Differential cross section for ionisation

In the case of ionisation the channel states of relative motion are defined by the momenta k, kj of the two electrons. Our derivation parallels closely the derivation for scattering in section 6.7. 

It is convenient at this stage to redefine the notation for energy. We drop the channel index from the total energy E, since it is the same in all channels. This is expressed for example by the energy-conserving delta function in (6.39). We now use a subscripted energy variable to refer to the kinetic energy of an electron, for example in channel 0 or i. The density of 

---

Brauner, M., Briggs, J.S. and Klar, H. (1989). Triply-differential cross sections for ionisation of hydrogen atoms by electrons and positrons. J. Phys. B At. Mol. Opt. Phys. 22 2265-2287. 

The differential cross section for ionisation is given by (6.60). To formulate the T-matrix element we partition the total Hamiltonian H into a channel Hamiltonian K and a short-range potential V and use the distorted-wave representation (6.77). The three-body model is defined as follows. 

Scattering experiments are usually not very sensitive to structure. On the other hand the differential cross section for ionisation in a kinematic region where the plane-wave impulse approximation is valid gives a direct representation (10.31) of the structure of simple targets in the form of the momentum-space orbital of a target electron. 

---