  We discuss the effect of using potentials with a Coulomb tail and different
degrees of softening in the photoelectron momentum distributions (PMDs) using
the recently implemented hybrid forward-boundary CQSFA (H-CQSFA). We show that
introducing a softening in the Coulomb interaction influences the ridges
observed in the PMDs associated with backscattered electron trajectories. In
the limit of a hard-core Coulomb interaction, the re-scattering ridges close
along the polarization axis, while for a soft-core potential, they are
interrupted at ridge-specific angles. We analyze the momentum mapping of the
different orbits leading to the ridges. For the hard-core potential, there
exist two types of saddle-point solutions that coalesce at the ridge. By
increasing the softening, we show that two additional solutions emerge as the
result of breaking a hidden dynamical symmetry associated exclusively with the
Coulomb potential. Further signatures of this symmetry breaking are encountered
in subsets of momentum-space trajectories. Finally, we use scattering theory to
show how the softening affects the maximal scattering angle and provide
estimates that agree with our observations from the CQSFA. This implies that,
in the presence of residual binding potentials in the electron's continuum
propagation, the distinction between purely kinematic and dynamic caustics
becomes blurred.
