Before decay, the nucleus is in state with total angular momentum J and symmetry axis quantization M :

Say, the emitted radiation (can be EM wave or particle ) carries angular momentum l and axis quantization m, its wavefunction is:

then the daughter nucleus has angular momentum j and , the wave function is

their relation is:

where the $Latex \left< l m j m_j | JM \right> $ is Clebsch-Gordan coefficient.

The wave function of the emitted radiation from a central interaction takes the form:

The angular distribution is:

for a fixed distance detector, the radial part is a constant. Moreover, not every spherical harmonic contribute the same weight, there is weighting factor due to Clebsch-Gordan coefficient. Thus, the angular distribution is proportional to:

For example, JM=00, The possible (l, j) are (0,0), (1,1), (2,2) and so on, the . The C-G coefficient are

$Latex \left<0 0 0 0 |0 0\right> = 1 $

$Latex \left<1 m 1 -m |0 0\right> = \frac{1}{sqrt{3} $

$Latex \left<l m l -m |0 0\right> = \frac{1}{sqrt{2l+1} $

thus,

Thus, the angular distribution is isotropic.

### Like this:

Like Loading...

## Leave a Reply