The hybrid surface flux method for the ionization amplitude extraction from the calculated wavefunction

A method is proposed for extracting ionization amplitudes from the solution of the time-dependent Schr\"odinger equation (TDSE) describing a system in a time-dependent external field. The method is a hybrid of two earlier developed methods, the time-dependent surface flux (t-SURFF) method and the method using the propagated wavepacket as the source term in a time-independent driven Schr\"odinger equation with the field-free Hamiltonian. It is demonstrated that the method combines the advantages of the parent ones and allows the extraction of ionization amplitudes by solving the TDSE within a small spatial domain (with the boundary conditions provided by exterior complex scaling) and a time interval, not exceeding the external field pulse duration.