The atomic nucleus is a quantum many-body system whose constituent nucleons (protons and neutrons) are subject to complex nucleon-nucleon interactions that include spin- and isospin-dependent components. For stable nuclei, several decades ago, emerging seemingly regular patterns in some observables could already be described successfully within a shell-model picture that results in particularly stable nuclei at certain magic fillings of the shells with protons and/or neutrons: N, Z=8, 20, 28, 50, 82, 126. However, in short-lived, so-called exotic nuclei or rare isotopes, characterized by a large N/Z asymmetry and located far from the valley of β stability on the nuclear chart, these magic numbers, viewed through observables, were shown to change. These changes in the regime of exotic nuclei offer an unprecedented view at the roles of the various components of the nuclear force when theoretical descriptions are confronted with experimental data on exotic nuclei where certain effects are enhanced. This article reviews the driving forces behind shell evolution from a theoretical point of view and connects this to experimental signatures.

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Evolution of shell structure in exotic nuclei

Retardation of B(E2; 01+ → 21+) rates in 90–96Sr and strong subshell closure effects in the A ~ 100 region

We first review the shell evolution in exotic nuclei driven by nuclear forces. We then demonstrate that the underlying mechanism played by the balance of the tensor and central components in the effective nucleon–nucleon interaction is crucial when describing shape coexistence. This effect will be referred to as type II shell evolution, while the shell evolution passing through a series of isotopes or isotones is denoted as type I. We describe type II shell evolution in some detail for the case of the Ni nucleus as an example. We present how the fission dynamics can be related to enhanced deformation triggered by type II shell evolution, at its initial stage. It is suggested that the island of stability may be related to the suppression of this mechanism.

https://iopscience.iop.org/article/10.1088/0954-3899/43/2/024009/pdf

The role of shell evolution in shape coexistence

At the radioactive ion beam facility REX-ISOLDE, neutron-rich zinc isotopes were investigated using low-energy Coulomb excitation These experiments have resulted in B(E2, 2(1)(+)-> 0(1)(+)) values in Zn74-80, B(E2, 4(1)(+)-> 2(1)(+)) values in Zn-74,Zn-76 and the determination of the energy of the first excited 2(1)(+) states in Zn-78,Zn-80 The zinc isotopes were produced by high-energy proton- (A = 74, 76, 80) and neutron-(A = 78) induced fission of U-238, combined with selective laser ionization and mass separation The isobaric beam was postaccelerated by the REX linear accelerator and Coulomb excitation was induced on a thin secondary target, which was surrounded by the MINIBALL germanium detector array In this work, it is shown how the selective laser ionization can be used to deal with the considerable isobaric beam contamination and how a reliable normalization of the experiment can be achieved The results for zinc isotopes and the N = 50 isotones are compared to collective model predictions and state-of-the-art large-scale shell-model calculations, including a recent empirical residual interaction constructed to describe the present experimental data up to 2004 in this region of the nuclear chart

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Low-energy Coulomb excitation of neutron-rich zinc isotopes

Background: The mass region with $A\ensuremath{\approx}100$ and $Z\ensuremath{\approx}40$ is known to experience a sudden onset of deformation. The presence of the subshell closure $Z=40$ makes it feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region.Purpose: The aim of this work is to describe excitation energies, transition rates, radii, and two-neutron separation energies for the even-even $^{94\ensuremath{-}110}\mathrm{Zr}$ nuclei and, moreover, to obtain information about wave functions and deformation.Method: The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2particle-2hole excitations. On one hand, the parameters appearing in the Hamiltonian and in the $E2$ transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes.Results: Spectra, transition rates, radii, ${\ensuremath{\rho}}^{2}(E0)$, and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too.Conclusions: The importance of shape coexistence has been shown to correctly describe the $A\ensuremath{\approx}100$ mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of $^{94\ensuremath{-}98}\mathrm{Zr}$ and its deformed nature for $^{100\ensuremath{-}110}\mathrm{Zr}$ isotopes. The sudden onset of deformation in $^{100}\mathrm{Zr}$ is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes.

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A. Etchegoyen

Papers

Quenching of the 2p12−2p32 proton spin-orbit splitting in the Sr−Zr region