  A new $^{11}$Be($d,p$)$^{12}$Be transfer reaction experiment was carried out
in inverse kinematics at 26.9$A$ MeV, with special efforts devoted to the
determination of the deuteron target thickness and of the required optical
potentials from the present elastic scattering data. In addition, a direct
measurement of the cross sections for the 0$_2^+$ state was realized by
applying an isomer-tagging technique. The s-wave spectroscopic factors of
0.20(0.04) and 0.41(0.11) were extracted for the 0$_1^+$ and 0$_2^+$ states,
respectively, in $^{12}$Be. Using the ratio of these spectroscopic factors,
together with the previously reported results for the p-wave components, the
single-particle component intensities in the bound 0$^+$ states of $^{12}$Be
were deduced, allowing a direct comparison with the theoretical predictions. It
is evidenced that the ground-state configuration of $^{12}$Be is dominated by
the d-wave intruder, exhibiting a dramatic evolution of the intruding mechanism
from $^{11}$Be to $^{12}$Be, with a persistence of the $N = 8$ magic number
broken.
