We present a new effective interaction for shell-model calculations in the model space consisting of the single-particle orbits 1p 3/2 , 0f 5/2 , 1p 1/2 , and 0g 9/2 . Starting with a realistic interaction based on the Bonn-C potential, 133 two-body matrix elements and four single-particle energies are modified empirically so as to fit 400 experimental energy data out of 69 nuclei with mass numbers A = 63 ∼ 96. The systematics of binding energies, electromagnetic moments and transitions, and low-lying energy levels are described. The soft Z = 28 closed core is observed, in contrast to the stable N = 50 shell closure. The new interaction is applied to systematic studies of three different chains of nuclei, Ge isotopes around N = 40, N = Z nuclei with A = 64 ∼ 70, and N = 49 odd-odd nuclei, focusing especially on the role of the g 9/2 orbit. The irregular behavior of the 0 + 2 state in Ge isotopes is understood as a result of detailed balance between the N = 40 single-particle energy gap and the collective effects. The development of the band structure in N = Z nuclei is interpreted in terms of successive excitations of nucleons into the g 9/2 orbit. The triaxial/γ -soft structure in 64 Ge and the prolate/oblate shape coexistence in 68 Se are predicted, showing a good correspondence with the experimental data. The isomeric states in 66 As and 70 Br are obtained with the structure of an aligned proton-neutron pair in the g 9/2 orbit. Low-lying energy levels in N = 49 odd-odd nuclei can be classified as proton-neutron pair multiplets, implying that the obtained single-particle structure in this neutron-rich region appears to be appropriate. These results demonstrate that, in spite of the modest model space, the new interaction turns out to describe rather well properties related to the g 9/2 orbit in various cases, including moderately deformed nuclei.

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Atomic nuclei are finite quantum systems composed of two distinct types of fermion--protons and neutrons. In a manner similar to that of electrons orbiting in an atom, protons and neutrons in a nucleus form shell structures. In the case of stable, naturally occurring nuclei, large energy gaps exist between shells that fill completely when the proton or neutron number is equal to 2, 8, 20, 28, 50, 82 or 126 (ref. 1). Away from stability, however, these so-called 'magic numbers' are known to evolve in systems with a large imbalance of protons and neutrons. Although some of the standard shell closures can disappear, new ones are known to appear. Studies aiming to identify and understand such behaviour are of major importance in the field of experimental and theoretical nuclear physics. Here we report a spectroscopic study of the neutron-rich nucleus (54)Ca (a bound system composed of 20 protons and 34 neutrons) using proton knockout reactions involving fast radioactive projectiles. The results highlight the doubly magic nature of (54)Ca and provide direct experimental evidence for the onset of a sizable subshell closure at neutron number 34 in isotopes far from stability.

We show how shape transitions in the neutron-rich exotic Si and S isotopes occur in terms of shell-model calculations with a newly constructed Hamiltonian based on VMU interaction. We first compare the calculated spectroscopic-strength distributions for the proton 0d 5/2,3/2 and 1s 1/2 orbitals with results extracted from a 48 Ca(e,e'p) experiment to show the importance of the tensorforce component of the Hamiltonian. Detailed calculations for the excitation energies, B(E2) and two-neutron separation energies for the Si and S isotopes show excellent agreement with experimental data. The potential energy surface exhibits rapid shape transitions along the isotopic chains towards N =28 that are different for Si and S. We explain the results in terms of an intuitive picture involving a Jahn-Teller-type effect that is sensitive to the tensor-force-driven shell evolution. The closed sub-shell nucleus 42 Si is a particularly good example of how the tensor-force-driven Jahn-Teller mechanism leads to a strong oblate rather than spherical shape.