Matrix elements 8 decay probability, factorization

The matrix elements in angle brackets contain nuclear factors and (in the case of charged particles) the Coulomb barrier penetration probabilities or Gamow factors, originally calculated in the theory of a-decay, which can be roughly estimated as follows (Fig. 2.7). 

As is shown in the appendix (Section V), the matrix element determining the probability of / decay is factorized in the following way ... 

The spectrum of / decay, or the (i spectrum, is a distribution of ejection probabilities for the ji electron versus its kinetic energy. As an initial formula for deriviing an expression for the / spectrum we will use Eq. (8). As was mentioned above, the ft decay in a molecule is a multichannel process owing to the fact that both the parent and the daughter molecules may be in different electronic, vibrational, and rotational states. Thus, Eq. (8) should be employed for each channel of the reaction. Using the energy conservation law and the factorization of the matrix element, Eq. (12), we obtain the following expression for the probability of ft decay in the channel 0 n ... 

---