Cranked Skyrme-Hartree-Fock-Bogoliubov approach for a mean-field description of nuclear rotations near the drip line

To describe the yrast states in weakly bound nuclei, I directly solve the coordinate-space cranked Skyrme-Hartree-Fock-Bogoliubov equation on a three-dimensional lattice with the continuum states discretized in a box. After the numerical demonstration for the ground-state band in a medium-mass nucleus, I apply the newly developed method to neutron-rich even-$N$ Mg isotopes. I find that the appearance of the significantly low $I^{\pi }=2^{+}$ state in ${}^{40}\mathrm{Mg}$ is mainly due to the suppression of pairing. The calculation predicts that the $2^{+}$ state in ${}^{42}\mathrm{Mg}$ appears as high in energy as in ${}^{34–38}\mathrm{Mg}$ whereas the triaxial deformation is enhanced in nonzero spin states. The present numerical framework offers a practical approach for investigating the near yrast states systematically and revealing structures unique in drip-line nuclei.

Figure 1

Kinematic moments of inertia ${\mathcal{J}}^{\left(1\right)}$ as functions of the rotational frequency. The experimental data [39] are denoted by open symbols. Dependence of ${\mathcal{J}}^{\left(1\right)}$ evaluated at ${\omega }_{\mathrm{rot}}=0.05$ MeV on the parameters $h$ and $M$ is shown in the inset.

Figure 2

Similar to Fig. 1 but for ${}^{34}\mathrm{Mg}$. The results obtained by using several pairing interactions are displayed. The experimental data are obtained from Ref. [46].

Figure 3

(a) Similar to Fig. 2 but for ${}^{36,38,40}\mathrm{Mg}$. The experimental data, denoted by open symbols, are taken from Refs. [20, 24]. (b) Calculated ${\mathcal{J}}^{\left(1\right)}$ for ${}^{40}\mathrm{Mg}$ obtained with the box sizes $M=8$, 10, and 12. Results without the pairing are also depicted.

Figure 4

Calculated $E\left(2^{+}\right)$ (upper) and $R_{4/2}$ (lower) values with the SkM* (squares) and SLy4 (circles) functionals. The results obtained by using $M=10$ and 14 are depicted by open and filled symbols, respectively. The result without the pairing is shown by a diamond for SkM* at $N=28$. The experimental data are displayed by open triangles.

Figure 5

Deformation parameters of protons in ${}^{34,36,38,40}\mathrm{Mg}$.