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We conclude this section by stating the modified form of the cross sections and collision strengths in the new coupling schemes. In the pair-coupling scheme we have 20 P. G. BURKE AND W. EISSNER in units of a~, and (52) while in the intermediate coupling scheme we have and fl(i, j) is again given by Eq. (52). Although Eqs. (51) and (53) are formally similar, the respective T matrices must be calculated in the appropriate representations corresponding to Eqs. (43) and (45). 2. Use of the Dirac Hamiltonian.
Again the radius r = a of the inner region is chosen so that electron exchange and correlation effects can be neglected for r ;;;. a. The objective of the method is then to calculate the R matrix, which is defined by the equation i = 1, ... , n (83) by solving the collision problem in the inner region. Here F; and dFJ dr are the solutions of Eq. (27) defined on the boundary r = a, and the bj are parameters whose choice is usually arbitrary. We solve the collision problem in the inner region by expanding the total wave function, in analogy with Eq.
However, now both the bound orbitals in the target and correlation functions and the orbitals representing the scattered electron are given by Dirac orbitals. These are defined in terms of large and small components P(r) and Q(r) by (55) for the bound orbitals and (56) ELECTRON COLLISIONS WITH COMPLEX ATOMS AND IONS for the continuum orbitals, where a function Xxm is defined by = nKm, C = kKm, 21 and the spin-angle The angular state is defined by the K quantum number, already defined by Eq. (48), or alternatively by the quantum numbers (I, j).