  The isovector scalar correlator is studied using a class of finite energy sum
rules shown recently to be very well satisfied in the vector isovector channel.
The values of the $a_0$ scalar decay constants extracted in this analysis,
which describe the couplings of the $a_0(980)$ and $a_0(1450)$ to the isovector
scalar current, are shown to be comparable, strongly disfavoring any scenario
in which the $a_0(980)$ is interpreted as a loosely bound $K\bar{K}$ molecule
and the $a_0(1450)$ is assigned to the same flavor multiplet as the
$K_0^*(1430)$. The $a_0$ decay constants are also compared to the analogous
decay constant describing the coupling of the $K_0^*(1430)$ to the divergence
of the strange vector current (which may be obtained from experimental $K_{e3}$
and $K\pi$ phase shift data), and implications of the relative magnitudes for
the interpretation of the nature of the $a_0$ states discussed.
