Particle-hole symmetry breaking due to Pauli blocking

Particle-hole symmetry has been used on several occasions in nuclear structure over the years. We prove that particle-hole symmetry is broken in nuclear shells possessing the proxy-SU(3) symmetry. The breaking of the symmetry is rooted in the Pauli principle and the short range nature of the nucleon-nucleon interaction. The breaking of the symmetry explains the dominance of prolate over oblate shapes in deformed nuclei and determines the regions of prolate to oblate shape transitions in the nuclear chart. Furthermore, it is related to the existence of specific regions of shape coexistence across the nuclear chart, surrounded by regions in which shape coexistence does not occur.