  While the Sauter-Schwinger effect describes nonperturbative electron-positron
pair creation from vacuum by a strong and slowly varying electric field
$E_{\mathrm{strong}}$ via tunneling, the dynamically assisted Sauter-Schwinger
effect corresponds to a strong (exponential) enhancement of the pair-creation
probability by an additional weak and fast electric or electromagnetic pulse
$E_{\mathrm{weak}}$. Using the WKB and worldline instanton method, we find that
this enhancement mechanism strongly depends on the shape of the fast pulse. For
the Sauter profile $1/\cosh^2(\omega t)$ considered previously, the threshold
frequency $\omega_{\mathrm{crit}}$ (where the enhancement mechanism sets in) is
basically independent of the magnitude $E_{\mathrm{weak}}$ of the weak
pulse---whereas for a Gaussian pulse $\exp(-\omega^2t^2)$, an oscillating
profile $\cos(\omega t)$ or a standing wave $\cos(\omega t)\cos(kx)$, the value
of $\omega_{\mathrm{crit}}$ does depend (logarithmically) on
$E_{\mathrm{weak}}/E_{\mathrm{strong}}$.
