*Article* **Strong-Field Ionization Amplitudes for Atomic Many-Electron Targets**

**Stephan Fritzsche 1,2,3,\* and Birger Böning 1,2**


**Abstract:** The strong-field approximation (SFA) has been widely applied in the literature to model the ionization of atoms and molecules by intense laser pulses. A recent re-formulation of the SFA in terms of partial waves and spherical tensor operators helped adopt this approach to account for realistic atomic potentials and pulses of different shape and time structure. This re-formulation also enables one to overcome certain limitations of the original SFA formulation with regard to the representation of the initial-bound and final-continuum wave functions of the emitted electrons. We here show within the framework of JAC, the Jena Atomic Calculator, how the direct SFA ionization amplitude can be readily generated and utilized in order to compute above-threshold ionization (ATI) distributions for many-electron targets and laser pulses of given frequency, intensity, polarization, pulse duration and carrier–envelope phase. Examples are shown for selected ATI energy, angular as well as momentum distributions in the strong-field ionization of atomic krypton. We also briefly discuss how this approach can be extended to incorporate rescattering and high-harmonic processes into the SFA amplitudes.

**Keywords:** atomic; Coulomb–Volkov; direct amplitude; distorted-Volkov; electron emission; Jena Atomic Calculator; partial-wave representation; relativistic; strong-field approximation; strongfield ionization
