K. Heyde

Coexistence in even-mass nuclei

Abstract Shape coexistence in doubly even nuclei is reviewed. Two main theoretical approaches are presented. The first is essentially the shell model with the excitation of pairs of protons and/or neutrons across closed shells or subshells together with a residual proton-neutron interaction. The second is the deformed mean-field approach. The first is broadly defined so that it includes various truncation schemes to the shell model including generalized seniority and the interacting boson model. The presentation of the theory has two main aims: to provide a framework into which the majority of theoretical studies of shape coexistence can be placed and to provide a framework within which a unified view can be discussed. Selected experimental data are shown from 16 O to 238 U. Our criteria for selection emphasize detailed spectroscopic evidence (“fingerprints”) for coexisting shapes.

Coexistence in odd-mass nuclei

Abstract Shape coexistence in odd-mass nuclei near closed shells (±1 and ±3 nucleons) is reviewed. Two main approaches are presented. The more historical one starts from the explicit introduction of a deformation degree of freedom and allows particular Nilsson orbitals to occur very low in excitation energy. A second approach starts from spherical particle-hole (p-h) excitations across a closed shell and allows interactions with quadrupole vibrations of the underlying core nucleus. The equivalence between the two approaches is discussed in some detail. Attention is given also to other approaches to the description of coexistence. A detailed review of the experimental evidence for coexistence in odd-mass nuclei near the Z = 28, 50, 82 and N = 28, 50, 82 closed shells is made. In addition, the fingerprints of coexisting states, i.e. the most pronounced nuclear structure properties characterizing such states, are presented. These fingerprints provide a necessary (though not sufficient) set of conditions for identifying coexistence throughout the nuclear mass table. At the end, we briefly describe the connection of the present study to other areas of nuclear structure such as related configurations in doubly-even nuclei, many-particle many-hole excitations, deep-lying hole states, and the possibility of incorporating these degrees of freedom into an Interacting Boson Approximation (IBA) framework. A major conclusion of this review is that there is a clear connection between shape coexistence and shell-model intruder states. A variety of topics is suggested for future experimental and theoretical investigation.

A triplet of differently shaped spin-zero states in the atomic nucleus 186 Pb

Understanding the fundamental excitations of many-fermion systems is of significant current interest. In atomic nuclei with even numbers of neutrons and protons, the low-lying excitation spectrum is generally formed by nucleon pair breaking and nuclear vibrations or rotations. However, for certain numbers of protons and neutrons, a subtle rearrangement of only a few nucleons among the orbitals at the Fermi surface can result in a different elementary mode: a macroscopic shape change. The first experimental evidence for this phenomenon came from the observation of shape coexistence in 16O (ref. 4). Other unexpected examples came with the discovery of fission isomers and superdeformed nuclei. Here we find experimentally that the lowest three states in the energy spectrum of the neutron deficient nucleus 186Pb are spherical, oblate and prolate. The states are populated by the α-decay of a parent nucleus; to identify them, we combine knowledge of the particular features of this decay with sensitive measurement techniques (a highly efficient velocity filter with strong background reduction, and an extremely selective recoil-α-electron coincidence tagging method). The existence of this apparently unique shape triplet is permitted only by the specific conditions that are met around this particular nucleus.

Collective bands in even mass Sn isotopes

Abstract Positive parity bands in 112, 114, 116, 118Sn have been excited up to levels with spin and parity Jπ = 12+ using Cd(α, 2nγ)Sn reactions. The experiments consisted of γ-ray excitation function, γ-γ coincidence, lifetime, γ-ray angular distribution, γ-ray linear polarization and conversion electron measurements. The observed bands show strong resemblances with ground-state bands of transitional nuclei in this mass region. It is pointed out that the Jπ = 0+ band-heads originate from 2p-2h excitations in the Z = 50 proton shell. The excitation energies of the band-heads are calculated by means of the macroscopic-microscopic renormalization method. Pair correlations between the 2h and 2p configurations are included separately in a phenomenological way by taking into account the pairing energies of the Cd and Te ground states with respect to the Sn ground state.

The F-spin symmetric limits of the neutron-proton interacting boson model

Abstract The F -spin symmetric limits U (5), SU (3), and O (6) of the neutron-proton interacting boson model are studied. The conditions for and consequences of F -spin symmetry are investigated. In each of the three limits closed expressions for the following properties are given: the excitation energies; the M 1, E 2, and M 3 excitation strengths from the ground state to all 1 + , 2 + , and 3 + states; the M 1 and E 2 decay of the nonsymmetric 1 + and 2 + states; and the dipole and quadrupole moments of maximal F -spin states and of the nonsymmetric 1 + and 2 + states. The predictions for these properties are compared with the experimental data.

A shell-model description of 0+ intruder states in even-even nuclei

Abstract Starting from the nuclear shell structure in medium-heavy and heavy nuclei, the excitation energy for low-lying 0 + intruder states is studied. Taking as a simplified model two particle-two hole (2p-2h) excitations across closed shells, the effects of the pairing and the proton-neutron (monopole and quadrupole component) residual interaction on the unperturbed energies are calculated. Application to major closed-shell ( fZ = 50, Z = 82) and to subshell ( Z = 40, Z = 64) regions is performed. We especially concentrate on 0 + intruder states in the even-even Pb nuclei.

Electric monopole transitions from low energy excitations in nuclei

Abstract Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ 2 (E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd- A nuclei, and illustrate a suggested relation between ϱ 2 (E0) and isotopic shifts.

An effective Skyrme-type interaction for nuclear structure calculations: (I). Ground-state properties

Abstract A “universal” effective NN interaction of the Skyrme type has been proposed which is suitable for both ground and excited states in nuclei throughout the nuclear mass table. The analytical structure of the proposed interaction SkE is presented and discussed. The spin stability of the force is studied by deriving the corresponding Landau-Migdal interaction for uniform nuclear matter. An equivalent set of force parameters starting from a realistic interaction after application of the local-density approximation (LDA) and the density-matrix expansion (DME) is derived. The behavior of the SkE interaction in describing charge properties is extensively discussed by carrying out a detailed and elaborate study of nucleon and charge distributions in 58 Ni, the Ca and Pb isotopes.

The interplay of γ-softness and triaxiality in O(6)-like nuclei

Abstract It is shown that the empirical deviations from the O(6) limit of the IBA, in the Pt and Xe, Ba regions, are nearly identical and that both can be interpreted very simply by introducing explicitly triaxial degrees of freedom to the IBA potential via an additional cubic interaction in the hamiltonian. This simultaneously improves the energy staggering in the γ-band, the energy of the first excited 0 + state, and the spacings among high ρ-states. A physical interpretation of the results in terms of the effective mean γ and the dynamic fluctuations in γ (zero-point motion) is presented.

An extension of the interacting boson model and its application to the even-even Gd isotopes

Abstract In order to obtain a more complete description of the low-lying collective states of even-even nuclei, we present an extended version of the interacting boson model. Besides s- and d-bosons we also consider s′-, d′- and g-bosons as elementary building blocks. The model is applied on even-even Gd isotopes (Z = 64; 90 ⩽ N ⩽ 96). We present the results of calculations of energy spectra, EQ, E2 and E4 transition properties of these nuclei.