In discussing unstable states, we have in mind a system like an excited nucleus, or a β-unstable nucleus. An unstable state of a system will decay, and often there are several alternative modes of decay. For example, an excited state of a nucleus can have several states of lower energy to which it can decay by emitting a photon, and some β-unstable nuclei can decay by either β+ or β- -emission. Such distinct modes of decay are called decay channels.

An unstable state has certain probabilities per unit time, called partial decay rates, to decay into any of its channels. We shall denote these probabilities by 1/τi, where the Xi have the dimension of time and i labels the ith decay channel. The total decay rate 1/τ is the sum of the partial decay rates:

We shall also find it useful to define partial widths Гi and total widths Г by Гi = ћ/τi, Г = ћ/τ. These have the dimensions of energy, and clearly