  Recollision processes are fundamental to strong-field physics and
attoscience, thus models connecting recolliding trajectories to quantum
amplitudes are a crucial part in furthering understanding of these processes.
We report developments in the semiclassical path-integral-based Coulomb
quantum-orbit strong-field approximation model for strong-field ionization by
including an additional phase known as Maslov's phase and implementing a new
solution strategy via Monte-Carlo-style sampling of the initial momenta. In
doing so, we obtain exceptional agreement with solutions to the time-dependent
Schr\"odinger equation for hydrogen, helium, and argon. We provide an in-depth
analysis of the resulting photoelectron momentum distributions for these
targets, facilitated by the quantum-orbits arising from the solutions to the
saddle-point equations. The analysis yields a new class of rescattered
trajectories that includes the well-known laser-driven long and short
trajectories, along with novel Coulomb-driven rescattered trajectories. By
virtue of the precision of the model, it opens the door to detailed
investigations of a plethora of strong-field phenomena such as photoelectron
holography, laser-induced electron diffraction and high-order above threshold
ionization.
