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

A description of high-spin phenomena in atomic nuclei is presented from both the experimental and theoretical points of view. The characteristic features of collective nuclear motion, such as rotational bands, band crossings, and backbending, as well as noncollective aspects, like high-spin isomers and irregular decay patterns, are discussed in detail. Recent achievements of the cranking model including the independent quasiparticle and the shell correction methods are reviewed. Changes in the structure of nuclei excited up to the highest possible angular momenta are analyzed; in particular, angular momentum alignment effects, shape changes, possible phase transitions, and sudden rearrangements in the single-particle structure are discussed. Phenomena related to the nuclear quasicontinuum spectra are also examined.

High-spin phenomena in atomic-nuclei

Gamma-ray spectroscopy was revolutionized with the introduction of high energy-resolution semiconductor germanium (Ge) detectors in the early 1960s. This led to the large increase in sensitivity realized by today’s arrays of Compton-suppressed Ge detectors. A still larger increase in sensitivity is expected by implementing the new concept of tracking. A tracking array consists of highly segmented Ge detectors (that can cover the full 4π solid-angle) in which γ rays will be identified by measuring and tracking every γ -ray interaction. This article reviews the physics motivation for such detectors and the development of the new technologies involved. The concept of tracking is explained using the example of a proposed array called γ -ray energy tracking array (GRETA).

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Developments in large gamma-ray detector arrays

The article reviews the general version of the Bohr collective model for the description of quadrupole collective states, including a detailed discussion of the model's kinematics. The quadrupole coordinates, momenta and angular momenta are defined and the structure of the isotropic tensor fields as functions of the tensor variables is investigated. After a comprehensive discussion of the quadrupole kinematics, the general form of the classical and quantum Bohr Hamiltonian is presented. The electric and magnetic multipole moment operators acting in the collective space are constructed and the collective sum rules are given. A discussion of the tensor structure of the collective wavefunctions and a review of various methods of solving the Bohr Hamiltonian eigenvalue equation are also presented. Next, the methods of derivation of the classical and quantum Bohr Hamiltonian from the microscopic many-body theory are recalled. Finally, the microscopic approach to the Bohr Hamiltonian is applied to interpret collective properties of 12 heavy even–even nuclei in the Hf–Hg region. Calculated energy levels and E2 transition probabilities are compared with experimental data.

https://iopscience.iop.org/article/10.1088/0954-3899/36/12/123101/pdf

Quadrupole collective states within the Bohr collective Hamiltonian

A new experimental approach has been implemented for accurate measurements of neutron capture cross sections in the energy range from 5 to 200 keV. The Karlsruhe 4π barium fluoride detector consists of 42 crystals shaped as hexagonal and pentagonal truncated pyramids forming a spherical shell with 10 cm inner radius and 15 cm thickness. All crystals are supplied with reflector and photomultiplier, thus representing independent gamma-ray detectors. The energy resolution of the 4π detector is 14% at 662 keV and 7% at 2.5 MeV gamma-ray energy, the overall time resolution is 500 ps and the peak efficiency 90% at 1 MeV. The detector allows to register capture cascades with 95% probability above a threshold energy of 2.5 MeV. Neutrons are produced via the 7Li(p, n)7Be reaction using the pulsed proton beam of a Van de Graaff accelerator. A collimated neutron beam is passing through the detector and hits the sample in the centre. The energy of captured neutrons is determined via time of flight, the primary flight path being 77 cm. The combination of short primary flight path, a 10 cm inner radius of the spherical BaF2 shell, and the low capture cross section of barium allows to discriminate background due to capture of sample-scattered neutrons in the scintillator by time of flight, leaving part of the neutron energy range completely undisturbed. This feature, together with the high efficiency and good energy resolution for capture gamma-rays, allows to separate the various background components reliably enough, that the capture cross section ratio of two isotopes can be determined with an accuracy of ≤ 1.0%. The detector will be used for nuclear astrophysics to investigate the origin of the heavy elements in the slow neutron capture process.

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The Karlsruhe 4π barium fluoride detector

Experimental and Theoretical Investigations of Quadrupole Collective Degrees of Freedom in 104Ru

/pdf/angular-momentum-selection-using-total-gamma-ray-energies-4nt9x3zotl.pdf

Angular momentum selection using total gamma-ray energies

Isometric trapping following Coulomb excitation of high spin states in 178Hf

The in-plane and out-of-plane anisotropy has been measured for ..gamma.. rays in coincidence with deep-inelastic products from the 1064-MeV /sup 136/Xe+/sup 197/Au reaction. The ..gamma..-ray energy spectra exhibit a bump corresponding to a dominantly stretched-E2 cascade, but only a small out-of-plane anisotropy, indicating a misalignment of the fragment spins. A simple model is used to extract a rms misalignment angle of 34/sup 0/ +- 7/sup 0/.

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Fragment spin orientation in deep-inelastic reactions from anisotropy measurements of continuum. gamma. rays

The interest in highly excited nuclei with large angular momentum has prompted this proposal of a universal ..gamma..-ray spectrometer (called the Crystal Ball) consisting of a 4..pi.. modularized NaI(Tl) detector system with 162 elements of equal solid angle. The proposed detector has an overall spherical shape with an inner radius of 22.86 cm and an outer radius of 38.10 cm. Performance specifications and cost data are presented.

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D. Habs

Papers

Experimental and Theoretical Investigations of Quadrupole Collective Degrees of Freedom in 104Ru

Angular momentum selection using total gamma-ray energies

Isometric trapping following Coulomb excitation of high spin states in 178Hf

Fragment spin orientation in deep-inelastic reactions from anisotropy measurements of continuum. gamma. rays

A proposal for a crystal-ball detector system