The Coulomb Direct and Exchange Integrals

In the Hamiltonian of the many-electron atom the interelectronic repulsion term has the form Two particular matrix elements 

These may be written as (ab q ab) = J a, b) and ab q ba) = K a, b), respectively. J a, b) is termed the Coulomb or direct integral and corresponds to the classical Interaction of the electronic charge distributions and K a, b) is termed the exchange integral. They may be written 

The and are integrals dependent on the radial functions and the Slater parameters take the form Fj = F jDy. and Gy. G jDy so that 

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