  Experimental results of the $p(^{13}{\rm B},d)^{12}{\rm B}$ transfer reaction
to the low-lying states in $^{12}$B are reported. The optical potential
parameters for the entrance channel are extracted from the elastic scattering
$p$($^{13}{\rm B}$, $p$) measured in the same experiment, while those for the
exit channel are global ones. Spectroscopic factors associated with the $p$-,
$s$-, and $d$-wave neutron transfer to the known $^{12}$B states, are extracted
by comparing the deuteron angular distributions with the calculation results.
The separated $s$- and $d$-wave intruder strengths in $^{13}{\rm B}_{\rm g.s.}$
were determined to be $10(2)\%$ and $6(1)\%$, respectively, which follow
roughly the systematics for the $N$ = 8 neutron-rich isotones. The measured
total intruder strength is in good agreement with the shell model calculation,
while the individual ones evolve quite differently. Particularly, the sudden
change of the $d$-wave intensity between $^{13}$B and $^{12}$Be needs further
theoretical interpretation.
