$\alpha$-cluster structure in ${}^{19}\mathrm{F}$ and ${}^{19}\mathrm{Ne}$ in resonant scattering

The nuclear structure of ${}^{19}\mathrm{F}$ and ${}^{19}\mathrm{Ne}$ is important for understanding of $\alpha$ clustering in the $A=20$ mass region and in questions related to astrophysics. However, the only high-resolution broad angular and energy range study of the ${}^{19}\mathrm{F}$ resonance structure in $\alpha +{}^{15}\mathrm{N}$ scattering was published over 60 years ago, and a detailed analysis of complex excitation functions of overlapping resonances with several decay channels was simply impossible at that time. We performed a modern $R$-matrix analysis of these old data to assign spins and specify resonant parameters of levels up to excitation energy of 8.2 MeV in ${}^{19}\mathrm{F}$. We successfully tested our $R$-matrix parameters in a fit of the recent data on $\alpha +{}^{15}\mathrm{N}$ obtained by thick target inverse kinematics (TTIK) method at 180 degrees. We used the new parameters for ${}^{19}\mathrm{F}$ to fit TTIK data for $\alpha +{}^{15}\mathrm{O}$, the mirror resonant reactions. The comparison of the data for isobaric mirror resonant reactions provides an interesting insight into the nuclear structure.

Figure 1

Excitation functions for the $\alpha +{}^{15}\mathrm{N}$ elastic scattering [5] and $R$-matrix fit. See text for explanations. Top panel for 70${}^{\circ }$ compares our calculations to those with parameters from La Cognata 2019 in Ref. [8]; the next panel for 90${}^{\circ }$ includes comparison with the fit with parameters of Bardayan et al. in Ref. [6]; inset magnifies the area around 7 MeV.

Figure 2

Excitation functions for the $\alpha +{}^{15}\mathrm{N}$ elastic scattering measured by the TTIK approach (Volya et al. [7] and La Cognata 2019 [8]) and $R$-matrix fit. See text for details.

Figure 3

Excitation function for the $\alpha +{}^{15}\mathrm{O}$ elastic scattering, points show data from Torresi et al, [9]. Inset shows the mirror excitation function for $\alpha +{}^{15}\mathrm{N}$ scattering and data from La Cognata 2019 [8].

Figure 4

Scheme of the lowest levels in mirror nuclei ${}^{19}\mathrm{F}$ and ${}^{19}\mathrm{Ne}$.

Figure 5

$\mathrm{\Delta }$E, shift of excitation energies of levels in ${}^{19}\mathrm{Ne}$ relative to their mirror counterpart in ${}^{19}\mathrm{F}$ calculated in the potential model (see text for explanations).