Formation and decay of resonance state in $^{9}$Be and $^{9}$B nuclei. Microscopic three-cluster model investigations

We study nature of the low-lying resonance states in mirror nuclei $^{9}$Be and $^{9}$B. Investigations are performed within a three-cluster model. The model makes use of the hyperspherical harmonics, which provides convenient description of three-cluster continuum. The dominant three-cluster configurations $\alpha+\alpha+n$ and $\alpha+\alpha+p$ in $^{9}$Be and $^{9}$B, respectively, are taken into account. Dominant decay channels for all resonance states in $^{9}$Be and $^{9}$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 energy and width of three-cluster resonances in the mirror nuclei $^{9}$Be and $^{9}$B. We also search for the Hoyle-analogue state which is a key step for alternative way of $^{9}$Be and $^{9}$B syntheses in a triple collision of clusters in a stellar environment.