By I. PRIGOGINE
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Extra resources for ADVANCES IN CHEMICAL PHYSICS VOLUME 6
183)reduces to Eq. (160) with converted notation and replacement of F , and y,,with plane waves. This latter comment provides us with the name of the method, as the waves F , and $, partially take into account the distortion of the incident and scattered waves caused by the interaction potential, represented in the first instance by V t l ( r )and in the second by V,,,(r). (3) Strong Coupling The need for another form of approximate solution for Eq. (178) appears when k , sk,, where often all U , , are small enough to overlook except U,, and Unzrwhich may be rather large.
18Ob) is reduced to the form of Eq. (168), so that F, has the asymptotic The term with U,,, is probably as large, and when we omit it we rationalize that the method followed in the solution of Eqs. (180) is one of successive approximationsto the equationsderived when Us, is not ignored. ANALYTIC THEORY OF CHEMICAL REACTIONS 51 behavior given in Eq. (172). Substitution of such a solution for F , into Eq. (180b) yields [Vz + X + unnIFn(r) = Gn(riO*+) (181) where, as manifested, G, is a function of r, 8, and 4.
83)may be divided into so-called coulomb and exchange integrals. ’(1)~~(2)B’(2)91~(3)a’(3)~~(4)B’(4) (Vor H ) 91a1)a’(1)91;1(2)8’(2)v23) 43)&(4)B’ (4) dx (97) where complex conjugates are suppressed. The above is a coulomb integral. If, for instance, electrons 2 and 3 with the same spin functions were interchanged with regard to position functions, we would label the resulting exchange integral as By. Because of spin orthogonality all nonvanishing integrals must have the same spin functions for the same electrons on both sides of the operator.
ADVANCES IN CHEMICAL PHYSICS VOLUME 6 by I. PRIGOGINE