  The $\phi^4$ double-well theory admits a kink solution, whose rich
phenomenology is strongly affected by the existence of a single bound
excitation called the shape mode. We find that the leading quantum correction
to the energy needed to excite the shape mode is $-0.115567\lambda/m$ in terms
of the coupling $\lambda/4$ and the meson mass $m$ evaluated at the minimum of
the potential. On the other hand, the correction to the continuum threshold is
$-0.433\lambda/m$. A naive extrapolation to finite coupling then suggests that
the shape mode melts into the continuum at the modest coupling of
$\lambda/4\sim 0.106 m^2$, where the $\mathbb{Z}_2$ symmetry is still broken.
