(De-)Exciting the third Pöschl-Teller kink

A bstract There is a series of scalar models possessing reflectionless kinks whose linear perturbations are described by a Pöschl-Teller potential at integer level σ . The cases σ = 1 and 2 are the well-known Sine-Gordon and ϕ 4 double-well models. The σ = 3 kink has received relatively little attention because it exhibits a ϕ 8/3 potential, whose third derivative diverges in the vacuum. In old-fashioned perturbation theory this yields a cubic interaction that diverges far from a kink. We nonetheless use this interaction to calculate the amplitudes and probabilities for incoming radiation to excite or de-excite one of the kink’s two shape modes. As each shape mode is localized about the kink, the leading order amplitudes are nonetheless finite. This suggests that the σ = 3 model is not pathological, but rather its mesons are quantum field theoretic extensions of Znojil’s bound states.