New double-magic nucleus 96Zr and conditions for existence of new magic nuclei

New information about energies and occupation probabilities of neutron and proton single-particle (hole) subshells in even-even nuclei was obtained in previous studies applying the method of putting into correspondence all available data on one-nucleon pickup and stripping reactions. The most important and interesting result was identification of several nuclei as new magic ones. Namely, itwas found that a filling of the neutron 2d5/2 subshell in 96Zr makes this nuclide a magic one. Moreover, changes in proton subshell energies with increasing neutron number N are accompanied by an increasing energy gap between closed 2p1/2 and empty 1g9/2 subshells. Thus, the neutron number N = 56 appears to be a magic one if the proton number Z is equal to 40. The proton number Z = 40 manifests properties of the magic number in 96Zr. Therefore, 96Zr was identified as a new double-magic nucleus. Further investigations revealed that the energy of the first 2+ state E(21+) in 96Zr is much higher than that in the neighboring isotopes and isotones, whereas the ratio E(41+)/E(21+) and the quadrupole deformation parameter β2 are, vice versa, clearly lower. Moreover, the A dependence of the neutron separation energy B(n) in Zr isotopes has an irregularity at N = 56 which is typical of magic nuclei. As a result of these investigations, it was found that, near the Fermi energy, there are two closed subshells with the same (and large) angular momentum j 5/2 (viz. π1f5/2 and ν2d5/2). We call this situation the jj connection. The magic numbers under discussion (Z = 40 and N = 56) are achieved at the points where both subshells are closed, and in addition, the closed subshell with j = 1/2, π2p1/2, occurs above the proton π1f5/2 subshell. This looks like a result of some additional attractive proton-neutron interaction. It was found that application of this scheme (jj connection) to other subshells reveals several other new magic nuclei: 54Ca (closed π1d3/2 and ν2p3/2 together with closed ν2p1/2), 30S and 30Si (closed π1d5/2 and ν1d5/2 together with closed (π/ν)2s1/2), and 14O and 14C (closed π1p3/2 and ν1p3/2 together with closed ν2p1/2)