Self-intersecting Regge trajectories in multi-channel scattering

We present a simple direct method for calculating Regge trajectories for a multichannel scattering problem. The approach is applied to the case of two coupled Thomas-Fermi type potentials, used as a crude model for electron-atom scattering below the second excitation threshold. It is shown that non-adiabatic interaction may cause formation of loops in Regge trajectories. The accuracy of the method is tested by evaluating resonance contributions to elastic and inelastic integral cross sections.Comment: 5 pages, 4 figure

Pseudospin symmetry in the relativistic Killingbeck potential: quasi-exact solution

The Killingbeck potential consisting of the harmonic oscillator-plus-Cornell potential, is of great interest in high energy physics. The solution of Dirac equation with the Killingbeck potential is studied in the presence of the pseudospin (p-spin) symmetry within the context of the quasi-exact solutions. Two special cases of the harmonic oscillator and Coulomb potential are also discussed.Comment: 10 pages, to appear in Zeitschrift fur Naturforschung (2012

Nonlinear Supersymmetric (Darboux) Covariance of the Ermakov-Milne-Pinney Equation

It is shown that the nonlinear Ermakov-Milne-Pinney equation $\rho^{\prime\prime}+v(x)\rho=a/\rho^3$ obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using supersymmetric, or Darboux, transformations. The general solution of the transformed equation is expressed in terms of the solution of the original one. Both iterations of these transformations and irreducible transformations of second order in derivatives are considered to obtain the chain of mutually related Ermakov-Milne-Pinney equations. The behaviour of the Lewis invariant and the quantum number function for bound states is investigated. This construction is illustrated by the simple example of an infinite square well.Comment: 8 page