Suppose that 
and 
with three momenta 
produce an extended
scalar meson in its rest frame. The interaction Hamiltonian 
is in
general a function of momentum. Now make the replacement 
, expand 
to leading order in e and one
finds a new electromagnetic contribution
The effect of this form factor is readily seen in time ordered perturbation theory. There are
four contributions: (
are figs 2a, c, while 
are fig b where the 
is emitted from the 
or 
leg). We write these (for momentum routing see fig 3)
where
where 
is the energy of a kaon with momentum P.
Note that 
is the (form factor modified) contact diagram and 
is the new
contribution arising from the extended 
vertex.
After some manipulations their sum can be written
If 
we may integrate the final
term in eq (2.18) by parts and obtain for it
This is identical to the 
limit of 
, and hence we
see explicitly that the 
term (i.e. the
as calculated above) is effectively subtracted
at
q=0 due to the partial integration of the 
contribution, 
.
If one now has a model for 
one can perform the integrals in eq (2.18)
numerically.
For the KK molecule the wavefunction
is a solution of the Schrodinger equation
where (ref 13) one approximates
with 
and hence E=- 10 MeV. This equation may be solved numerically
and, for analytic purposes, we find that the 
is well approximated by
(fig 4)
where 
(thus 
, see also ref
13). The momentum space wave function that is used in our computation is thus
The rate for 
is shown as a function of
in fig (5). The non relativistic approximation eqs (2.12-2.19) is valid for
which is applicable to the KK molecule: for 
the
fully relativistic formalism is required and has been included in the curve displayed in fig
5. As 
and 
we recover the
numerical result of the pointlike field theory whereas for the specific 
molecule
wavefunction above one predicts a branching ratio of some 
(width
). This is only
of the pointlike field theory result but is larger than that expected for the
production rate of a
scalar meson.
Note that at 
the system is in some sense a mixture between genuinely separate
(which require 
) and a compact 
system.
These results and their interpretation are still preliminary. Some of the questions that
they bear on are discussed in the next section.