Mihai Horoi

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.

Structure, bonding, and magnetism in manganese clusters

We investigate the structures and magnetic properties of small Mn(n) clusters in the size range of 2-13 atoms using first-principles density functional theory. We arrive at the lowest energy structures for clusters in this size range by simultaneously optimizing the cluster geometries, total spins, and relative orientations of individual atomic moments. The results for the net magnetic moments for the optimal clusters are in good agreement with experiment. The magnetic behavior of Mn(n) clusters in the size range studied in this work ranges from ferromagnetic ordering (large net cluster moment) for the smallest (n=2, 3, and 4) clusters to a near degeneracy between ferromagnetic and antiferromagnetic solutions in the vicinity of n=5 and 6 to a clear preference for antiferromagnetic (small net cluster moment) ordering at n=7 and beyond. We study the details of this evolution and present a picture in which bonding in these clusters predominantly occurs due to a transfer of electrons from antibonding 4s levels to minority 3d levels.

Scanning the potential energy surface of iron clusters: A novel search strategy

A new methodology for finding the low-energy structures of transition metal clusters is developed. A two-step strategy of successive density functional tight binding (DFTB) and density functional theory (DFT) investigations is employed. The cluster configuration space is impartially searched for candidate ground-state structures using a new single-parent genetic algorithm [I. Rata et al., Phys. Rev. Lett. 85, 546 (2000)] combined with DFTB. Separate searches are conducted for different total spin states. The ten lowest energy structures for each spin state in DFTB are optimized further at a first-principles level in DFT, yielding the optimal structures and optimal spin states for the clusters. The methodology is applied to investigate the structures of Fe4, Fe7, Fe10, and Fe19 clusters. Our results demonstrate the applicability of DFTB as an efficient tool in generating the possible candidates for the ground state and higher energy structures of iron clusters. Trends in the physical properties of iron clu...

Chaos vs thermalization in the nuclear shell model.

Generic signatures of quantum chaos found in realistic shell model calculations are compared with thermal statistical equilibrium. We show the similarity of the informational entropy of individual eigenfunctions in the mean-field basis to the thermodynamical entropy found from the level density. Mean occupation numbers of single-particle orbitals agree with the Fermi-Dirac distribution despite the strong nucleon interaction.

New T = 1 effective interactions for the f 5 ∕ 2 p 3 ∕ 2 p 1 ∕ 2 g 9 ∕ 2 model space: Implications for valence-mirror symmetry and seniority isomers

New shell model Hamiltonians are derived for the

Z = 50 shell gap near 100Sn from intermediate-energy Coulomb excitations in even-mass 106-112Sn isotopes.

T=1

Information entropy, chaos and complexity of the shell model eigenvectors

part of the residual interaction in the

Scaling behaviour in cluster decay

{f}_{5∕2}\phantom{\rule{0.3em}{0ex}}{p}_{3∕2}\phantom{\rule{0.3em}{0ex}}{p}_{1∕2}\phantom{\rule{0.3em}{0ex}}{g}_{9∕2}

Computational nuclear quantum many-body problem: The UNEDF project

model space based on the analysis and fit of the available experimental data for

Shell model analysis of the neutrinoless double-{beta} decay of {sup 48}Ca

_{28}^{57}\mathrm{Ni}_{29}--_{28}^{78}\mathrm{Ni}_{50}