Research on the halo in ${}^{31}\mathrm{Ne}$ with the complex momentum representation method

Halo is one of the most interesting phenomena in exotic nuclei especially for ${}^{31}\mathrm{Ne}$, which is deemed to be a halo nucleus formed by a $p$-wave resonance. However, the theoretical calculations do not suggest a $p$-wave resonance using the scattering phase shift approach or complex scaling method. Here, we apply the complex momentum representation method to explore resonances in ${}^{31}\mathrm{Ne}$. We have calculated the single-particle energies for bound and resonant states together with their evolutions with deformation. The results show that the $p$-wave resonances appear clearly in the complex momentum plane accompanied by a $p\text{−}f$ inversion in the single-particle levels. Because the $p\text{−}f$ inversion happens, calculated energy, width, and occupation probabilities of major components in the level occupied by the valance neutron support a $p$-wave halo for ${}^{31}\mathrm{Ne}$.

Figure 1

Single-particle spectra for the states ${\mathrm{\Omega }}^{\pi }=1/2^{-}$ with ${\beta }_2=0.2$ in complex momentum plane, where the red open circles, blue hollow squares, green hollow rhombus, and magenta points represent the resonant states in four different contours, respectively. The other is the continuum following the contours in a grey solid line.

Figure 2

Radial density distributions as a function of the coordinate $r$ for the single-particle states 1/2[110] and 1/2[310] with ${\beta }_2=0.2$ and 3/2[321] with ${\beta }_2=0.5$. The left four lines belong to 1/2[110], the upper four lines on the right belong to 3/2[321], and those in the lower belong to 1/2[310]. The four contours are the same as those in Fig. 1.

Figure 3

Single-particle spectra of ${}^{31}\mathrm{Ne}$ for the states ${\mathrm{\Omega }}^{\pi }=1/2^{\pm },3/2^{\pm },\cdots ,9/2^{\pm }$ in several different deformations. The black open circles and purple solid line represent respectively the continuum and contour of momentum integration, and the other symbols represent the resonant states.

Figure 4

Neutron single-particle levels as a function of quadruple deformation ${\beta }_2$. The bound levels and resonant levels are marked by the solid and dashed lines, respectively.

Figure 5

Calculated occupation probabilities of the major components $p_{3/2},f_{7/2},p_{1/2}$, and $f_{5/2}$ in the 1/2[310] level.

Figure 6

Calculated occupation probabilities of major components $f_{7/2},p_{3/2},f_{5/2}$, and $h_{11/2}$ in the 3/2[321] level.

Figure 7

Same as Fig. 4, but for the width of resonant states.

Figure 8

Radial-momentum probability distributions for the state 1/2[310] with ${\beta }_2=0.25$ and 3/2[321] with ${\beta }_2=0.5$, where the upper and lower four lines belong to 1/2[310] and 3/2[321], respectively.