B. Alex Brown

Magic Numbers in Exotic Nuclei and Spin-Isospin Properties of the NN Interaction

The magic numbers in exotic nuclei are discussed, and their novel origin is shown to be the spin-isospin dependent part of the nucleon-nucleon interaction in nuclei. The importance and robustness of this mechanism is shown in terms of meson exchange, G-matrix, and QCD theories. In neutron-rich exotic nuclei, magic numbers such as N = 8, 20, etc. can disappear, while N = 6, 16, etc. arise, affecting the structure of the lightest exotic nuclei to nucleosynthesis of heavy elements.

The nuclear shell model as a testing ground for many-body quantum chaos

Abstract Atomic nuclei analyzed in the framework of the shell model provide a good example of a many-body quantum system with strong interactions between its constituents. As excitation energy and level density increase, the system evolves in the direction of very complicated (“stochastic”) dynamics. Energy levels and stationary wave functions obtained in realistic shell-model calculations are studied from the viewpoint of signatures of quantum chaos and complexity. The standard characteristics of local level statistics, such as nearest level spacing distribution or spectral rigidity, manifest chaoticity which agrees with the GOE predictions. Going beyond that, we analyze the structure of the eigenfunctions and the distribution function of the eigenvector components using basis-dependent quantitative criteria such as information entropy. The degree of complexity is shown to be a smooth function of excitation energy. The representation dependence provides additional physical information on the interrelation between the eigenbasis and the representation basis. The exceptional role of the mean field basis is discussed. The spreading width and the shape of the strength function of the original simple states are also studied. The generic wave functions in the chaotic region have similar observable properties which can be characterized by the average single-particle occupation numbers. Agreement with the Fermi-Dirac distribution manifests the correspondence between chaotic dynamics and thermalization. The information entropy in the mean field basis gives an equivalent temperature scale which confirms this correspondence. Pairing correlations display a phase transition to the normal state with a long tail of fluctuational enhancement above the level expected for a heated Fermi gas.

Effective interaction for pf shell nuclei

An effective interaction is derived for use in the full pf basis. Starting from a realistic G-matrix interaction, 195 two-body matrix elements and 4 single-particle energies are determined by fitting to 699 energy data in the mass range 47 to 66. The derived interaction successfully describes various structures of pf-shell nuclei. As examples, systematics of the energies of the first 2+ states in the Ca, Ti, Cr, Fe, and Ni isotope chains and energy levels of 56,57,58Ni are presented. The appearance of a new magic number 34 is seen.

Exact solution of the nuclear pairing problem

Abstract In many applications to finite Fermi-systems, the pairing problem has to be treated exactly. We suggest a numerical method of exact solution based on SU(2) quasispin algebras and demonstrate its simplicity and practicality. We show that the treatment of binding energies with the use of the exact pairing and uncorrelated monopole contribution of other residual interactions can serve as an effective alternative to the full shell-model diagonalization in spherical nuclei.

Information entropy, chaos and complexity of the shell model eigenvectors

Abstract The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Realistic shell model calculations are performed in the JT -scheme for 12 particles in the sd -shell. Local level statistics are in perfect agreement with the GOE predictions whereas the eigenvectors show evidence for non-complete energy dependent chaoticity. The information entropy of individual eigenvectors turns out to be a convenient measure of degree of complexity of individual wave functions. We discuss the representation dependence and the sensitivity to the interaction strength. The exceptional role of the mean field basis is stressed.

Shape transitions in exotic Si and S isotopes and tensor-force-driven Jahn-Teller effect

We show how shape transitions in the neutron-rich exotic Si and S isotopes occur in terms of shell-model calculations with a newly constructed Hamiltonian based on VMU interaction. We first compare the calculated spectroscopic-strength distributions for the proton 0d5/2,3/2 and 1s1/2 orbitals with results extracted from a 48 Ca(e, ep) experiment to show the importance of the tensor-force component of the Hamiltonian. Detailed calculations for the excitation energies, B(E2), and two-neutron separation energies for the Si and S isotopes show excellent agreement with experimental data. The potential-energy surface exhibits rapid shape transitions along the isotopic chains towards N = 28 that are different for Si and S. We explain the results in terms of an intuitive picture by involving a Jahn-Teller-type effect that is sensitive to the tensor-force-driven shell evolution. The closed subshell nucleus 42 Si is a particularly good example of how the tensor-force-driven Jahn-Teller mechanism leads to a strong oblate rather than a spherical shape. a strong oblate shape (rather than spherical) due to the tensor- force-driven shell evolution. These PES results are interpreted in an intuitive picture which involves shell gaps and the Jahn- Teller-type effect. Two-neutron separation energies are also discussed. Weoutlinethepresentshell-modelcalculations.The sdand pf shells are taken as the valence shell with protons in sdand neutrons in pf .The interactions within each of these shells are based on existing interactions: USD (20) (GXPF1B (21) 2 )f or the sd (pf ) shell, except for the monopole interactions (4,23) V T =0,1 0d3/2,0d5/2 based on SDPF-M (24) due to a problem in USD as

Invariant correlational entropy and complexity of quantum states

We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent Hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation independent, and can be calculated as a trace functional of the density matrix which describes the system in its interaction with the noise source. We analyze perturbation theory in order to show the evolution from the pure state to the mixed one. Exactly solvable examples illustrate the use of correlational entropy as a measure of the degree of complexity in comparison with other available suggestions such as basis-dependent information entropy. It is shown in particular that a harmonic oscillator in a uniform field of random strength comes to a quasithermal equilibrium; we discuss the relation between effective temperature and canonical equilibrium temperature. The notion of correlational entropy is applied to a realistic numerical calculation in the framework of the nuclear shell model. In this system, which reveals generic signatures of quantum chaos, correlational entropy and information entropy calculated in the mean field basis display similar qualitative behavior.

Constraints on the Skyrme equations of state from properties of doubly magic nuclei.

I use properties of doubly magic nuclei to constrain symmetric nuclear matter and neutron matter equations of state. I conclude that these data determine the value of the neutron equation of state at a density of ρ(on)=0.10  nucleons/fm3 to be 11.4(10) MeV. The slope at that point is constrained by the value of the neutron skin. Analytical equations are given that show the dependence of the Skyrme equations of state on the neutron skin.

Quenching of Spectroscopic Factors for Proton Removal in Oxygen Isotopes

We present microscopic coupled-cluster calculations of the spectroscopic factors for proton removal from the closed-shell oxygen isotopes (14,16,22,24,28)O with a chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. We include coupling-to-continuum degrees of freedom by using a Hartree-Fock basis built from a Woods-Saxon single-particle basis. This basis treats bound and continuum states on an equal footing. We find a significant quenching of spectroscopic factors in the neutron-rich oxygen isotopes, pointing to enhanced many-body correlations induced by strong coupling to the scattering continuum above the neutron emission thresholds.

Modification of the Brink-Axel hypothesis for high-temperature nuclear weak interactions

Author(s): Misch, GW; Fuller, GM; Brown, BA | Abstract: