Drastic change in inelastic scattering depending on the development of dineutron correlation in $^{10}$Be

We investigated the development and breaking of the dineutron correlation in $^{10}$Be by analyzing the elastic and inelastic scatterings with a framework combing the microscopic structure and reaction models. For studying the structure, the $^{10}$Be nucleus was constructed under the assumption of a four-body ($alpha + alpha + n + n$) cluster model. In this work, we focused on the change in the inner structure for the 0$_1^+$, 2$_1^+$, and 2$_2^+$ states when the strength of the spin-orbit interaction is varied. The inner structure, including various physical quantities such as energy, radius, and transition strength, is drastically influenced by the strength of the spin-orbit interaction. In particular, the development and breaking of the dineutron correlation is governed by the spin-orbit strength. The differences in the inner structure can be manifested by applying the obtained wave functions to elastic and inelastic scatterings with a proton target at $E/A =$ 59.4 and 200 MeV. Although the 0$_1^+$ and 2$_1^+$ states are significantly influenced by the spin-orbit strength of the nuclear structure calculation, the elastic and inelastic cross sections are not much affected. On the other hand, the inelastic cross section of the 2$_2^+$ state depends greatly on the spin-orbit strength of the structure calculation. Thus, we discovered a way to measure the degree of the development of dineutron cluster structure based on its sensitivity to the inelastic cross section of the 2$_2^+$ state of $^{10}$Be.