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.
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