Shape coexistence in nuclei appears to be unique in the realm of finite many-body quantum systems It differs from the various geometrical arrangements that sometimes occur in a molecule in that in a molecule the various arrangements are of the widely separated atomic nuclei In nuclei the various ''arrangements'' of nucleons involve (sets of) energy eigenstates with different electric quadrupole properties such as moments and transition rates, and different distributions of proton pairs and neutron pairs with respect to their Fermi energies Sometimes two such structures will ''invert'' as a function of the nucleon number, resulting in a sudden and dramatic change in ground-state properties in neighboring isotopes and isotones In the first part of this review the theoretical status of coexistence in nuclei is summarized Two approaches, namely, microscopic shell-model descriptions and mean-field descriptions, are emphasized The second part of this review presents systematic data, for both even- and odd-mass nuclei, selected to illustrate the various ways in which coexistence is observed in nuclei The last part of this review looks to future developments and the issue of the universality of coexistence in nuclei Surprises continue to be discovered With the major advances in reaching to extremes of proton-neutronmore » number, and the anticipated new ''rare isotope beam'' facilities, guidelines for search and discovery are discussed« less

Shape coexistence in atomic nuclei

The first excited 2(+) state of the unstable isotope Sn-110 has been studied in safe Coulomb excitation at 2.82 MeV/u using the MINIBALL array at the REX-ISOLDE post accelerator at CERN. This is the first measurement of the reduced transition probability of this state using this method for a neutron deficient Sn isotope. The strength of the approach lies in the excellent peak-to-background ratio that is achieved. The extracted reduced transition probability, B(E2 : 0(+) -> 2(+)) 0.220 +/- 0.022e(2) b(2), strengthens the observation of the evolution of the B(E2) values of neutron deficient Sn isotopes that was observed recently in intermediate-energy Coulomb excitation of Sn-108. It implies that the trend of these reduced transition probabilities in the even-even Sn isotopes is not symmetric with respect to the midshell mass number A = 116 as Sn-100 is approached.

/pdf/sub-barrier-coulomb-excitation-of-sn-110-and-its-52oxxhes0v.pdf

Sub-barrier Coulomb excitation of Sn-110 and its implications for the Sn-100 shell closure

/pdf/an-experimental-view-on-shape-coexistence-in-nuclei-3ia9nv9j.pdf

An experimental view on shape coexistence in nuclei

The heart of every ISOL (isotope separation on-line) facility is its target and ion source system. Its efficiency, selectivity and rapidity is decisive for the production of intense and pure ion beams of short-lived isotopes. Recent progress in ISOL target and ion source technology is discussed at the examples of radioactive ion beams of exotic zinc and tin isotopes that were purified by isothermal chromatography and molecular sideband separation respectively. An outlook is given to which other elements these purification methods are applicable.

Progress in ISOL target ion source systems

Low-energy Coulomb excitation provides a well-understood means of exciting atomic nuclei and allows measuring electromagnetic moments that can be directly related to the nuclear shape. The availability of radioactive ion beams (RIBs) at energies near the Coulomb barrier has made it possible to study shape coexistence in a variety of short-lived exotic nuclei. This review presents a short overview of the methods related to multi-step Coulomb excitation experiments, followed by a discussion of several examples. The focus is on two mass regions where recent Coulomb excitation experiments have contributed to the quantitative understanding of shape coexistence: nuclei with mass near the N = Z line and nuclei with near neutron number N = 60. Experimental results are summarized and their significance for understanding shape coexistence is discussed. Experimental observables such as quadrupole moments and electromagnetic transition strengths represent furthermore important benchmarks for advancing theoretical nuclear structure models. With several new RIB facilities planned and under construction, Coulomb excitation will remain to be an important tool to extend the studies of nuclear shapes toward more exotic systems, and to obtain a more comprehensive and quantitative understanding of shape coexistence.

https://iopscience.iop.org/article/10.1088/0954-3899/43/2/024002/pdf

Coulomb excitation studies of shape coexistence in atomic nuclei

Using a method whereby molecular and atomic ions are independently selected, an isobarically pure beam of Se-70 ions was postaccelerated to an energy of 206 MeV using REX-ISOLDE. Coulomb-excitation yields for states in the beam and target nuclei were deduced by recording deexcitation gamma rays in the highly segmented MINIBALL gamma-ray spectrometer in coincidence with scattered particles in a silicon detector. At these energies, the Coulomb-excitation yield for the first 2(+) state is expected to be strongly sensitive to the sign of the spectroscopic quadrupole moment through the nuclear reorientation effect. Experimental evidence is presented here for a prolate shape for the first 2(+) state in Se-70, reopening the question over whether there are, as reported earlier, deformed oblate shapes near to the ground state in the light selenium isotopes.

/pdf/measurement-of-the-sign-of-the-spectroscopic-quadrupole-3mvm39uz89.pdf

Measurement of the sign of the spectroscopic quadrupole moment for the 2(1)(+) state in Se-70: No evidence for oblate shape

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Measurement of the sign of the spectroscopic quadrupole moment for the 2(1)(+) state in Se-70: No evidence for oblate shape