  In the present work, the influence of ultra-intense laser fields on the
$\alpha$ decay half-life of the deformed ground state even-even nucleus with
the mass number $52 \leq Z \leq 118$ is systematically studied. The
calculations show that the laser field changes the $\alpha$ decay half-life by
varying the $\alpha$ decay penetration probability in a small range. Moreover,
the analytical formulas for the rate of change of the $\alpha$ decay
penetration probability in the ultra-intense laser fields have been derived by
the spherical approximation, which agrees well with the numerical solutions for
nuclei with more significant proton numbers. This provides a fast way to
estimate the rate of change of the $\alpha$ decay penetration probability for
superheavy nuclei. Furthermore, the relationship between laser properties and
the average rate of change of the $\alpha$ decay penetration probability is
investigated. The calculations indicate that the shorter the wavelength of the
laser pulse is, the larger the average rate of change of the penetration
probability.
