Formulation in the approach of angular momentum transfer

Within the dipole approximation (jphoton = 1) and for the example of photoionizing an wp-electron from a closed-shell atom (J = 0), the photoelectron angular momentum is either t = 0 or 2 and, hence, 

To each ionic state Jj and angular momentum transfer jx belongs a reduced scattering amplitude S jt) - the name for which originates from the formulation of photoionization as a half-scattering process. (In a scattering process with real particles the scattered particle still exists after the interaction, but in photoionization the primary incident particle, the photon, is annihilated.) The angular momentum transfer formulation allows a partition of the amplitudes into two classes, parity-favoured and parity-unfavoured, where 

the photoionization process under consideration is determined 

If these scattering amplitudes are inserted in the general expressions for a and / one obtains 

In this general formulation no information is required concerning the underlying coupling scheme used for the description of the photoionization channels. 

---