Formation and decay of resonance states in ${}^9\mathrm{Be}$ and ${}^{9}B$ nuclei: Microscopic three-cluster model investigations

We study the nature of the low-lying resonance states in mirror nuclei ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$. Investigations are performed within a three-cluster model. The model makes use of the hyperspherical harmonics, which provides a convenient description of the three-cluster continuum. The dominant three-cluster configurations $\alpha +\alpha +n$ and $\alpha +\alpha +p$ in ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$, respectively, are taken into account. Dominant decay channels for all resonance states in ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$ are explored. Much attention is paid to the controversial $1/2^{+}$ resonance states in both nuclei. We study effects of the Coulomb interaction on the energy and width of three-cluster resonances in the mirror nuclei ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$. We also search for the Hoyle-analog state, which is a key step for alternative ways to synthesize ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$ in triple collisions of clusters in a stellar environment.

Figure 1

Spectra of rotational bands in ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$.

Figure 2

Experimental (Exp) and calculated spectra of ${}^9\mathrm{Be}$ determined with the MHNP and MP.

Figure 3

Experimental and calculated spectra of ${}^9\mathrm{B}$.

Figure 4

Comparison of some resonance states in ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$ calculated with the MHNP and MP potentials and with experimental data.

Figure 5

Phase shifts ${\delta }_{\mathrm{cc}}$ and inelastic parameters ${\eta }_{\mathrm{cc}}$ for the $3\Rightarrow 3$ scattering for the $J^{\pi }=1/2^{+}$ state in ${}^9\mathrm{Be}$.

Figure 6

Phase shifts ${\delta }_{\mathrm{cc}}$ and inelastic parameters ${\eta }_{\mathrm{cc}}$ for the $3\Rightarrow 3$ scattering for the $J^{\pi }=1/2^{+}$ state in ${}^9\mathrm{B}$.

Figure 7

Weights of different oscillator shells in the wave functions of $1/2^{+}$ resonance states in ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$.

Figure 8

Structure of the wave function of the $3/2^{-}$ resonance state in ${}^9\mathrm{B}$.

Figure 9

Spectra of bound and resonance states in ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$ calculated with the MHNP.

Figure 10

Displacement of resonance states due to the Coulomb interaction.

Figure 11

Weights of different oscillator shells in the wave function of the $5/2^{-}$ resonance state in ${}^9\mathrm{Be}$.

Figure 12

Structure of the wave function of the $5/2^{-}$ resonance state in ${}^9\mathrm{B}$. The result is obtained with the MHNP.