  We describe an approach defining instantaneous ionization rate (IIR) as a
functional derivative of the total ionization probability. The definition is
based on physical quantities which are directly measurable, such as the total
ionization probability and the waveform of the pulse. The definition is,
therefore, unambiguous and does not suffer from gauge non-invariance. We
compute IIR by solving numerically the time-dependent Schrodinger equation for
the hydrogen atom in a strong laser field. We find that the IIR lags behind the
electric field, but this lag is entirely due to the long tail effect of the
Coulomb field. In agreement with the previous results using attoclock
methodology, therefore, the IIR we define does not show measurable delay in
strong field tunnel ionization.
