Microscopic three-cluster study of light exotic nuclei

I develop a microscopic three-cluster model for exotic light nuclei. I use the hyperspherical formalism, associated with the generator coordinate method. This model is well adapted to halo nuclei, since the long-range part of the radial wave functions is accurately reproduced. The core wave functions are described in the shell model, including excited states. This technique provides large bases, expressed in terms of projected Slater determinants. Matrix elements involve seven-dimension integrals, and therefore require long calculation times. I apply the model to ${}^{11}\mathrm{Li}, {}^{14}\mathrm{Be}, {}^{15}\mathrm{B}$, and ${}^{17}\mathrm{N}$ described by two neutrons surrounding a ${}^9\mathrm{Li}, {}^{12}\mathrm{Be}, {}^{13}\mathrm{B}$, and ${}^{15}\mathrm{N}$ core, respectively. The ${}^{17}\mathrm{Ne}$ (as ${}^{15}\mathrm{O}+\mathrm{p}+\mathrm{p}$) and ${}^{15}\mathrm{Ne}$ (as ${}^{13}\mathrm{O}+\mathrm{p}+\mathrm{p}$) mirror nuclei are briefly discussed. I present the spectra and some spectroscopic properties, such as r.m.s. radii or $E2$ transition probabilities. I also analyze the importance of core excitations.

Figure 1

Three-cluster configuration using the generator coordinates ${\mathit{R}}_1$ and ${\mathit{R}}_2$ [see Eq. (7)].

Figure 2

Ground-state energies (with respect to the core $+$ n $+$ n threshold) as a function of the maximum hypermomentum $K_{\max }$. The dotted lines are obtained by neglecting core excitations.

Figure 3

${}^{12}\mathrm{Be}+\mathrm{n}+\mathrm{n}$ energy curves (20) for different $J\pi$-values.

Figure 4

Convergence of ${}^{14}\mathrm{Be}$ energies with respect to the maximum generator coordinate $R_{\max }$.

Figure 5

Convergence of the ${}^{14}\mathrm{Be}$ squared radius as a function of the maximum generator coordinate $R_{\max }$. The two first $0^{+}$ and $2^{+}$ eigenvalues are shown.

Figure 6

(a) ${}^{13}\mathrm{B}+\mathrm{n}+\mathrm{n}$ energy curves (20) for different $J\pi$ values. For negative parity, two eigenvalues are displayed. (b) ${}^{13}\mathrm{O}+\mathrm{p}+\mathrm{p}$ energy curves.

Figure 7

${}^{15}\mathrm{B}$ and ${}^{15}\mathrm{Ne}$ energy spectra, compared with experiment [33, 36]. Numbers at the left of the GCM states correspond to the amount of ${}^{13}\mathrm{B}\left(\text{g.s.}\right)+\text{n}+\text{n}$ configuration (in %). For ${}^{15}\mathrm{Ne}$, the hatched areas indicate broad resonances.

Figure 8

${}^{15}\mathrm{N}+\mathrm{n}+\mathrm{n}$ energy curves (20) for different $J\pi$ values.

Figure 9

${}^{17}\mathrm{N}$ and ${}^{17}\mathrm{Ne}$ energy spectra, compared with experiment [44]. Only negative-parity states are shown. Numbers at the left of GCM states correspond to the amount of ${}^{15}\mathrm{N}\left(\text{g.s.}\right)+\text{n}+\text{n}$ configuration (in %).

Figure 10

${}^9\mathrm{Li}+\mathrm{n}+\mathrm{n}$ energy curves (20) for different $J\pi$ values.