Lifetimes of proton unstable states in 113I measured by the particle-X-ray coincidence technique

The -delayed proton decay of ¹¹³Xe was investigated by means of a total absorption -ray spectrometer and a telescope for particle detection. The energy window available for the -delayed proton decay of ¹¹³Xe and the relative branching ratios for proton transitions to the ¹¹²Te states were remeasured. The lifetimes of proton unstable ¹¹³I states populated in the electron capture decay of ¹¹³Xe were determined by means of the particle-X-ray coincidence technique. The results of the lifetime measurements are compared with statistical-model calculations.     

Discovery of doubly magic 48Ni

In an experiment at the SISSI/LISE3 facility of GANIL, we used the projectile fragmentation of a primary 58Ni26+ beam at 74.5 MeV/nucleon with an average current of 3 &mgr;A on a natural nickel target to produce very neutron-deficient isotopes. In a 10-day experiment, 287 42Cr isotopes, 53 45Fe isotopes, 106 49Ni isotopes, and 4 48Ni isotopes were unambiguously identified. The doubly magic nucleus 48Ni, observed for the first time, is the most proton-rich isotope ever identified with an isospin projection T(z) = -4. It is probably the last doubly magic nucleus with "classical" shell closures accessible for present-day facilities. Its observation allows us to deduce a lower limit for the half-life of 48Ni of 0.5 &mgr;s.     

On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids

We consider finite difference approximations of solutions of inverse Sturm‐Liouville problems in bounded intervals. Using three‐point finite difference schemes, we discretize the equations on so‐called optimal grids constructed as follows: For a staggered grid with 2 k points, we ask that the finite difference operator (a k × k Jacobi matrix) and the Sturm‐Liouville differential operator share the k lowest eigenvalues and the values of the orthonormal eigenfunctions at one end of the interval. This requirement determines uniquely the entries in the Jacobi matrix, which are grid cell averages of the coefficients in the continuum problem. If these coefficients are known, we can find the grid, which we call optimal because it gives, by design, a finite difference operator with a prescribed spectral measure. We focus attention on the inverse problem, where neither the coefficients nor the grid are known. A key question in inversion is how to parametrize the coefficients, i.e., how to choose the grid. It is clear that, to be successful, this grid must be close to the optimal one, which is unknown. Fortunately, as we show here, the grid dependence on the unknown coefficients is weak, so the inversion can be done on a precomputed grid for an a priori guess of the unknown coefficients. This observation leads to a simple yet efficient inversion algorithm, which gives coefficients that converge pointwise to the true solution as the number k of data points tends to infinity. The cornerstone of our convergence proof is showing that optimal grids provide an implicit, natural regularization of the inverse problem, by giving reconstructions with uniformly bounded total variation. The analysis is based on a novel, explicit perturbation analysis of Lanczos recursions and on a discrete Gel'fand‐Levitan formulation. © 2005 Wiley Periodicals, Inc.     

Almost Automorphic Functions in Frechet Spaces and Applications to Differential Equations

In this paper we first develop a theory of almost automorphic functions with values in Frechet spaces. Then, we consider the semilinear differential equation x'(t) = A x(t) + f(t, x(t)), t ∈ ℝ in a Frechet space X, where A is the infinitesimal generator of a C₀-semigroup satisfying some conditions of exponential stability. Under suitable conditions on f, we prove the existence and uniqueness of an almost automorphic mild solution to the equation.     

Crossed products and entropy of automorphisms

Let be an exact C∗-algebra, let G be a locally compact group, and let be a C∗-dynamical system. Each automorphism α_g induces a spatial automorphism Ad_λg on the reduced crossed product . In this paper we examine the question, first raised by E. Størmer, of when the topological entropies of α_g and Ad_λg coincide. This had been answered by N. Brown for the particular case of discrete abelian groups. Using different methods, we extend his result to preservation of entropy for α_g when the subgroup of Aut(G) generated by the corresponding inner automorphism Ad_g has compact closure. This property is satisfied by all elements of a wide class of groups called locally [FIA]⁻. This class includes all abelian groups, both discrete and continuous, as well as all compact groups.     

Shape Coexistence and the N=28 Shell Closure Far from Stability

A mass measurement experiment by a time of flight method with the SPEG spectrometer at GANIL has been performed to investigate the N=20 and N=28 shell closures far from stability. The masses of 31 neutron-rich nuclei in the range A=29–47 have been measured. The precision of 19 masses has been significantly improved and 12 masses were measured for the first time. The neutron-rich Cl, S and P isotopes are seen to exhibit a change in shell structure around N=28. Comparison with shell model and relativistic mean field calculations demonstrate that the observed effects arise from deformed prolate ground state configurations associated with shape coexistence. The evidence of an isomeric state in the ⁴³S and its interpretation by a shell model calculation confirm the analysis of the masses and constitutes the first evidence of the predicted shape coexistence around N=28. This revised version was published online in July 2006 with corrections to the Cover Date.     

First measurement of β-decay properties of the proton drip-line nucleus 60Ga

By using the fusion-evaporation reaction ²⁸Si(³⁶Ar,p3n) and spectroscopy of β-delayed γ-rays and charged particles on mass-separated sources, β-decay properties of the neutron-deficient isotope ⁶⁰Ga were studied for the first time. The half-life of ⁶⁰Ga was determined to be 70(15) ms, and, based on βγγ coincidences, the isobaric-analogue state in ⁶⁰Zn was identified at 4851.9(7) keV. A semiempirical proton separation energy value of 40(70) keV was deduced for ⁶⁰Ga. The experimental results on half-life, mass excess, proton separation energy, and structure of the ⁶⁰Zn daughter states are discussed in comparison with various model predictions, including large-scale shell model calculations. Received: 4 September 2001 / Accepted: 12 November 2001     

Smooth Scalar-on-Image Regression via Spatial Bayesian Variable Selection

We develop scalar-on-image regression models when images are registered multidimensional manifolds. We propose a fast and scalable Bayes’ inferential procedure to estimate the image coefficient. The central idea is the combination of an Ising prior distribution, which controls a latent binary indicator map, and an intrinsic Gaussian Markov random field, which controls the smoothness of the nonzero coefficients. The model is fit using a single-site Gibbs sampler, which allows fitting within minutes for hundreds of subjects with predictor images containing thousands of locations. The code is simple and is provided in the online Appendix (see the “Supplementary Materials” section). We apply this method to a neuroimaging study where cognitive outcomes are regressed on measures of white-matter microstructure at every voxel of the corpus callosum for hundreds of subjects.     

An Exact Class of Bulk Field Potentials onto the 5D-Warp of de Sitter Spacetime

In the five-dimensionally warped FRW Universe, we integrate the corresponding Einstein equations for a scalar source depending only on the extra-dimension. It yields a de Sitter brane and a specific warp factor for which we derive the effective bulk field potentials. These are generalizing some of the previously proposed forms in the literature.