Scattering of metastable lumps in a model with a false vacuum

In this work we consider the scalar field model with a false vacuum proposed by A. T. Avelar, D. Bazeia, L. Losano and R. Menezes, Eur. Phys. J. C 55, 133-143 (2008). The model depends on a parameter $s>0$. The model has unstable nontopological lump solutions with a bell shape for small $s$, acquiring a flat plateau around the maximum for large $s$. For $s\to\infty$ the $\phi^4$ model is recovered. We show that for $s\gtrsim 2$ the lump is metastable with the only negative mode very close to zero. Metastable lumps can propagate and survive long enough to produce dynamical effects. Due to their simplicity, they can be an alternative to the procedure of stabilization which requires, for instance, a complex scalar field to construct nontopological solitons. We study lump-lump collisions in this model, describing the main characteristics of the scattering products at their dependence on $s$ and the initial velocity modulus of each lump.