  For $\alpha$ decay half-life calculations in this work, the Coulomb and
proximity potential model with a new semiempirical formula for diffuseness
parameter developed in previous work [Phys. Rev. C 100, 024601 (2019)] is used.
The present model in this work is compared with the generalized liquid-drop
model (GLDM), universal decay law (UDL), and experimental half-lives in the
region $Z=104-118$. Next, the predicted half-lives of 51 superheavy nuclei
(SHN) with $Z=122-125$ by the present model are compared with those of GLDM,
and UDL. The present model is revealed to be more accurate in reproducing
experimental half-lives compared to GLDM and UDL. Moreover, it is found that
the predictions of the present model and UDL are highly consistent while GLDM
largely deviates from the other two. A study of the competition between
$\alpha$ decay and spontaneous fission (SF) shows that $\alpha$ decay is the
dominant mode. Among the studied SHN with $Z=122-125$, ${}^{295-307}122$ and
${}^{314-320}125$ are identified as potential candidates whose half-lives are
relatively long enough to be experimentally detected in the future through
their $\alpha$-decay chains. The identified candidates are in good agreement
with other recent work.

Nuclear Theory