Creating kinks with quantum mediation

We consider the creation of kink-antikink pairs of a scalar field $\phi$ by the scattering of classical wavepackets of a second scalar field, $\psi$, when there are no direct interactions between $\phi$ and $\psi$. The creation becomes possible only due to a quantum field that interacts with both $\phi$ and $\psi$. We scan parameter space and find it favorable for kink production when the initial wavepackets have large total energy and wide spatial extent but scatter at low velocities.