Treatment of pairing correlations in nuclei close to drip lines

We discuss the HFB equations in coordinate representation,a suitable method for handling the full effects of the continuous quasiparticle spectrum. We show how the continuum HFB equations can be solved with the correct asymptotic conditions instead of the discretization conditions which are commonly used in the literature. The continuum HFB method is illustrated with a model where the mean field and pairing field have simple forms. The relationship with the continuum Hartree-Fock-BCS (HF-BCS) approximation is also discussed. Realistic HFB and HF-BCS calculations based on Skyrme interactions are compared for the case of a neutron-rich nucleus.Comment: 12 pages, 4 Postscript figures, uses KapProc.cls, to appear in Proceedings of NATO School " Nuclei far from stability and astrophysics", Predeal, Romania, 200

Sustainable Recycling of Insoluble Rust Waste for the Synthesis of Iron-Containing Perovskite-Type Catalysts

Insoluble rust waste from the scraping of rusted iron-containing materials represents a cheap, eco-friendly, and available source of iron. LaFeO3 perovskite-type powders were successfully prepared by solution combustion synthesis using rust waste from an electricity transmission tower manufacturer. Solution combustion synthesis enabled introduction of this insoluble iron precursor directly into the final product, bypassing complex extraction procedures. Catalytic activity in the propylene oxidation of the waste-derived LaFeO3 with stoichiometric Fe/La ratio was almost identical to the commercial iron nitrate-derived LaFeO3 , thus demonstrating the viability of this recycling solution. The amount of waste iron precursor was varied and its effect on the powder properties was investigated. A lesser stoichiometric amount of precursor produced a LaFeO3 -La2O3 binary system, whereas a higher stoichiometric amount led to a LaFeO3 -Fe2O3 binary system. Catalytic activity of iron-rich compositions in the propylene oxidation was only slightly lower than the stoichiometric one, whereas iron-poor compositions were much less active. This eco-friendly methodology can be easily extended to other iron perovskites with different chemical compositions and to other iron-containing compounds

On the Validity of the Geiger-Nuttall Alpha-Decay Law and its Microscopic Basis

The Geiger-Nuttall (GN) law relates the partial $\alpha$-decay half-life with the energy of the escaping $\alpha$ particle and contains for every isotopic chain two experimentally determined coefficients. The expression is supported by several phenomenological approaches, however its coefficients lack a fully microscopic basis. In this paper we will show that: 1) the empirical coefficients that appear in the GN law have a deep physical meaning and 2) the GN law is successful within the restricted experimental data sets available so far, but is not valid in general. We will show that, when the dependence of logarithm values of the $\alpha$ formation probability on the neutron number is not linear or constant, the GN law is broken. For the $\alpha$ decay of neutron-deficient nucleus $^{186}$Po, the difference between the experimental half-life and that predicted by the GN Law is as large as one order of magnitude.Comment: 4 pages, 5 figures, to appear in Phys. Lett.

Molecular structure of highly-excited resonant states in 24^{24}Mg and the corresponding 8^8Be+16^{16}O and 12^{12}C+12^{12}C decays

Exotic $^8$Be and $^{12}$C decays from high-lying resonances in $^{24}$Mg are analyzed in terms of a cluster model. The calculated quantities agree well with the corresponding experimental data. It is found that the calculated decay widths are very sensitive to the angular momentum carried by the outgoing cluster. It is shown that this property makes cluster decay a powerful tool to determine the spin as well as the molecular structures of the resonances.Comment: 17 pages, no figur

Abrupt changes in alpha decay systematics as a manifestation of collective nuclear modes

An abrupt change in $\alpha$ decay systematics around the N=126 neutron shell closure is discussed. It is explained as a sudden hindrance of the clustering of the nucleons that eventually form the $\alpha$ particle. This is because the clustering induced by the pairing mode acting upon the four nucleons is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.Comment: 6 pages, 3 figures, submitted to Phys. Rev. C, a few new references adde

Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends

We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two pairs of crossing edges share two vertices. We study the relations of these beyond-planar graph classes (beyond-planar graphs is a collective term for the primary attempts to generalize the planar graphs) to right-angle crossing (RAC) graphs that admit compact drawings on the grid with few bends. We present four drawing algorithms that preserve the given embeddings. First, we show that every $n$-vertex NIC-planar graph admits a NIC-planar RAC drawing with at most one bend per edge on a grid of size $O(n) \times O(n)$. Then, we show that every $n$-vertex 1-planar graph admits a 1-planar RAC drawing with at most two bends per edge on a grid of size $O(n^3) \times O(n^3)$. Finally, we make two known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at most one bend per edge and for drawing IC-planar RAC graphs straight-line

Temperature dependent BCS equations with continuum coupling

The temperature dependent BCS equations are modified in order to include the contribution of the continuum single particle states. The influence of the continuum upon the critical temperature corresponding to the phase transition from a superfluid to a normal state and upon the behaviour of the excitation energy and of the entropy is discussed.Comment: 9 pages, 3 figures, to appear in Phys. Rev.

Ultrasonographic measurements of abdominal lymph nodes in growing puppies

The sonographic appearance of the normal abdominal lymph nodes in adult dogs has been well described, but the data in puppies are scarce and of poor quality. The aim of the current study was to evaluate any differences in abdominal lymph node sonographic measurements in puppies of various sizes and to determine whether any differences were correlated with growth and weight gain during the first 10 weeks of life. By an approach based on prospective and serial measurements, length, width and thickness of jejunal, medial iliac and hypogastric nodes were obtained in twenty-one healthy puppies of various sizes, at six (T0), eight (T1) and ten (T2) weeks of age. The relationship between body weight and length, width and thickness of lymph nodes was evaluated using a Pearson correlation analysis. An ANOVA test was used to compare the measurements at different ages. Jejunal and iliac lymph nodes were the largest in large breed dogs. In large-sized puppies only the length of the jejunal lymph nodes correlated positively with width and body weight. Length of medial iliac lymph nodes correlated positively with width and body weight in all three sizes. None of the measurements of hypogastric lymph nodes were related to body weight. In large-sized puppies jejunal and iliac lymph nodes increased in length and width with age; in medium-sized puppies only iliac lymph nodes increased; in small-sized puppies jejunal and iliac lymph nodes significantly decreased in length and thickness. In conclusion, the lymph node sizes in young animals are directly related to body weight and do not decrease with growth during the first 10 weeks of life, except in small-sized puppies