  We study the long time behavior of solutions to the nonlocal diffusion
equation $\partial_t u=J*u-u$ in an exterior one-dimensional domain, with zero
Dirichlet data on the complement. In the far field scale,
$\xi_1\le|x|t^{-1/2}\le\xi_2$, $\xi_1,\xi_2>0$, this behavior is given by a
multiple of the dipole solution for the local heat equation with a diffusivity
determined by $J$. However, the proportionality constant is not the same on
$\mathbb{R}_+$ and $\mathbb{R}_-$: it is given by the asymptotic first momentum
of the solution on the corresponding half line, which can be computed in terms
of the initial data. In the near field scale, $|x|\le t^{1/2}h(t)$,
$\lim_{t\to\infty}h(t)=0$, the solution scaled by a factor $t^{3/2}/(|x|+1)$
converges to a stationary solution of the problem that behaves as $b^\pm{x}$ as
$x\to\pm\infty$. The constants $b^\pm$ are obtained through a matching
procedure with the far field limit. In the very far field, $|x|{\ge}t^{1/2}
g(t)$, $g(t)\to\infty$, the solution has order $o(t^{-1})$.
