Degenerate vacua to vacuumless model and kink-antikink collisions

In this work we investigate a Z2 symmetric model of one scalar field ϕ in (1,1) dimension. The model is characterized by a continuous transition from a potential V(ϕ) with two vacua to the vacuumless case. The model has kink and antikink solutions that minimize energy. Stability analysis is described by a Schrödinger-like equation with a potential that transits from a volcano-shape with no vibrational states (in the case of vacuumless limit) to a smooth valley with one vibrational state. We are interested in the structure of two-bounce windows present in kink-antikink scattering processes. The standard mechanism of Campbell-Schonfeld-Wingate (CSW) requires the presence of one vibrational state for the occurrence of two-bounce windows. We report that the effect of increasing the separation of vacua from the potential V(ϕ) has the consequence of trading some of the first two-bounce windows predicted by the CSW mechanism by false two-bounce windows. Another consequence is the appearance of false two-bounce windows of zero-order.