Now that the basis we are going to work with is specified, we turn to those parts of the interaction that have not been considered in its determination and consequently cause transitions between basis states. Apart from the residual strong interaction this includes the electromagnetic, weak, and other possible forces. In occupation number formalism, a K-body operator
has the form
with the totally antisymmetric matrix element 
. How is this
representation affected by the transition to the exciton picture? The
range of summation of every index is split into two parts, body
operators are replaced by exciton operators according to
eq. (2.9), and the resulting terms are brought into normal
order and grouped according to particle-hole structure. For K=2, the
result is given in refs. [5, 7, 9] and is reproduced in
Tab. I. The interaction is the sum of the fourteen terms 
listed there
together with their Feynman diagrams [9]. The diagrams
facilitate the visualization of the systematics in and the
generalization of the contents of Tab. I, see Fig. 1 . The
exciton operators can be classified by the three numbers k,a, and
q. The rank k of is half the number of external lines in the
corresponding diagram. One finds 
. The parameter a
is the number of particle-hole pairs created by : the interaction does not
conserve the number of excitons; the conservation of the number of
physical bodies, however, requires that the exciton number changes by
particle-hole pairs. The range of a obviously is 
. Finally, q is the number of upward arrows in the diagram. One
recognizes that q changes in steps of two, since for fixed a every
additional particle before the interaction leads to an additional
particle after the interaction . The range of q is found to be 
. Hence,
On the table, the operators with k<2 have contracted hole lines that
represent the interaction of the excitons with the nuclear core. It
is easily seen (and holds for arbitrary K as well) that the number
of particle and hole lines before and after the interaction is given
by 
and 
, respectively. Out of these
there are 
particles and 
holes. We give a few identities that clarify
the significance of these quantities:
Furthermore, we introduce 
, which is the number of
contracted hole indices of . The contracted indices never appear with exciton
operators. Since as a consequence of (2.9) hole indices
associated with creators (annihilators) appear in the bra (ket) of the
matrix element, the general structure of is [10]:
