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

Cluster structures are well known to appear in the excited states of light nuclear systems. A typical example is the $\alpha + ^{16}$O cluster structures in $^{20}$Ne, and the $\alpha + ^{15}$N structures are also deeply analyzed in $^{19}$F, which is one proton deficient system of $^{20}$Ne. However, the $\alpha + ^{15}$O structure, corresponding to the neutron deficient system of $^{20}$Ne, still remains unclear. In the present study, we investigate the $\alpha + ^{15}$O structure in $^{19}$Ne by employing a simple potential model. We assume the Wood-Saxon potential for the nuclear potential of $\alpha + ^{15}$O, and its parameter set is fixed by solving the $\alpha + ^{15}$N elastic scattering. From the nuclear potential determined from the $\alpha + ^{15}$N scattering problem, we calculate the energy levels in the $^{19}$Ne $= \alpha + ^{15}$O system by adding the Coulomb interaction to the $\alpha + ^{15}$N system. The absorbing boundary condition is imposed on the unbound states in $\alpha + ^{15}$O, and the resonant levels in $^{19}$Ne are identified. We have also calculated the excitation function of the resonant $\alpha + ^{15}$O elastic scattering under the same condition as the recent experiments. In the present report, we will show our prediction of the $\alpha + ^{15}$O rotational bands and the cross sections in the resonant $\alpha $ scattering. Moreover, we will also report the application of the microscopic cluster model to the $^{19}$Ne $= \alpha + ^{15}$O system.