*2.7. N = 34 New Magic Number as a Consequence of the Shell Evolution*

Among various cases of shell evolution, a notable impact was made by predicting a new magic number *N* = 34. Figure 7 displays the shell evolution of some neutron orbits from Ni back to Ca isotopes, as *Z* decreases from 28 to 20. The 1 *f*5/2 orbit is between the 2*p*3/2 and 2*p*1/2 in Mayer–Jensen's shell model (see Figure 1). By loosing eight protons lying in the 1 *f*7/2 orbit of Ni isotopes (blue circles in Figure 7 left), this canonical shell structure is destroyed as the 1 *f*5/2 orbit moves up above the 2*p*1/2 orbit. This movement of 1 *f*5/2 orbit creates the *N* = 32 gap as a byproduct [44]. The energy shift in the 1 *f*5/2 orbit is due to the central and tensor forces by almost equal amounts. We mention that the *N* = 34 magic gap would not appear, if the Mayer–Jensen scheme holds, as expected, in Ni isotopes but this shift did not occur. The appearance of the *N* = 34 magic number was predicted as a result of a spin–isospin interaction in [45]. However, 12 years were required [46] until the experimental verification became feasible [47] (see Figure 7 right). The measured 2<sup>+</sup> energy levels are included in Figure 2b. More details are presented in [15]. Further evidences have been obtained recently by different experimental probes as reported in [48,49].

**Figure 7. Left**: Schematic illustration of the shell evolution from Ni back to Ca for neutron orbits. Blue circles denote protons. The wavy line is the interaction between the proton 1 *f*7/2 orbit and the neutron 1 *f*5/2 orbit. The numbers in circles indicate magic numbers. Taken from Figure 3 of [24]. **Right**: Observed excitation energies of the 2<sup>+</sup> <sup>1</sup> states. Taken from Figure 2c of [47].
