Partial Dynamical SU(3) Symmetry and the Nature of the Lowest K=0 Collective Excitation in Deformed Nuclei

We discuss the implications of partial dynamical SU(3) symmetry (PDS) for the structure of the lowest K=0^{+} (K=0_2) collective excitation in deformed nuclei. We consider an interacting boson model Hamiltonian whose ground and gamma bands have good SU(3) symmetry while the K=0_2 band is mixed. It is shown that the double-phonon components in the K=0_2 wave function arise from SU(3) admixtures which, in turn, can be determined from absolute E2 rates connecting the K=0_2 and ground bands. An explicit expression is derived for these admixtures in terms of the ratio of K=0_2 and gamma bandhead energies. The SU(3) PDS predictions are compared with existing data and with broken-SU(3) calculations for ^{168}Er.Comment: 12 pages, 2 figure

Maximal chordal subgraphs

AbstractAn algorithm for finding maximal chordal subgraphs is developed that has worst-case time complexity of O(|E|Δ), where |E| is the number of edges in G and Δ is the maximum vertex degree in G. The study of maximal chordal subgraphs is motivated by their usefulness as computationally efficient structures with which to approximate a general graph. Two examples are given that illustrate potential applications of maximal chordal subgraphs. One provides an alternative formulation to the maximum independent set problem on a graph. The other involves a novel splitting scheme for solving large sparse systems of linear equations

Energy Level Statistics of the U(5) and O(6) Symmetries in the Interacting Boson Model

We study the energy level statistics of the states in U(5) and O(6) dynamical symmetries of the interacting boson model and the high spin states with backbending in U(5) symmetry. In the calculations, the degeneracy resulting from the additional quantum number is eliminated manually. The calculated results indicate that the finite boson number $N$ effect is prominent. When $N$ has a value close to a realistic one, increasing the interaction strength of subgroup O(5) makes the statistics vary from Poisson-type to GOE-type and further recover to Poisson-type. However, in the case of $N \to \infty$, they all tend to be Poisson-type. The fluctuation property of the energy levels with backbending in high spin states in U(5) symmetry involves a signal of shape phase transition between spherical vibration and axial rotation.Comment: 38 pages, 13 figure

Quadrupole shape invariants in the interacting boson model

In terms of the Interacting Boson Model, shape invariants for the ground state, formed by quadrupole moments up to sixth order, are studied in the dynamical symmetry limits and, for the first time, over the whole structural range of the IBM-1. The results are related to the effective deformation parameters and their fluctuations in the geometrical model. New signatures that can distinguish vibrator and gamma-soft rotor structures, and one that is related to shape coexistence, are identified.Comment: 10 pages, ReVTeX, epsf, 2 Postscript figures include

Critical test of multi-{\it j} supersymmetries from magnetic moment measurements

Magnetic moment measurements in odd nuclei directly probe the distribution of fermion states and hence provide one of the most critical tests for multi-$j$ supersymmetries in collective nuclei. Due to complexity of calculations and lack of data, such tests have not been performed in the past. Using the Mathematica software, we derive analytic expressions for magnetic moments in the $SO^{(BF)}(6) \times SU^{(F)}(2)$ limit of the $U(6/12)$ supersymmetry and compare the results with recent measurements in $^{195}$Pt.Comment: 10 pages with 1 figur

Spectroscopy of the N=Z-2 nucleus Cr46 and mirror energy differences

Excited states in Cr46 were sought using the C12(Ar36,2n) reaction. Gamma rays were detected with the Gammasphere array, and the Z value of the reaction products was determined with an ionization chamber located at the focal plane of the Fragment Mass Analyzer. In addition to the ground-state band observed up to IÏ€=10+ (tentatively 12+), five states are proposed to belong to the 3- band. The mirror energy differences with the analog states in Ti46 present a pronounced staggering effect between the odd and even spin members that is reproduced well by shell-model calculations incorporating the different Coulomb contributions, monopole, multipole, and single-particle effects together with an isospin-nonconserving interaction that accounts for the so-called J=2 anomaly. Dramatically different E1 decay patterns for members of the 3- band between the Cr46 and Ti46 mirrors are also observed

Observation of 46Cr and testing and isobaric multiplet mass equation at high spin

An experimental study was carried out to observe excited states in 46Cr using the 12C(36Ar,2n) reaction with GAMMASPHERE and the FMA. The yrast band in 46Cr and the T=1 states in 46V were established up to (tentatively) 12+, the highest spin T=1 triplet unknown. The results were used to test f p-shell model calculations

Near yrast study of the fpg shell nuclei 58Ni, 61Cu, and 61Zn

The medium spin, near yrast states of the fpg shell nuclei 58Ni, 61Cu, and 61Zn have been studied following the fusion evaporation of a 24Mg beam and a 40Ca target. Discrete transitions were unambiguously identified using the AYEBALL gamma-ray array in conjunction with the Argonne fragment mass analyzer and a split anode ionization chamber. The decay schemes of 5828Ni, 6129Cu, and 6130Zn have been extended with the results of gamma-gamma coincidences and directional correlation from oriented state measurements used to determine the level excitation energies, spins, and parities of a number of near yrast states. The decay schemes deduced are compared with previous work and interpreted in terms of shell model calculations, with a restricted basis of the f5/2, p3/2, p1/2 orbitals outside a 5628Ni core, and either the g9/2 orbital with a closed core, or f7/2 excitations from the core

Competing T = 0 and T = 1 structures in the N = Z nucleus 3162Ga

The low-lying levels in the odd-odd N = Z nucleus 62Ga have been identified for the first time. These data reveal a cascade of stretched-E2 transitions based on a T = 0, 1+ bandhead which decays directly to the T = 1, 0+ ground state. The observed levels are interpreted in the context of theshell model, using as a basis, the pf5/2g9/2 orbits with a 56Ni core

All-sky search for long-duration gravitational wave transients with initial LIGO

We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10-500 s in a frequency band of 40-1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between 3.4×10-5 and 9.4×10-4 Mpc-3 yr-1 at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves. © 2016 American Physical Society