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

Coexistence in odd-mass nuclei

The concept of boson realization (or mapping) of Lie algebras appeared first in nuclear physics in 1962 as the idea of expanding bilinear forms in fermion creation and annihilation operators in Taylor series of boson operators, with the object of converting the study of nuclear vibrational motion into a problem of coupled oscillators. The physical situations of interest are quite diverse, depending, for instance, on whether excitations for fixed- or variable-particle number are being studied, on how total angular momentum is decomposed into orbital and spin parts, and on whether isotopic spin and other intrinsic degrees of freedom enter. As a consequence, all of the semisimple algebras other than the exceptional ones have proved to be of interest at one time or another, and all are studied in this review. Though the salient historical facts are presented in the introduction, in the body of the review the progression is (generally) from the simplest algebras to the more complex ones. With a sufficiently broad view of the physics requirements, the mathematical problem is the realization of an arbitrary representation of a Lie algebra in a subspace of a suitably chosen Hilbert space of bosons (Heisenberg-Weyl algebra). Indeed, if one includes the study of odd nuclei, one is forced to consider the mappings to spaces that are direct-product spaces of bosons and (quasi)fermions. Though all the methods that have been used for these problems are reviewed, emphasis is placed on a relatively new algebraic method that has emerged over the past decade. Many of the classic results are rederived, and some new results are obtained for odd systems. The major application of these ideas is to the derivation, starting from the shell model, of the phenomenological models of nuclear collective motion, in particular, the geometric model of Bohr and Mottelson and the more recently developed interacting boson model of Arima and Iachello. A critical discussion of those applications is interwoven with the theoretical developments on which they are based; many other applications are included, some of practical interest, some simply to illustrate the concepts, and some to suggest new lines of inquiry.

Boson realizations of Lie algebras with applications to nuclear physics

An adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

Termination of rotational bands: disappearance of quantum many-body collectivity

A Microscopic Theory of Large Amplitude Nuclear Collective Motion

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Chapter I Formation of the Viewpoint, Alpha-Like Four-Body Correlations and Molecular Aspects in Nuclei

A possible explanation of the characteristic systematic behaviour of the first excited 0'' states in even-even nuclei with N or Z=40 is given by taking account of an important effect of the mutual interplay between the pairing and quadrupole correlations. After making it clear what physical situation in shell structure is essential for the appearance of the anoma­ lous low-lying excited 0'' states, we predict another possible mass-number region where the anomalous 0'' states may be also realized.

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Structure of the Anomalous 0+′ Excited States in Spherical Even-Even Nuclei with N or Z ≈40

Various electromagnetic properties of the anomalous coupling states with spin (j-1) are shown to be well explained by the new viewpoint of the dressed n-quasi-particle modes proposed in a previous paper. In this point of view, the anomalous coupling collective states with spin (j -1) are considered as the dressed three-quasi-particle modes, which are regarded as a kind of elementary excitation modes in odd-mass nuclei. The effects of couplings between dressed three-quasi-particle modes and one-quasi-particle mode~ are also discussed in this connection, including those with spin j, (j-1) and (j-2).

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. III: Electromagnetic Properties of the Anomalous Coupling States

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Toshio Marumori

Papers

A Microscopic Theory of Large Amplitude Nuclear Collective Motion

Chapter I Formation of the Viewpoint, Alpha-Like Four-Body Correlations and Molecular Aspects in Nuclei

Structure of the Anomalous 0+′ Excited States in Spherical Even-Even Nuclei with N or Z ≈40

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. III: Electromagnetic Properties of the Anomalous Coupling States

Part III. Analysis of Low-Lying States in Spherical Odd-Mass Nuclei. Chapter 3. Structure of the Anomalous Coupling States with Spin I = (j−1)