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Fermi's golden rule is a way to calculate the transition rate between two states of a system, according to a perturbation theory, which means it's an approximation. The transition probability per unit of time is given by:
Where M is the matrix element for the interaction and ρ is the density of final states.
The expression of this matrix element is:
For example, the value of the matrix element without considering the spin is of 2 in the case of a beta decay without change of the total angular momentum of the nucleon, and if the parity of the nucleon is conserved.