  We evaluate for the inhomogeneous static electric Sauter step potential the
imaginary part of the emerging homogeneous in electric field effective
Euler-Heisenberg-Schwinger action sourced by vacuum fluctuations of a charged
particle with magnetic moment of arbitrary strength. The result is convergent
for all values of gyromagnetic ratio $g$, periodic in $g$, with a cusp at
$g=2$. We consider the relation to the QED beta-function which is also found to
be periodic in $g$. We confirm presence of asymptotic freedom conditions using
this novel method and document a wider range of $g$-values for which asymptotic
freedom is present.
