False vacuum decay in kink scattering

In this work we consider kink-antikink and antikink-kink collisions in a modified $\phi^4$ model with a false vacuum characterized by a dimensionless parameter $\epsilon$. The usual $\phi^4$ model is recovered for $\epsilon=0$. We investigate the $\epsilon<<1$ regime where the kink in the presence of false vacuum can be understood as a small deformation of the standard kink for the $\phi^4$ model. We show that the attractive interaction between the kink-antikink pair leads to a rich scattering pattern, in some cases delaying considerably the false vacuum decay.