We use Feshbach's p r o j e c t i o n formalism t o w r i t e an equation f o r the
wave f u n c t i o n t h a t describes the r e l a t i v e distance between the centers o f mass o f the
two ions. We assume t h a t the Q-space can be truncated a t the e x c i t a t i o n o f l p - l h
i n e i t h e r one or the other ion, leaving one o f them i n i t s ground s t a t e . I n the propagator
o f the e f f e c t i v e p o t e n t i a l , the two-body i n t e r a c t i o n i s replaced by the ioni
o n mean f i e l d VMF. The m a t r i x elements o f the elementary i n t e r a c t i o n are o f f i n i t e
range, represented by an e f f e c t i v e Wigner force. The t o t a l many-body wave f u n c t i o n i s
antisymmetrized only i n the p a r t i a l i n t r i n s i c wave f u n c t i o n o f each i o n . C a l c u l a t i o n s
are done i n the Thomas Fermi approximation. The Coulomb energy i s not considered.