$\alpha +{}^{15}\mathrm{O}$ cluster structure in ${}^{19}\mathrm{Ne}$ and resonant $\alpha$ scattering

The rotational bands of $\alpha +{}^{15}\mathrm{O}\left(12^{-}\right)$ in ${}^{19}\mathrm{Ne}$ are calculated by employing a simple potential model. The $\alpha -{}^{15}\mathrm{O}$ interaction potential is constructed from the calculation of the ${}^{20}\mathrm{Ne}=\alpha +{}^{16}\mathrm{O}$ structure and the $\alpha +{}^{15}\mathrm{N}$ elastic scattering. The resonant levels and their decay width are identified by imposing the absorbing boundary condition. The present calculations predict the sequence of the discrete and overlapping resonances in the negative- and positive-parity states of ${}^{19}\mathrm{Ne}$, respectively. The excitation function of the $\alpha +{}^{15}\mathrm{O}$ elastic scattering is also calculated, and the appropriate condition to observe the resonances is discussed.

Figure 1

Energy spectra of ${}^{20}\mathrm{Ne}$. The left three groups of the levels represent the experimental spectra, while the right levels show the theoretical calculation obtained by the $\alpha +{}^{16}\mathrm{O}$ cluster model. In individual groups, the left, middle, and right levels have the $N=8$, 10, and 9, respectively, where $N$ denotes the total oscillator quanta of the harmonic oscillator potential.

Figure 2

Differential cross sections of the $\alpha +{}^{15}\mathrm{N}$ elastic scattering. The dots show the experimental data, while the solid curves represent the theoretical calculation. The differential cross sections are plotted in the Rutherford ratio.

Figure 3

Energy spectra of ${}^{19}\mathrm{Ne}$ with the negative parities $(N=8$ and even $L)$. The levels at the left side show the experimental spectra, while the middle and right levels show the theoretical calculations for ${}^{19}\mathrm{Ne}(=\alpha +{}^{15}\mathrm{O})$ and ${}^{20}\mathrm{Ne}(=\alpha +{}^{16}\mathrm{O})$, respectively. The $LS$ splitting states of ${}^{19}\mathrm{Ne}$ from ${}^{20}\mathrm{Ne}$ are indicated by the dotted lines.

Figure 4

Same as Fig. 3, except for the $N=9$ (odd $L)$ band. The shade attached to the levels represents the decay width. See text for details.

Figure 5

Excitation function of the $\alpha +{}^{15}\mathrm{O}$ elastic scattering at ${\theta }_{c.m.}={170}^{\circ }$. The solid curve shows the strength of the elastic scattering, while the solid circles show the energies of the resonant states identified by the ABC method. The error bars attached to the resonant levels represent the decay width.