  We study the possibility to use the cluster-daughter overlap as a new probe
of alpha-cluster formation in medium-mass and heavy even-even nuclei. We
introduce a dimensionless parameter $\mathfrak{O}$, which is the ratio between
the root-mean-square (rms) intercluster separation and the sum of rms point
radii of the daughter nucleus and the alpha particle, to measure the degree of
the cluster-daughter overlap quantitatively. By using this parameter, a large
(small) cluster-daughter overlap between the alpha cluster and daughter nucleus
corresponds to a small (large) $\mathfrak{O}$ value. The alpha-cluster
formation is shown explicitly, in the framework of the quartetting wave
function approach, to be suppressed when the $\mathfrak{O}$ parameter is small,
and be favored when the $\mathfrak{O}$ parameter is large. We then use this
$\mathfrak{O}$ parameter to explore systematically the landscape of
alpha-cluster formation probabilities in medium-mass and heavy even-even
nuclei, with $\mathfrak{O}$ being calculated from experimentally measured
charge radii. The trends of alpha-cluster formation probabilities are found to
be generally consistent with previous studies. The effects of various shell
closures on the alpha-cluster formation are identified, along with some hints
on a possible subshell structure at $N=106$ along the Hg and Pb isotopic
chains. The study here could be a useful complement to the traditional route to
probe alpha-cluster formation in medium-mass and heavy even-even nuclei using
alpha-decay data. Especially, it would be helpful in the cases where the target
nucleus is stable against alpha decay or alpha-decay data are currently not
available.
