The n-electron Coulomb continuum

It is shown that, when the n-electron continuum state is treated in LS-coupling, both the amplitude and the cross section for photo-and electron-impact ionization to such a state can be expressed as a linear combination of n-polar harmonics in the angles of emission of the n electrons. The analysis utilizes re-coupling techniques, largely avoiding redundant sums over products of Clebsch-Gordan coefficients. The Clebsch-Gordan series is generalized to n particles. Two selection rules are proved and the operation of such selection rules is illustrated by calculations of-the differential cross section for (i) the complete photo-fragmentation of the lithium atom and (ii) the complete fragmentation of the helium atom under electron impact.