Transition Rate vs. Probability

[AriAstronomer]

Hey everyone,
So I'm doing a bit of research on transition probabilities for a presentation, and it seems like, from checking different resources, that in the atomic nucleus the process of transition rates to describe the rate of emission/absorption between 2 energy levels is used interchangeably with transition probability. I'm not so sure though that they are the same thing, but I'm sure perhaps that they are related.

For instance, some textbooks describe the Einstein coefficients (Aij, Bij, Bji) as measuring transition rates (and it makes sense, I mean the units of them are s-1), but others say they measure probabilities. Are they equivalent, are they simply related, or is it simply different textbooks being lazy and really rates and probabilities are 2 different things?

Thanks,
Ari

 

[mathman]

They are closely related. Probabilities (by definition) add up to 1. Rates are determined by probabilities and are usually expressed as average number events per unit time.