Effective potential from zero-momentum potential

Abstract

We obtain the centre-of-mass frame effective potential from the zeromomentum potential in Ruijsenaars-Schneider type 1-dimensional relativistic mechanics using classical inverse scattering methods.

Effective potential for relativistic scattering

“…The Ruijsenaars-Schneider (RS) model [12,13] is an integrable relativistic quantum mechanical model whose dynamics and S-matrix is completely equivalent to that of the SG field theory. From the RS description it is possible to read off the corresponding zero-momentum potential [13,11]. In our conventions it reads (after restoring the constants , c)…”

“…The Ising model and the O(3) nonlinear σ-model were studied and it was found that at low energies the energy-dependent U E (x) can be well approximated by its zero-momentum limit (corresponding to the case where the relative momentum of the two-particle state vanishes). The problem was also studied in the Sine-Gordon (SG) model [11]. In the semiclassical limit an energy-independent effective potential was constructed, which exactly reproduces the semiclassical time delays for all energies.…”