Research on deformed exotic nuclei by relativistic mean field theory in complex momentum representation

The exotic nuclei have attracted extensive attention in nuclear physics recently. The resonant states are thought to play a critical role at the formation of these exotic phenomena. Here, the complex momentum representation (CMR) method for resonances is combined with the relativistic mean field (RMF) theory applicable to deformed system. The RMF-CMR method for deformed exotic nuclei is established. The theoretical formalism and numerical details are presented. ${}^{75}\mathrm{Cr}$ is chosen as an example, the energies and widths of single-particle levels and their evolutions to deformation ${\beta }_2$ are obtained for resonant states together with bound states. The available potential energy curve shows that ${}^{75}\mathrm{Cr}$ is a deformed nucleus with ${\beta }_2=0.333$. Wave function of the orbit occupied by the last valence neutron consists mainly of $d$-wave components. The corresponding density represents a considerably diffuse distribution, which suggests that ${}^{75}\mathrm{Cr}$ is a $d$-wave deformed halo nucleus. The predication is helpful to explore the deformation halos in experiment for the nuclei in the medium mass region.

Figure 1

The binding energy per nucleon $E/A$ in ${}^{75}\mathrm{Cr}$ and its evolution to the quadruple deformation ${\beta }_2$.

Figure 2

The single-particle spectra in the deformed nucleus ${}^{75}\mathrm{Cr}$ for states ${\mathrm{\Omega }}^{\pi }=1/2^{+},3/2^{+},...,9/2^{+}$ on the complex momentum plane. The bound states and the continuous spectrum are marked with blue open boxes and black open circles, respectively. The resonant states with different quantum numbers are marked with different colored labels.

Figure 3

The single-particle levels and their evolutions to the quadruple deformation ${\beta }_2$ in ${}^{75}\mathrm{Cr}$. These levels for axially deformed nuclei are labeled with the asymptotic quantum numbers $\mathrm{\Omega }\left[N{n}_z\mathrm{\Lambda }\right]$. The corresponding spherical labels are placed in the position ${\beta }_2=0$. A shorter vertical line marks the location of the ground-state deformation with ${\beta }_2=0.333$. The numerical data are supplied as Supplemental Material [68].

Figure 4

Real part of the configuration occupation probabilities and their evolutions to the quadruple deformation parameter ${\beta }_2$. For the single-particle state 1/2[411], these configurations are $s_{1/2},d_{3/2},d_{5/2},g_{7/2},g_{9/2},i_{11/2},i_{13/2}$, and $k_{15/2}$ in the present calculations. The corresponding imaginary parts are too small on the order of ${10}^{-12}$ and not displayed here. The same as Fig. 3, a shorter vertical line marks the location of the ground-state deformation.

Figure 5

Real part of radial density distributions for the single-particle states 1/2[411], 3/2[411], 7/2[413], and 9/2[404] in ${}^{75}\mathrm{Cr}$ with deformation ${\beta }_2=0.333$. The insertion is the imaginary part of radial density distributions for the resonant state 9/2[404] multiplied by ${10}^8$. The imaginary part of the three weakly bound states is at the power of ${10}^{-12}$ and not shown here.

Figure 6

The same as Fig. 5 but for the RMF-CMR calculations with the interactions PK1.