On the equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei

The present paper establishes a link between pairing correlations in rotating nuclei and collective vortical modes in the intrinsic frame. We show that the latter can be embodied by a simple S-type coupling a la Chandrasekhar between rotational and intrinsic vortical collective modes. This results from a comparison between the solutions of microscopic calculations within the HFB and the HF Routhian formalisms. The HF Routhian solutions are constrained to have the same Kelvin circulation expectation value as the HFB ones. It is shown in several mass regions, pairing regimes, and for various spin values that this procedure yields moments of inertia, angular velocities, and current distributions which are very similar within both formalisms. We finally present perspectives for further studies.Comment: 8 pages, 4 figures, submitted to Phys. Rev.

Loop models on random maps via nested loops: case of domain symmetry breaking and application to the Potts model

We use the nested loop approach to investigate loop models on random planar maps where the domains delimited by the loops are given two alternating colors, which can be assigned different local weights, hence allowing for an explicit Z_2 domain symmetry breaking. Each loop receives a non local weight n, as well as a local bending energy which controls loop turns. By a standard cluster construction that we review, the Q = n^2 Potts model on general random maps is mapped to a particular instance of this problem with domain-non-symmetric weights. We derive in full generality a set of coupled functional relations for a pair of generating series which encode the enumeration of loop configurations on maps with a boundary of a given color, and solve it by extending well-known complex analytic techniques. In the case where loops are fully-packed, we analyze in details the phase diagram of the model and derive exact equations for the position of its non-generic critical points. In particular, we underline that the critical Potts model on general random maps is not self-dual whenever Q \neq 1. In a model with domain-symmetric weights, we also show the possibility of a spontaneous domain symmetry breaking driven by the bending energy.Comment: 44 pages, 13 figure

Observation of the lowest energy gamma-ray in any superdeformed nucleus : 196Bi

New results on the superdeformed $^{196}$Bi nucleus a re reported. We have observed with the EUROBALL IV $\gamma$-ray spectrometer array a superdeformed trans ition of 124 keV which is the lowest observed energy $\gamma$-ray in any superdeformed nucleus. We have de velopped microscopic cranked Hartree-Fock-Bogoliubov calculations using the SLy4 effective force and a realistic surface p airing which strongly support the $K^\pi=2^-$($\pi$[651]1/2$\otimes \nu$[752]5/2) assignment of this su perdeformed band

High-spin structures of 88Kr and 89Rb: Evolution from collective to single-particle behaviors

The high-spin states of the two neutron-rich nuclei, 88Kr and 89R have been studied from the 18O + 208Pb fusion-fission reaction. Their level schemes were built from triple gamma-ray coincidence data and gamma-gamma angular correlations were analyzed in order to assign spin and parity values to most of the observed states. The two levels schemes evolve from collective structures to single-particle excitations as a function of the excitation energy. Comparison with results of shell-model calculations gives the specific proton and neutron configurations which are involved to generate the angular momentum along the yrast lines.Comment: 12 pages, 9 figures, Physical Review C (2013) in pres

Time-odd components in the mean field of rotating superdeformed nuclei

Rotation-induced time-odd components in the nuclear mean field are analyzed using the Hartree-Fock cranking approach with effective interactions SIII, SkM*, and SkP. Identical dynamical moments ${{\cal J}^{(2)}}$ are obtained for pairs of superdeformed bands $^{151}$Tb(2)--$^{152}$Dy(1) and $^{150}$Gd(2)--$^{151}$Tb(1). The corresponding relative alignments strongly depend on which time-odd mean-field terms are taken into account in the Hartree-Fock equations.Comment: 23 pages, ReVTeX, 6 uuencoded postscript figures include

High-spin structures of 136Cs

Odd-odd 136Cs nuclei have been produced in the 18O + 208Pb and 12C + 238U fusion-fission reactions and their gamma rays studied with the Euroball array. The high-spin level scheme has been built up to ~ 4.7 MeV excitation energy and spin I ~ 16 hbar from the triple gamma-ray coincidence data. The configurations of the three structures observed above ~ 2 MeV excitation energy are first discussed by analogy with the proton excitations identified in the semi-magic 137Cs nucleus, which involve the three high-j orbits lying above the Z=50 gap, pi g_{7/2}, pi d_{5/2} and pi h_{11/2}. This is confirmed by the results of shell-model calculations performed in this work.Comment: 6 pages, 4 figures, 3 table

Cranked Relativistic Hartree-Bogoliubov Theory: Superdeformed Bands in the A∼190A\sim 190 Region

Cranked Relativistic Hartree-Bogoliubov (CRHB) theory is presented as an extension of Relativistic Mean Field theory with pairing correlations to the rotating frame. Pairing correlations are taken into account by a finite range two-body force of Gogny type and approximate particle number projection is performed by Lipkin-Nogami method. This theory is applied to the description of yrast superdeformed rotational bands observed in even-even nuclei of the $A\sim 190$ mass region. Using the well established parameter sets NL1 for the Lagrangian and D1S for the pairing force one obtains a very successful description of data such as kinematic ($J^{(1)}$) and dynamic ($J^{(2)}$) moments of inertia without any adjustment of new parameters. Within the present experimental accuracy the calculated transition quadrupole moments $Q_t$ agree reasonably well with the observed data.Comment: 6 pages including 4 PostScript figures, uses RevTex, revised version, Phys.Rev. C, Rapid Communications, in pres

Superdeformed rotational bands in the Mercury region; A Cranked Skyrme-Hartree-Fock-Bogoliubov study

A study of rotational properties of the ground superdeformed bands in \Hg{0}, \Hg{2}, \Hg{4}, and \Pb{4} is presented. We use the cranked Hartree-Fock-Bogoliubov method with the {\skm} parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of \Hg{2}.Comment: 26 LaTeX pages, 14 uuencoded postscript figures included, Preprint IPN-TH 93-6

The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting

Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probabilit