Role of triaxiality in deformed halo nuclei

It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider nonaxially symmetric deformations. With triaxial deformation, the $\mathrm{\Omega }$ quantum number is admixed in a single-particle wave function, where $\mathrm{\Omega }$ is the projection of the single-particle angular momentum on the symmetric axis, and the halo structure may arise even when it is absent with the axially symmetric deformation. In this way, the area of halo nuclei may be extended when triaxial deformation is considered. We demonstrate this idea using a deformed Woods-Saxon potential for nuclei with neutron number $N=13$ and 43.

Figure 1

Neutron levels as a function of the quadrupole deformation parameter $\beta$ obtained with an axially deformed Woods-Saxon potential.

Figure 2

(a) The fraction of the $s$-wave component, (b) the expectation value of the total single-particle angular momentum $j_z$, and (c) the root-mean-square (rms) radius for the 43rd neutron orbital in a deformed Woods-Saxon potential. These are plotted as a function of the single-particle energy for several values of triaxiality parameter $\gamma$ with $\beta =0.3$.

Figure 3

Similar to Fig. 2, but as a function of $\gamma$ for $S_n=0.2$ MeV.

Figure 4

A Nilsson diagram for neutron levels around $N=13$.

Figure 5

Relation between the single-particle energy of the valence neutron in ${}^{19}\mathrm{C}$ and the root-mean-square (rms) radius for several values of the triaxial deformation parameter $\gamma$. The deformation parameter $\beta$ is fixed to be 0.343. The boxes with the right diagonal lines and the left diagonal lines show the experimental values of the rms radius from Nakamura et al. (1999) [36] and Kanungo et al.( 2016) [38], respectively, together with the empirical separation energy $S_n=160\pm 110$ keV from Ref. [44].