Prediction of halo structure in nuclei heavier than ${}^{37}\mathrm{Mg}$ with the complex momentum representation method

The discovery of the halo phenomenon has changed the traditional understanding of nuclear structure and opened up a new frontier in nuclear physics. The resonant states are thought to play a critical role at the formation of a halo. In this paper, we adopt the complex momentum representation method to explore the single-particle resonances for several slightly heavier nuclei than those halo nuclei found in experiment. The single particle bound and resonant levels and their evolution with the quadruple deformation ${\beta }_2$ are obtained and accompanied by a clear shell structure. The configuration occupations and density distributions of valence nucleon support the existence of halo structure. Namely, an $s$-wave halo may be formed in the range of $-0.06\le {\beta }_2\le 0.13$ ($-0.12\le {\beta }_2\le 0.12$) in ${}^{77}\mathrm{Fe}$ (${}^{75}\mathrm{Cr}$), and a $p$-wave halo may be formed in the range of $0.09\le {\beta }_2\le 0.13$ in ${}^{53}\mathrm{Ar}$. This prediction is of referential value for the exploration of heavier halo nuclei in experiment.

Figure 1

Neutron single-particle levels in ${}^{77}\mathrm{Fe}$ and their evolutions with quadruple deformation ${\beta }_2$. The bound levels and resonant levels are marked respectively by the solid line and dashed line with the Nilsson labels $\mathrm{\Omega }\left[N{n}_z\mathrm{\Lambda }\right]$ on the lines.

Figure 2

The occupation probabilities of major configurations as a function of ${\beta }_2$ for the single-particle level 1/2[400] in ${}^{77}\mathrm{Fe}$.

Figure 3

The radial density distributions multiplied by $r^2$ for the single-particle states 1/2[400], 1/2[440], and 3/2[413] with ${\beta }_2=-0.04$ in ${}^{77}\mathrm{Fe}$.

Figure 4

The radial density distributions multiplied by $r^2$ for the single-particle states 1/2[400], 9/2[404], and 7/2[413] with ${\beta }_2=0.06$ in ${}^{77}\mathrm{Fe}$.

Figure 5

${}^{75}\mathrm{Cr}$: Neutron single-particle levels as a function of quadruple deformation ${\beta }_2$, where the bound and resonant levels are marked respectively by the solid and dashed lines with the Nilsson labels on the line. Every level is labeled with the asymptotic quantum numbers $\mathrm{\Omega }\left[N{n}_z\mathrm{\Lambda }\right]$.

Figure 6

${}^{75}\mathrm{Cr}$: The occupation probabilities $P_{\mathrm{\Omega }}^i$ of major configurations as a function of ${\beta }_2$ for the single-particle state 1/2[400], where $i$ represents the configurations $s_{1/2}$, $d_{3/2}$, $d_{5/2}$, $g_{7/2}$, $g_{9/2}$, etc.

Figure 7

${}^{75}\mathrm{Cr}$: The radial density distributions multiplied by $r^2$ for the single-particle states 1/2[400], 1/2[440], and 3/2[413] with ${\beta }_2=-0.1$.

Figure 8

${}^{75}\mathrm{Cr}$: The radial density distributions multiplied by $r^2$ for the single-particle states 1/2[400], 9/2[404], and 7/2[413] with ${\beta }_2=0.1$.

Figure 9

Neutron single-particle levels in ${}^{53}\mathrm{Ar}$ as a function of quadruple deformation ${\beta }_2$, where the bound and resonant levels are marked respectively by the solid and dashed lines with the Nilsson labels on the lines. Every level is labeled with the asymptotic quantum numbers $\mathrm{\Omega }\left[N{n}_z\mathrm{\Lambda }\right]$.

Figure 10

The occupation probabilities of the major configurations as a function of ${\beta }_2$ for the single-particle state 1/2[321] in ${}^{53}\mathrm{Ar}$.

Figure 11

The radial density distributions multiplied by $r^2$ for the single-particle levels 1/2[321], 3/2[312], and 1/2[301] with ${\beta }_2=0.1$ in ${}^{53}\mathrm{Ar}$.