Lattice simulation of nucleon distribution and shell closure in the proton-rich nucleus ²²Si

The proton-rich nucleus ²²Si is studied using Nuclear Lattice Effective Field Theory with high-fidelity chiral forces. Our results indicate that ²²Si is more tightly bound than ²⁰Mg, thereby excluding the possibility of two-proton emission. The Z=14 shell closure in ²²Si is investigated through the evolution of the 2⁺ state in the neighboring nuclei. We then focus on the charge radius and spatial distribution information of ²²Si, considering the novel phenomena that may emerge due to the small two-proton separation energy and the shell closure. We present the distribution of the 14 protons and 8 neutrons obtained from our lattice simulation, revealing insights into the spatial arrangement of the nucleons. Moreover, the spatial localization of the outermost proton and neutron suggests that ²²Si is a doubly magic nucleus. Furthermore, we develop the pinhole method based on the harmonic oscillator basis, which gives insight into the nuclear structure in terms of the shell model picture from lattice simulations. Our calculated occupation numbers support that Z=14 and N=8 are the shell closures and show that the π1s_1/2 orbital component is minor in ²²Si.