The nucleus can be regarded as as set of moving changes and magnetic moments of size R, the nuclear radius.
Two regions are important:
Here, the fields are determined by the instantaneous positions of the charges and moments.
Here the fields are retarded, vary as and are transverse to .
Classically, an alternating charge dipole where p=ed radiates an average energy per unit time of
and an alternating magnetic dipole
In quantum mechanics, the dipole moment p=ed=2ez is replaced by an expectation value for the position operator z,
Then for electric dipole (E1) transitions
and for magnetic dipole (M1) transitions
The decay constant is then
The dipole width . The matrix element is of the order of the nuclear size, and so