Semiclassical introduction to radiation

The nucleus can be regarded as as set of moving changes and magnetic moments of size R, the nuclear radius.

Two regions are important:

• The near zone, where .

  Here, the fields are determined by the instantaneous positions of the charges and moments.

• The far or radiation zone, where .

  Here the fields are retarded, vary as and are transverse to .

In the near zone the charge distribution can be decomposed into multipoles; similarly the gamma readiation is a sum of multipole contributions. A multiploe of order L carries an orbital angular momentum of .

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