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For kink-antikink scattering within the \phi^4 non--linear field theory inone space and one time dimension resonance type configurations emerge when therelative velocity between kink and antikink falls below a critical value. Ithas been conjectured that the vibrational excitation of the kink would be thesource for these resonances because (simplified) collective coordinatecalculations, that emphasized on this excitation, qualitatively reproducedthose resonances. Surprisingly a numerical study in the \phi^6 field theoryalso exhibited such resonances even though it does not contain the vibrationalexcitation. To explore this contradiction we start from the working hypothesisthat in either model any collective coordinate ansatz which includes a degreeof freedom similar to the vibrational excitation leads to resonances,regardless of whether or not this mode emerges as a solution to the(linearized) field equations. To this end we compare numerical results in the\phi^4 and \phi^6 models that arise from the full set of partial differentialequations to those from the ordinary differential equations for a collectivecoordinate ansatz. An inaccuracy in literature formulas for the collectivecoordinate approach in the \phi^4 model requires to revisit those calculations.

Kink-Antikink Scattering in \phi^4 and \phi^6 Models