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Aiming at efficient numerical treatment of tunneling ionization of atoms andmolecules by mid-infrared (IR) lasers, exterior time scaling (ETS) theory isformulated as a generalization of the time-scaled coordinate approach. The keyidea of ETS is the division of the spatial volume into a small region aroundthe nucleus and its outside; the radial coordinates are time scaled only in theouter region. The continuum components of photoelectron wave packets areprevented from reaching the edge of the spatial simulation volume, enabling thelong-time evolution of wave packets with a relatively small number of basisfunctions without concerns of electron reflections. On the other hand, thebound-state components are free from shrinking toward the origin because ofnon-time scaling in the inner region. Hence, the equations of motion in ETS areless stiff than the ones in the original time-scaled coordinate approach inwhich the shrinking bound states make the equations of motion seriously stiff.For numerical implementation of ETS, the working equations are derived in termsof finite-element discrete-variable-representation functions. Furthermore, thestiffness-free Lanczos time propagator is introduced to remove any persistentstiffness in the treatment of mid-IR lasers due to the involvement of hundredsof angular-momentum states. The test calculations for atomic hydrogeninteracting with linearly polarized mid-IR pulses demonstrate the accuracy andnumerical efficiency of the new scheme, and exhibit its special capability ifthere is no recollision with the parent ion. Hence, ETS will show its truepotential for the detailed analysis of photoelectron wave packet dynamics incircularly or near-circularly polarized mid-IR fields.

Exterior time scaling with stiffness-free Lanczos time propagator: formulation and application to atoms interacting with strong mid-infrared lasers