Shell evolution and its indication on the isospin dependence of the spin-orbit splitting

The available experimental data on shell evolution indicate that the strength of the spin-orbit single-particle potential may be enhanced in neutron-rich nuclei. We observe that such a simple scheme destroys the harmonic oscillator magic numbers N=8 and 20 and generates new magic numbers like N=6, 14, 16, 32 and 34. The traditional magic numbers like N=28 and 50 and N=14 seen in 22O are eroded in neutron-rich nuclei due to the sensitivity of larger-l orbitals to the depth of the central potential but they are more robust than the harmonic oscillator magic numbers. The N=82 shell closure persists in neutron-rich nuclei while the previously proposed shell closures like N=40 and 70 do not emerge. Both mechanisms contribute to enhancing the N=56 and 90 gaps by splitting the 1d5/2 and 0g7/2 and the 0h9/2 and 1f7/2 orbitals.