  An investigation of the calculated $\alpha$ decay half-lives of super heavy
nuclei (SHN) reveals that the diffuseness parameter is a great bottleneck for
achieving accurate results and predictions. In particular, when universal
proximity function is adopted for nuclear potential, half-life is found to vary
significantly and nonlinearly as a function of diffuseness parameter. To
overcome this limiting hurdle, a new semiempirical formula for diffuseness that
is dependent on charge and neutron numbers is proposed in this work. With the
model at hand, half-lives of 218 SHN are computed, for 68 of which there exists
available experimental data and 150 of which are predicted. The calculations of
half-lives for 68 SHN are compared against experimental data and the calculated
data obtained by using deformed Woods-Saxon, deformed Coulomb potentials model,
and six semiempirical formulas. The predictions of 150 SHN are compared against
the predictions of seven of the current best semiempirical formulas.
Calculations of the present study are in good agreement with the experimental
half-lives outperforming all but ImSahu semiempirical formula. Moreover, the
predictions of our model are consistent with predictions of the semiempirical
formulas. We strongly conclude that more attention should be directed toward
obtaining accurate diffuseness parameter values for using it in nuclear
calculations.
