Resonant-continuum relativistic mean-field plus BCS in complex momentum representation

To develop methods for open quantum systems is one of the most important tasks in theoretical studies. We develop the resonant-continuum relativistic mean-field theory in complex momentum representation with the BCS approximation for pairing correlations in weakly bound nuclei. The bound states and resonant states are treated on the same footing and the physical resonant states are considered self-consistently in the present calculations. The Zr isotopes are chosen as illustrative examples. The calculated binding energies, two-neutron separation energies, and root-mean-square radii are in excellent agreement with the available data as well as the relativistic Hartree-Bogoliubov calculations. Especially, several resonant states lying near the continuum threshold are found to play important roles in the formation of exotic phenomena and support the prediction of giant halo in the Zr isotopes.

Figure 1

Neutron single-particle spectra for ${}^{124}\mathrm{Zr}$ in the complex $k$ plane. The red solid diamonds and black open circles represent the resonances and the continuum, respectively.

Figure 2

Neutron single-particle energies and widths for the states close to the continuum threshold in the Zr isotopes. The states are labeled as $n{l}_j$ with $n, l$, and $j$ the radial, orbital, and total angular momentum quantum numbers, respectively. The Fermi surface is marked by the dashed line in the top panel.

Figure 3

Two-neutron separation energies of even-even Zr isotopes as a function of the mass number A. The blue solid circles and red open diamonds correspond to the RMF-BCS-CMR and RHB calculations, respectively. The black open squares represent the experimental data.

Figure 4

Neutron rms radii for the even-even Zr isotopes as a function of the mass number $A$. The red solid circles and black open squares correspond to the RMF-BCS-CMR and RHB calculations, respectively.

Figure 5

Occupation probabilities of neutron single-particle levels as a function of the mass number $A$ for the Zr isotopes. Labels are the same as those in Fig. 2.

Figure 6

Density distributions in ${}^{124}\mathrm{Zr}$. The top panel displays the ratio of the neutron density of the single-particle levels to the total neutron density. The bottom panel displays the proton, neutron, and total matter densities marked by the black solid, red dot, and blue dashed lines, respectively.