Wave function expansions transition matrix elements

Nevertheless, the classification of P transitions according to ft values can only be made roughly. For the exact classification one must start from the interaction matrix element Hfl given in O Eq. (2.75), which involves the overlap integral of initial and final nuclear wave functions and the power expansions of and ip (O Eqs. (2.76) and (2.77)). 

The wave function for the exciton state is of the same form as that given by Eq. (5) for Cl wave functions, the expansion coefficients again being obtained as solutions of an appropriate set of secular equations, (see Eq. (6)). The Hamiltonian matrix elements, Hj, can be written in terms of the appropriate charge and transition density distributions, (i a, a) and (i a, j5), respectively, as [57]... 

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