Complex extension of potentials and trajectories of poles of the S-matrix element in the complex momentum plane

Kawasaki, M.; Maehara, T.; Yonezawa, M.

Complex extension of potentials and trajectories of poles of the S-matrix element in the complex momentum plane

Authors

Kawasaki, M.

Maehara, T.

Yonezawa, M.

Description

Searching for infrastructure of the quantum mechanical system, we study trajectories of the s-wave poles of the S-matrix element with respect to a real phase $α$ in the complex momentum plane for a complex extension of real potentials by a phase factor $e^{iα}$. This complex extension relates the pole spectrum of the physical system with a potential to the spectrum of another system with the potential of the same shape but of opposite sign. There appear trajectories with the periodicity of $2π$, $4π$, and $\infty$. The appearance of non-recurrent behavior of the trajectory for the change of phase $Δα=2π$ is clearly related with the existence of resonance poles for real repulsive potentials. Dynamical changes of trajectory structure are examined.
10 pages, 7 figures