Triaxial deformation in nuclei with realistic $NN$ interactions

The structure of finite nuclei is investigated by employing an interaction model which is based on the low-momentum interaction $V_{\mathrm{low}k}$. It is supplemented by a density-dependent contact interaction fitted to reproduce the saturation properties of infinite nuclear matter within the Hartree-Fock approach. The calculations of finite nuclei are performed in a basis of plane waves discretized in a Cartesian box of appropriate size. As a first example, the structure of Ne isotopes ranging from ${}^{18}\mathrm{Ne}$ to the neutron drip line is considered. Rather good agreement is obtained for the bulk properties of these nuclei without any free parameter. The basis is also appropriate for describing other deformed nuclei and the transition from discrete nuclei to homogeneous matter which is supposed to occur in the crust of neutron stars.

Figure 1

Single-particle energies for protons [(a) left panel] and neutrons [(b) right panel] obtained from Hartree-Fock calculations for various Ne isotopes with even nucleon number $A$. Note that each line represents the position of two degenerate states. The energies of all occupied and the lowest unoccupied levels are presented. The dashed lines represent the position of the Fermi energy.

Figure 2

The Fermi energies for the neutrons and the protons in neon isotopes.

Figure 3

The energy gap between the last occupied state and the first unoccupied state for various neon isotopes.

Figure 4

The neutron and proton root-mean-square radius of neon isotopes. The experimental data for the charge radii have been obtained from measurements of the optical isotope shifts in [29]. For a comparison we also present results for the charge radius given in Ref. [22]

Figure 5

Contour plots of the neutron and proton density distributions of ${}^{24}\mathrm{Ne}$ in the $xy$, $xz$, and $yz$ planes.

Figure 6

Contour plots of the neutron density distributions of ${}^{24}\mathrm{Ne}$ in planes parallel [(a) left panel] and perpendicular [(b) right panel] to the elongation axis. The contour lines represent eight densities ranging in equal step sizes between zero and maximal density.

Figure 7

The energy difference between calculations allowing for triaxial structures and calculations allowing only spherical structures. The binding energy results considered are those without center-of-mass correction in both cases.

Figure 8

Contour plots of the neutron density distributions of a quasi-nuclear structure with 10 protons and 32 neutrons in the $xz$ plane [(a) left panel] and $yz$ plane [(b) right panel] of the box considered in the calculation. The contour lines represent the densities 0.005, 0.02 0.045, 0.07, and 0.09 nucleons $\mathrm{fm}{}^{-3}$, respectively.