It has been proven that the idea of a shell structure may be considered as an essential concept in understanding the atomic nucleus. According to that picture, the nucleons in a nucleus occupy well defined orbitals what implies that they move in a well defined average potential. The non-uniformities of the quantum states distribution in energy form the shells separated by the energy gaps - complete filling of the shells in nuclei along the stability valley occurs at magic numbers of nucleons: 2, 8, 20, 28, 50, 82, and 126. Theoretical picture of a nucleus in which the single particle states are calculated in an average potential well, with addition of a spin-orbit term, was developed by Maria Goeppert-Maier and Hans Jensen in 1949 (they were awarded for it the Nobel Prize in 1963).

The idea of nuclear shell structure is very familiar to that known from theory of the atom: the elements with the outer shell fully filled with electrons are characterized by a particular chemical stability. These elements are the noble gases with a total numbers of electrons 2, 10, 18, 36, 54 and 86.

Whereas the atomic magic numbers are rather immutable, the numbers of protons or neutrons required to fill a nuclear shell are not as universal as one might think. Recent investigations have shown that in the regions of nuclear chart in which the balance between protons and neutrons is significantly different from that encountered in the stability valley, some nuclei that were expected to be magic do not exhibit the appropriate properties on one hand, and, on the other, there are indications of the existence of new magic numbers. Apparently, the gaps between nuclear levels responsible for the existence of shells and magic numbers evolve when moving away from the stability line.

. For many years our group used deep-inelastic heavy ion reactions and thick target gamma coincidence techniques to study the neutron-rich nuclei in several regions of the nuclidic chart. In a series of such experiments we revealed new structures in several neutron-rich isotopes from the doubly-magic ⁴⁸Ca region. In particular, our attention was focused on the neutron-rich titanium isotopes. We found that in ⁵⁴Ti, the energy spacing between the first three yrast excitations, i.e., the 2⁺, 4⁺ and 6⁺ members of the two valence proton (f_7/2)² multiplet, as well as the magnitude of the energy gap between the 6+ state and the higher-lying yrast levels, were found to be similar to those observed in the semi-magic nucleus ⁵⁰Ti. With this observation we confirmed the existence of a new subshell closure that occurs in neutron-rich nuclei at N=32. This closure reflects an energy gap between the p_3/2 orbital and the p_1/2, f_5/2 neutron states. It disappears when going toward the stability line due to the strong proton f_7/2 - neutron f_5/2 monopole interaction, primarily governed by the tensor force - such interaction causes a decrease in energy of the f_5/2 single-particle orbital with respect to the p_3/2 and p_1/2 levels as protons are added to the f_7/2 shell.