  We investigate the degree of $\alpha$ ($^4$He nucleus) clustering in the
ground-state density profiles of $^{44}$Ti and $^{52}$Ti. Two types of density
distributions, shell- and cluster-model configurations, are generated fully
microscopically with the antisymmetrized quasi-cluster model, which can
describe both the j-j coupling shell and $\alpha$-cluster configurations in a
single scheme. Despite both the models reproducing measured charge radius data,
we found that the $\alpha$ clustering significantly diffuses the density
profiles near the nuclear surface compared to the ideal j-j coupling shell
model configuration. The effect is most significant for $^{44}$Ti, while it is
less for $^{52}$Ti due to the occupation of the $0f_{7/2}$ orbits in the
$^{48}$Ca core. This difference can be detected by measuring proton-nucleus
elastic scattering or the total reaction cross section on a carbon target at
intermediate energies.
