Extend energy-conservation enforcement to Coulomb-distorted continuum approaches

Determine whether enforcing the energy-conservation condition n·ω = E_p + U_p + I_p on photoelectron momentum distributions computed via saddle-point approximations also remains valid for orbit-based strong-field ionization theories that fully incorporate the residual binding potential during continuum propagation (e.g., Coulomb-distorted approaches such as the Coulomb Quantum-Orbit Strong-Field Approximation), thereby preserving the agreement with numerical results and resolving time-window ambiguities observed in the Strong-Field Approximation.

Background

The paper shows that, within the Strong-Field Approximation (SFA) for above-threshold ionization without rescattering, manually imposing the energy-conservation condition n·ω = E_p + U_p + I_p on saddle-point results yields unique, symmetry-consistent photoelectron momentum distributions that agree closely with numerical integration, independent of the chosen ionization-time window.

For Coulomb-distorted approaches that include the residual binding potential in the electron’s continuum propagation (e.g., CQSFA and related semiclassical methods), direct numerical integration is generally unavailable and the field-dressed momentum is not conserved. Although the inter-cycle interference condition that produces ATI peaks and the Dirac delta comb remains the same in such methods, it is unclear whether the central finding here—energy-conservation enforcement recovering physically consistent spectra—extends to those theories.