  We utilize the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB)
model to describe the structure of neutron-rich carbon isotopes, taking into
account the continuum, pairing correlations, tensor force and their interplay.
In this scheme, one- and two-neutron separation energies of neutron-rich carbon
isotopes agree well with measured data, as well as the spin and parity
$J^\pi=1/2^+$ for the ground state of $^{19}$C, which is a long-standing
problem for theoretical structure models. With the structure input extracted
from the microscopic D-RHFB model, the reaction observables are well described
the Glauber model. In particular, this unified approach accurately reproduces
the inclusive longitudinal momentum distributions of the breakup reaction
$^{19}$C + $^{12}$C at 240 MeV/nucleon, which rule out the possibility of the
ground state of $^{19}$C being $J^\pi=3/2^+$. Moreover, the continuum plays a
crucial role in the formation of the halo, which is further confirmed by the
reaction cross sections and longitudinal momentum distributions. However, the
tensor force components carried by the $\pi$-coupling are not as significant as
anticipated. Consequently, the D-RHFB + Glauber approach turns out to be a
promising tool to search for halo candidates from the structure to the
reaction.
