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Recently, we applied an $ab$ $initio$ method, the no-core shell modelcombined with the resonating group method, to the transfer reactions with lightp-shell nuclei as targets and deuteron as the projectile. In particular, westudied the elastic scattering of deuterium on $^7$Li and the${}^{7}$Li($d$,$p$)${}^{8}$Li transfer reaction starting from a realistictwo-nucleon interaction. In this contribution, we review of our main results onthe ${}^{7}$Li($d$,$p$)${}^{8}$Li transfer reaction, and we extend the study ofthe relevant reaction channels, by showing the dominant resonant phase shiftsof the scattering matrix. We assess also the impact of the polarization effectsof the deuteron below the breakup on the positive-parity resonant states in thereaction. For this purpose, we perform an analysis of the convergence trend ofthe phase and eigenphase shifts, with respect to the number of deuteronpseudostates included in the model space.

${}^{7}$Li($d$,$p$)${}^{8}$Li transfer reaction in the NCSM/RGM approach