https://digital.library.unt.edu/ark:/67531/metadc888955/m2/1/high_res_d/900147.pdf

ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology

Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei

Energy levels of A = 21−44 nuclei (V)

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

Signatures of criticality in the evolution of the nuclear ground-state shapes across the NxZ plane are discussed. Attention is paid to specific data indicating sudden structural changes in various isotopic and isotonic chains of medium-mass and heavy even-even nuclei, as well as to diverse theoretical aspects of the models used to describe these changes. The interacting boson model and the geometric collective model, in particular, are discussed in detail, the former providing global predictions for the evolution of collective observables in nuclei between closed shells and the latter yielding a parameter-efficient description of nuclei at the critical points of shape transitions. Some issues related to the mechanism of first- and second-order quantum phase transitions in general many-body systems are also outlined.

Quantum phase transitions in the shapes of atomic nuclei

PART I: INTRODUCTION 1. Introduction 2. The Nuclear Landscape PART II: SHELL MODEL AND RESIDUAL INTERACTIONS 3. The Independent Particle Model 4. The Shell Model: Two-Particle Configurations 5. Multiparticle Configurations PART III: COLLECTIVITY, PHASE TRANSITIONS, DEFORMATION 6. Collective Excitations in even-even Nuclei: Vibrational and Rotational Motion 7. Evolution of Collectivity 8. The deformed Shell Model or Nilsson Model 9. Nilsson Model: Applications and Refinements 10. Microscopic Treatment of Collective Vibrations PART IV: EXPERIMENTAL TECHNIQUES 11. Exotic Nuclei and Radioactive Beams References Index

Nuclear Structure from a Simple Perspective

The IBA-1 is reviewed with particular emphasis on the symmetry structure that arises naturally from its inherently algebraic approach. The formulation of the model, in both its algebraic and its numerical aspects, is presented and the basic character of its predictions is discussed and compared with nuclear data. The limitations of the model, and efforts to ameliorate these by appropriate extensions, are also reviewed in some detail. An effort is made to provide a simple, transparent understanding of the basic physics by clarifying the relation of the mathematical structure to underlying physical ideas, and to provide guidance in understanding and carrying out practical calculations.

The interacting boson approximation

Evidence for the first empirical example of a transitional dynamical symmetry at a critical point is discussed in the spectrum of ${}^{134}\mathrm{Ba}$. The role of such classes of symmetries in nuclear structural evolution is also discussed.

Evidence for a Possible E(5) Symmetry in 134 Ba

Lifetimes of states in 150Nd were measured using the recoil distance method following Coulomb excitation of 150Nd by a 132 MeV 32S beam. The experiment was performed at the Yale Tandem accelerator, employing the SPEEDY gamma-ray detector array and the New Yale Plunger Device. Reduced transition probabilities in 150Nd are compared to the predictions of the critical point symmetry X(5) of the phase/shape transition that occurs for the N = 90 rare earth isotones. Very good agreement was observed between the parameter-free (apart from scale) X(5) predictions and the low-spin level scheme of 150Nd, revealing this as the best case thus far for the realization of the X(5) symmetry.

R. F. Casten

Papers

Quantum phase transitions in the shapes of atomic nuclei

Nuclear Structure from a Simple Perspective

The interacting boson approximation

Evidence for a Possible E(5) Symmetry in 134 Ba

B(E2) values in 150Nd and the critical point symmetry X(5).