Beyond the N = 50 shell closure: High-spin excitations of 87Kr and ground-state spin of 87Br

The ⁸⁷Kr nucleus has been produced as fission fragment in the fusion reaction ¹⁸O + ²⁰⁸Pb at 85MeV bombarding energy and studied with the Euroball IV array. High-spin states of this neutron-rich isotope have been identified for the first time. Its level scheme has been obtained up to 6.3MeV excitation energy and spin I ∼ 23/2ℏ. Its structure is interpreted by analogy with those of the heavier isotones. The proposed configurations involve both proton and neutron excitations from several sub-shells located close to the Fermi levels, particularly νd_5/2, πp_3/2f_5/2 and πg_9/2. Moreover, a revised spin value of 5/2^- for the ⁸⁷Br ground state is proposed.     

Isomers of astrophysical interest in neutron-deficient nuclei at masses A = 81, 85 and 86

Decay properties of neutron-deficient exotic nuclei close to A=80 have been investigated at the IGISOL facility. The studied nuclei, ⁸¹Y, ⁸¹Sr, ^81mKr, ⁸⁵Nb, ⁸⁵Zr, ⁸⁶Mo and ⁸⁶Nb, were produced by a ³²S beam from the Jyv?skyl? isochronous cyclotron on ⁵⁴Fe and ^natNi targets. The internal conversion coefficient for a 190.5 keV isomeric transition in ^81mKr has been measured and the internal transition rate has been determined. The internal transition rate has been used to estimate a neutrino capture rate on ⁸¹Br, which yields a log ft of 5.13±0.09 for the reaction ⁸¹Br( ν, e ^-)^81mKr. A new isomer with a half-life of 3.3±0.9 s has been observed in ⁸⁵Nb. The existence of an earlier reported isomer with a half-life of 56 s in ⁸⁶Nb has not been confirmed.     

Mass measurements of neutron-deficient nuclides close to A = 80 with a Penning trap

The masses of ^{80, 81, 82, 83}Y, ^{83, 84, 85, 86, 88}Zr and ^{85, 86, 87, 88}Nb have been measured with a typical precision of 7keV by using the Penning trap setup at IGISOL. The mass of ⁸⁴Zr has been measured for the first time. These precise mass measurements have improved S_p and Q_EC values for astrophysically important nuclides.     

Local field enhancements on gold and silver nanostructures for aperture near field spectroscopy

Optical properties of silver and gold semi-continuous films near the percolation threshold are investigated by scanning near field optical microscopy (SNOM) operating in the collection/transmission mode. The electromagnetic enhanced fields, due to plasmon-polariton localizations, are observed and the intensity distribution is shown to present high intensity variations that increase with the wavelength. The local fields are also demonstrated to be polarization dependent. The intensity distribution is investigated as function of the incident wavelength both for gold and silver films. The calculated probability distribution function (PDF) exhibits an exponential decay for large enhancement factors and is proved to be wavelength dependent.     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

Compact quantum groups and group duality

In this paper, we consider the *-representations of compact quantum groups and group duality. The main results in the paper are: (1) there is a one-to-one correspondence between the *-representations of compact quantum groups and *-representations of the dual Banach *-algebra; (2) the category of commutative compact quantum groups (semigroups) is a dual category to the category of compact groups (semigroups); (3) the dual category of the category of locally compact groups (semigroups) is the category of commutative Hopf C^*-algebras with a particular property. Our group duality has the flavor of a Gelfand-Naimark type theorem for compact quantum groups, and for Hopf C^*-algebras.     

A first-order system approach for diffusion equation. II: Unification of advection and diffusion

In this paper, we unify advection and diffusion into a single hyperbolic system by extending the first-order system approach introduced for the diffusion equation [J. Comput. Phys., 227 (2007) 315–352] to the advection–diffusion equation. Specifically, we construct a unified hyperbolic advection–diffusion system by expressing the diffusion term as a first-order hyperbolic system and simply adding the advection term to it. Naturally then, we develop upwind schemes for this entire   system; there is thus no need to develop two different schemes, i.e., advection and diffusion schemes. We show that numerical schemes constructed in this way can be automatically uniformly accurate, allow O(h)$O(h)$ time step, and compute the solution gradients (viscous stresses/heat fluxes for the Navier–Stokes equations) simultaneously to the same order of accuracy as the main variable, for all Reynolds numbers. We present numerical results for boundary-layer type problems on non-uniform grids in one dimension and irregular triangular grids in two dimensions to demonstrate various remarkable advantages of the proposed approach. In particular, we show that the schemes solving the first-order advection–diffusion system give a tremendous speed-up in CPU time over traditional scalar schemes despite the additional cost of carrying extra variables and solving equations for them. We conclude the paper with discussions on further developments to come.