  We formulate a many-body theory to calculate the cross section of direct
radiative neutron capture reaction by means of the Hartree-Fock-Bogoliubov
mean-field model and the continuum quasiparticle random phase approximation
(QRPA). A focus is put on very neutron-rich nuclei and low-energy neutron
kinetic energy in the range of O(1 keV) - O(1 MeV), relevant for the rapid
neutron-capture process of nucleosynthesis. We begin with the photo-absorption
cross section and the E1 strength function, then, in order to apply the
reciprocity theorem, we decompose the cross section into partial cross sections
corresponding to different channels of one- and two-neutron emission decays of
photo-excited states. Numerical example is shown for the photo-absorption of
$^{142}$Sn and the neutron capture of $^{141}$Sn.
