The Lowest Broad Alpha Cluster Resonances in $^{19}$F

There is a deep astrophysical interest in the structure of $^{19}$F states close to the alpha decay threshold. The nuclear structure of these states is important for understanding of the development of $\alpha$ clustering in the $^{20}$Ne region. Emergence of clustered states and generally states that favor coupling to reaction channels near the corresponding decay thresholds is currently of special interest in theoretical physics. Excitation function for $^{15}$N($\alpha$,$\alpha$) elastic scattering was measured by the TTIK method. These new data together with old, high energy resolution data, were analyzed using the R matrix approach. $^{19}$F nuclear structure was calculated using configuration interaction methods with the recently developed effective interaction Hamiltonian. The parameters of broad low spin $\ell = 0$ and 1 relative partial wave resonances close to the $\alpha$ decay threshold in $^{19}$F were identified. Detailed theoretical analysis was carried out identifying all states coupled to the $\ell = 0$ and 1 alpha cluster channels. Considering hierarchy of states with different harmonic oscillator shell excitations allows to evaluate coupling to the alpha channels with different number of nodes in the relative wave function and helps to explain the distribution of the clustering strength and emergence of broad clustering resonances. Comparison of clustering in $^{20}$Ne into $^{16}$O+$\alpha$ and consideration of spin-orbit splitting of the $^{15}$N+$\alpha$ channel provides additional evidence. Detailed analysis of new and old experimental data allows to identify a series of $\alpha$ clustering resonances in $^{19}$F and to assess the distribution of the clustering strength which is of importance to questions of astrophysics and for theoretical understanding of many-body physics and emergence of clustering in loosely bound or unstable nuclei.