Continuum quasiparticle random-phase approximation for astrophysical direct neutron capture reactions on neutron-rich nuclei

I 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 from 1 keV to several MeV, which is relevant to the rapid neutron capture process of nucleosynthesis. I begin with the photoabsorption cross section and the $E1$ strength function. Next, in order to apply the reciprocity theorem, I decompose the cross section into partial cross sections corresponding to different channels of one- and two-neutron emission decays of photo-excited states. A numerical example is shown for the photo-absorption of ${}^{142}\mathrm{Sn}$ and the neutron capture of ${}^{141}\mathrm{Sn}$.

Figure 1

A diagrammatic representation of the partial photoabsorption cross section ${\sigma }_{\gamma \to nlj,l^{\prime }{j}^{\prime }}^L\left(E_{\gamma }\right)$, Eq. (35), and the vertex associated with the self-consistent field $V_{\mathrm{scf}}\left(\omega \right)$.

Figure 2

Calculated one- and two-neutron separation energies $S_{1n}$ and $S_{2n}$ for even-even Sn isotopes, plotted with solid and dotted lines, respectively. The experimental values [46] are shown with squares and crosses for $S_{1n}$ and $S_{2n}$, respectively.

Figure 3

Calculated $E1$ strength function $dB\left(E1\right)/dE$ in ${}^{142}\mathrm{Sn}$. The solid curve is the strength obtained with a smearing width $\gamma =2\epsilon =100$ keV, while the dashed curve is for a smearing width of 1 MeV. The long and short arrows indicate the one- and two-neutron separation energies $S_{1n}$ and $S_{2n}$, respectively.

Figure 4

Total photoabsorption cross section and partial cross section for one-neutron emission decay, plotted with dotted and solid curves, respectively, calculated for ${}^{142}\mathrm{Sn}$.

Figure 5

Partial photoabsorption cross sections for specific channels of one-neutron emission decays, calculated for ${}^{142}\mathrm{Sn}$. The three solid curves are for channels $3p_{3/2}\otimes c{s}_{1/2},3p_{3/2}\otimes c{d}_{3/2}$, and $3p_{3/2}\otimes c{d}_{5/2}$ while the two dashed curves are for $3p_{1/2}\otimes c{s}_{1/2}$ and $3p_{1/2}\otimes c{d}_{3/2}$ (see text for details). The arrows indicate the threshold energies of these decay channels.

Figure 6

Calculated branching ratios for one-neutron decays from photoexcited $1^{-}$ states of ${}^{142}\mathrm{Sn}$ populating the $3p_{3/2}$ state of the daughter ${}^{141}\mathrm{Sn}$ (plotted with diamonds), the same but for the $3p_{1/2}$ state (squares), and that for two-neutron decays (circles), evaluated for various photon energies $E_{\gamma }$.

Figure 7

Partial photoabsorption cross sections for specific channels of one-neutron emission decay, obtained for the Hartree–Fock single-particle transitions. Decays populating the $3p_{3/2}$ and $3p_{1/2}$ states of the daughter ${}^{141}\mathrm{Sn}$ are evaluated, but the cross sections for the $3p_{1/2}$ state are calculated to be zero in this null-pairing case.

Figure 8

Neutron capture cross sections for three different entrance channels, consisting of the ground state with the $3p_{3/2}$ configuration of ${}^{141}\mathrm{Sn}$ and an incident neutron in the partial waves $s_{1/2},d_{3/2}$, and $d_{5/2}$, populating $1^{-}$ states decaying to the ground state of ${}^{142}\mathrm{Sn}$. The horizontal axis is the neutron kinetic energy $e$. The dotted lines show the power law scaling $\propto e^{l-1/2}$.

Figure 9

Comparison of the neutron capture cross section obtained in the full QRPA calculation (solid curves) and the one obtained for the Hartree–Fock single-particle transitions (dotted curves). See also the caption of Fig. 8.