  In this paper, we consider the problem of computing the self-force and
self-energy for a static scalar charge in a wormhole space-time with throat
profile $r(\rho)=\sqrt{\rho^{2}+a^{2}}$ for arbitrary coupling of the field to
the curvature. This calculation has previously been considered numerically by
Bezerra and Khusnutdinov, while analytic results have been obtained in the
special cases of minimal ($\xi=0$) coupling and conformal coupling ($\xi=1/8$
in three dimensions). We present here a closed form expression for the static
Green's function for arbitrary coupling and hence we obtain an analytic
expression for the self-force. The self-force depends crucially on the coupling
of the field to the curvature of the space-time and hence it is useful to
determine the dependence explicitly. The numerical computation can identify
some qualitative aspects of this dependence such as the change in the sign of
the force as it passes through the conformally coupled value, as well as the
fact that the self-force diverges for $\xi=1/2$. From the closed form
expression, it is straight-forward to see that there is an infinite set of
values of the coupling constant for which the self-force diverges, but we also
see that there is an infinite set of values for which the self-force vanishes.
