Large-scale shell-model calculations with the PFSDG-U interaction predict a new island of inversion at neutron number N=50N=50 that merges with the N=40N=40 island for proton number Z≤26Z\leq 26, so that spherical shell effects essentially vanish across the most neutron-rich chromium–iron region, while 78^{78}Ni retains a doubly magic spherical ground state coexisting with a low-lying deformed prolate band. Neither the experimental signatures (the deformed band in 78^{78}Ni, electromagnetic E2E2 strengths and two-neutron separation energies S2nS_{2n} in the heaviest Cr and Fe isotopes) nor a decisive microscopic theoretical confirmation have been established. The problem is to determine, experimentally and/or theoretically, whether the predicted fifth island of inversion and its merger with the N=40N=40 island actually occur, by mapping the onset and extent of deformation from 78^{78}Ni down through the neutron-rich Fe, Cr, and Ti isotopes and by identifying the shell-structure mechanism responsible.

Background

Atomic nuclei exhibit a shell structure analogous to electrons in atoms: protons and neutrons fill single-particle orbitals in shells separated by energy gaps at the "magic numbers" (e.g. Z=28Z=28, N=50N=50). A nucleus magic in both proton and neutron numbers, such as 78^{78}Ni (Z=28Z=28, N=50N=50), is expected to be spherical and stiff against deformation. Far from the valley of stability this picture can break down: in very neutron-rich nuclei, configurations in which neutrons are promoted across a nominal shell gap into intruder orbitals of higher principal quantum number (e.g. from the pfpf shell into the sdgsdg shell) can gain so much correlation (quadrupole-deformation) energy that they come down to the ground state. Regions of the nuclear chart where this happens are called islands of inversion (IoI); four are well documented at N=8N=8, 2020, 2828, and 4040 (the N=40N=40 IoI centered on the neutron-rich Cr, Fe, and Ni isotopes around 64^{64}Cr). Shape coexistence means that within one nucleus a spherical configuration and a deformed configuration lie close in energy and mix weakly; B(E2)B(E2) values (reduced electric-quadrupole transition probabilities, measured in units of e2fm4e^2\mathrm{fm}^4 or e2b2e^2\mathrm{b}^2) quantify quadrupole collectivity, and two-neutron separation energies S2nS_{2n} (the energy required to remove two neutrons) trace shell gaps through their odd-even staggering.

The configuration-interaction shell model describes nuclei by diagonalizing an effective Hamiltonian in a truncated valence space of single-particle orbitals around an inert core. Nowacki, Poves, Caurier, and Bounthong (Phys. Rev. Lett. 117, 272501 (2016); summarized in the source proceedings by Nowacki and Poves, J. Phys.: Conf. Ser. 966, 012023 (2018)) performed large-scale shell-model (LSSM) calculations in a valence space comprising the full proton pfpf shell and the full neutron sdgsdg shell (the interaction dubbed PFSDG-U), motivated by the harmonic-oscillator-like degeneracy of pfpf and sdgsdg shells in this neutron-rich regime and by approximate SU(3) quadrupole-collective algebra. Their central predictions are: (i) the deformation region of the heaviest Cr and Fe isotopes at and beyond N=40N=40 merges with a new IoI at N=50N=50, in an apparent parallel to the merged N=20N=20/N=28N=28 case in Ne and Mg isotopes; (ii) 78^{78}Ni keeps a doubly magic (spherical) ground state but hosts a well-deformed prolate band at low excitation energy, making it a shape-coexistence "stronghold" at the edge of the deformed region; (iii) consequently the spherical N=50N=50 shell effects should erode and disappear as ZZ decreases below 28, i.e. in 76^{76}Fe, 74^{74}Cr, 72^{72}Ti and neighbors. The calculations rely on phenomenological monopole (i.e. configuration-averaged two-body) terms fitted to emulate missing three-nucleon (3N) force effects, and on particle–hole truncations (up to eight particle–hole excitations) because full diagonalization would require matrices of order 2×10102\times10^{10} Slater determinants, at the edge of current supercomputing.

Experimental access to this region is extremely difficult: the nuclei are produced with tiny cross sections in fragmentation or fission of uranium beams at facilities such as RIKEN RIBF (using, e.g., the MINOS thick liquid-hydrogen target with in-beam γ\gamma-ray spectroscopy via proton-knockout reactions analyzed with distorted-wave impulse approximation (DWIA) reaction theory), FRIB, or FAIR. Before 2019, no excited states of 78^{78}Ni had ever been observed (only its β\beta-decay half-life and mass were known). The open problem raised by these predictions is the confirmation or refutation of the predicted N=50N=50 IoI and its merger with the N=40N=40 IoI; decisive evidence could come, for example, from direct spectroscopy of the predicted deformed band in 78^{78}Ni, precise E2E2 and S2nS_{2n} measurements in the heaviest Cr and Fe isotopes, and/or microscopic theoretical treatments (such as explicit 3N forces within the full pfpf–sdgsdg framework, and convergence control in the huge shell-model space). Modern ab initio approaches — coupled-cluster theory, the valence-space in-medium similarity renormalization group (VS-IMSRG), which derives an effective valence-space Hamiltonian from chiral two- and three-nucleon forces, and the Monte Carlo shell model (MCSM), a variational basis-sampling method for huge spaces — are the natural theoretical tools being brought to bear on this question.

Problem Statement

Determine whether the predicted fifth island of inversion at N=50N=50 exists and merges with the N=40N=40 island of inversion for Z≤26Z\leq 26 — that is, whether spherical shell effects at N=50N=50 erode and disappear across the most neutron-rich Fe, Cr, and Ti region while 78^{78}Ni itself remains a doubly magic shape-coexistence stronghold. Confirmation or refutation may rest on any decisive experimental and/or theoretical evidence. Illustrative, non-mandatory routes include: spectroscopy of the predicted low-lying deformed prolate band in 78^{78}Ni (its bandhead, in-band transitions, and electromagnetic E2E2 strengths), beyond the suggestive high-lying 2+2^+ states seen so far; E2E2 systematics and two-neutron separation energies S2nS_{2n} in the heaviest chromium and iron isotopes across N≈40N\approx 40–5050, sufficient to locate (or exclude) the predicted onset of deformation and vanishing of the N=50N=50 spherical shell gap below Z=28Z=28; and microscopic many-body treatments for the full proton-pfpf/neutron-sdgsdg valence space, whose computed spectra, B(E2)B(E2) values, and S2nS_{2n} trends can be confronted quantitatively with the experimental data. The objective is a validated determination of whether, where, and by which mechanism the spherical N=50N=50 shell structure breaks down in this region of the nuclear chart.

References

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