The astrophysical factor of $^8$B($p$,$gamma$)$^9$C at zero energy, $S_{18}(0)$, is determined by a three-body coupled-channels analysis of the transfer reaction $^{8}$B($d$,$n$)$^{9}$C at 14.4 MeV/nucleon. Effects of the breakup channels of $d$ and
$^9$C are investigated with the continuum-discretized coupled-channels method. It is found that, in the initial and final channels, respectively, the transfer process through the breakup states of $d$ and $^9$C, its interference with that through their ground states in particular, gives a large increase in the transfer cross section. The finite-range effects with respect to the proton-neutron relative coordinate are found to be about 20%. As a result of the present analysis, $S_{18}(0)=22 pm 6~{rm eV~b}$ is obtained, which is smaller than the result of the previous distorted-wave Born approximation analysis by about 51%.
Extensions of the eikonal approximation to low energy (20MeV/nucleon typically) are studied. The relation between the dynamical eikonal approximation (DEA) and the continuum-discretized coupled-channels method with the eikonal approximation (E-CDCC)
is discussed. When Coulomb interaction is artificially turned off, DEA and E-CDCC are shown to give the same breakup cross section, within 3% error, of $^{15}$C on $^{208}$Pb at 20MeV/nucleon. When the Coulomb interaction is included, the difference is appreciable and none of these models agrees with full CDCC calculations. An empirical correction significantly reduces this difference. In addition, E-CDCC has a convergence problem. By including a quantum-mechanical correction to E-CDCC for lower partial waves between $^{15}$C and $^{208}$Pb, this problem is resolved and the result perfectly reproduces full CDCC calculations at a lower computational cost.
