New magicity $N=32$ and $34$ triggered by strong couplings between Dirac inversion partners

Inspired by recent experiments, the successive new magicity N = 32 and 34 in Ca isotopes are studied within the relativistic density functional theory. It is illustrated that the strong couplings between the s1/2 and neutron (ν) ν2p1/2 orbits, here referred as ”Dirac inversion partners” (DIPs), play a key role in opening both subshells N = 32 and 34. Such strong couplings originate from the inversion similarity between the DIPs, that the upper component of the Dirac spinor of one partner shares the same orbital angular momentum as the lower component of the other, and vice versa. Following the revealed mechanism, it is predicted that the magicity N = 32 is reserved until S, but vanishes in Si.