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Continuum quasiparticle random phase approximation for astrophysical direct neutron capture reaction of neutron-rich nuclei

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.