Two-proton radioactivity of 45Fe

In an experiment at the SISSI-LISE3 facility of GANIL, the decay of the proton drip line nucleus 45Fe has been studied. Fragment-implantation events have been correlated with radioactive decay events in a 16x16 pixel silicon-strip detector. The decay-energy spectrum of 45Fe implants shows a distinct peak at (1.14+/-0.04) MeV with a half-life of T(1/2)=(4.7(+3.4)(-1.4)) ms. None of the events in this peak is in coincidence with beta particles. For a longer correlation interval, daughter decays of the two-proton daughter 43Cr can be observed after 45Fe implantation. The decay energy for 45Fe agrees nicely with several theoretical predictions for two-proton radioactivity.     

Study of 19Na at SPIRAL

The excitation function for the elastic-scattering reaction p( ¹⁸Ne, p) ¹⁸Ne was measured with the first radioactive beam from the SPIRAL facility at the GANIL laboratory and with a solid cryogenic hydrogen target. Several broad resonances have been observed, corresponding to new excited states in the unbound nucleus ¹⁹Na. In addition, two-proton emission events have been identified and are discussed.     

First observation of 54Zn and its decay by two-proton emission

The nucleus 54Zn has been observed for the first time in an experiment at the SISSI/LISE3 facility of GANIL in the quasifragmentation of a 58Ni beam at 74.5 MeV/nucleon in a (nat)Ni target. The fragments were analyzed by means of the ALPHA-LISE3 separator and implanted in a silicon-strip detector where correlations in space and time between implantation and subsequent decay events allowed us to generate almost background free decay spectra for about 25 different nuclei at the same time. Eight 54Zn implantation events were observed. From the correlated decay events, the half-life of 54Zn is determined to be 3.2(+1.8)(-0.8) ms. Seven of the eight implantations are followed by two-proton emission with a decay energy of 1.48(2) MeV. The decay energy and the partial half-life are compared to model predictions and allow for a test of these two-proton decay models.     

Beta-decay of 71Co and 73Co

A decay spectroscopy study of the neutron-rich cobalt isotopes has been performed using fragmentation of a ⁸⁶Kr³⁶⁺ beam and the new LISE2000 spectrometer at GANIL. For ⁷¹Co and ⁷³Co, the -delayed radiation has been observed for the first time, and the half-lives were found to be 79(5) ms and 41(4) ms, respectively. Features of the decay are discussed qualitatively in terms of nuclear models.     

In-beam γ spectroscopy using DIC with a radioactive Ne beam

A study of deep-inelastic and multi-nucleon transfer reactions to populate neutron-rich O, Ne and F nuclei is here presented. The reaction under analysis employed a beam of radioactive ²⁴Ne at 7.9 AMeV, provided by the SPIRAL facility at Ganil, impingin on a ²⁰⁸Pb target. The reaction products have been detected in the VAMOS spectrometer in coincidence with gamma rays measured by the EXOGAM array. Preliminary results here presented show a selectivity in the population of states of different nature.     

Dispersive white-light spectral interferometry including the effect of thin-film for distance measurement

A spectral-domain white-light interferometric technique is used for measuring distances in a Michelson interferometer with a mirror represented by a thin-film structure (TFS) on a substrate. A fibre-optic spectrometer is employed for recording spectral interferograms that include wide wavelength range effects of dispersion in a cube beam splitter and multiple reflection within the TFS. Knowing the effective thickness of the beam splitter, its dispersion and parameters of the TFS and substrate, the positions of the second interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones. We apply the technique to the beam splitter made of BK7 optical glass and to a uniform SiO₂ thin film on a silicon wafer. We compare the results of the processing that include and do not include the effect of the TFS.     

A note on statistical solutions of the three-dimensional Navier–Stokes equations: The stationary case

Stationary statistical solutions of the three-dimensional Navier–Stokes equations for incompressible fluids are considered. They are a mathematical formalization of the notion of ensemble average for turbulent flows in statistical equilibrium in time. They are also a generalization of the notion of invariant measure to the case of the three-dimensional Navier–Stokes equations, for which a global uniqueness result is not known to exist and a semigroup may not be well-defined in the classical sense. The two classical definitions of stationary statistical solutions are considered and compared, one of them being a particular case of the other and possessing a number of useful properties. Furthermore, the so-called time-average stationary statistical solutions, obtained as generalized limits of time averages of weak solutions as the averaging time goes to infinity are shown to belong to this more restrictive class. A recurrent type result is also obtained for statistical solutions satisfying an accretion condition. Finally, the weak global attractor of the three-dimensional Navier–Stokes equations is considered, and in particular it is shown that there exists a topologically large subset of the weak global attractor which is of full measure with respect to that particular class of stationary statistical solutions and which has a certain regularity property.     

A Capelli type theorem for multiplicative convolutions of polynomials

We prove a Capelli type theorem on the canonical decomposition for multiplicative convolutions of polynomials. We derive then some irreducibility criteria for convolutions of polynomials in several variables over a given field. The irreducibility conditions are expressed only in terms of the degrees of the polynomials in convolution, the degrees of their coefficients, and the degrees of some suitable divisors of the resulting leading coefficient. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameter estimation for stochastic equations with additive fractional Brownian sheet

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory.