization probability rate is given. I was told that it's not correct as a rule to get the ionization probability just by integrating the ionization rate over time, since it is possible sometimes to get a value over 1 by doing this. I'm looking for a rigorous mathematical development explaining the correct way to get total probability from probability rate. I will appreciate a reference for a good book in probability explaining this point.
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