Isobaric yield ratios in heavy-ion reactions, and symmetry energy of neutron-rich nuclei at intermediate energies

The isobaric yield ratios of the fragments produced in the neutron-rich 48Ca and 64Ni projectile fragmentation are analyzed in the framework of a modified Fisher model. The correlations between the isobaric yield ratios (R) and the energy coefficients in the Weisz\"acker-Beth semiclassical mass formula (the symmetry-energy term asym, the Coulomb-energy term ac, and the pairing-energy term ap) and the difference between the chemical potentials of the neutron and proton ({\mu}n-{\mu}p) are investigated. Simple correlations between ({\mu}n-{\mu}p)/T, ac/T, asym/T, and ap/T (where T is the temperature), and lnR are obtained. It is suggested that ({\mu}n-{\mu}p)/T, ac/T, asym/T, and ap/T of neutron-rich nuclei can be extracted using isobaric yield ratios for heavy-ion collisions at intermediate energies.Comment: 12 pages, 6 figure

Isospin dependence of projectile-like fragment production at intermediate energies

The cross sections of fragments produced in 140 $A$ MeV $^{40,48}$Ca + $^9$Be and $^{58,64}$Ni + $^9$Be reactions are calculated by the statistical abration-ablation(SAA) model and compared to the experimental results measured at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The fragment isotopic and isotonic cross section distributions of $^{40}$Ca and $^{48}$Ca, $^{58}$Ni and $^{64}$Ni, $^{40}$Ca and $^{58}$Ni, and $^{48}$Ca and $^{64}$Ni are compared and the isospin dependence of the projectile fragmentation is studied. It is found that the isospin dependence decreases and disappears in the central collisions. The shapes of the fragment isotopic and isotonic cross section distributions are found to be very similar for symmetric projectile nuclei. The shapes of the fragment isotopic and isotonic distributions of different asymmetric projectiles produced in peripheral reactions are found very similar. The similarity of the distributions are related to the similar proton and neutron density distributions inside the nucleus in framework of the SAA model.Comment: 7 pages, 4 figures; to be published in Phys Rev

Travelling waves for a non-monotone bistable equation with delay: existence and oscillations

We consider a bistable (0\textless{}\theta\textless{}1 being the three constant steady states) delayed reaction diffusion equation, which serves as a model in population dynamics. The problem does not admit any comparison principle. This prevents the use of classical technics and, as a consequence, it is far from obvious to understand the behaviour of a possible travelling wave in $+\infty$. Combining refined {\it a priori} estimates and a Leray Schauder topological degree argument, we construct a travelling wave connecting 0 in $-\infty$ to \lq\lq something" which is strictly above the unstable equilibrium $\theta$ in $+\infty$. Furthemore, we present situations (additional bound on the nonlinearity or small delay) where the wave converges to 1 in $+\infty$, whereas the wave is shown to oscillate around 1 in $+\infty$ when, typically, the delay is large

Poly[tetra­kis(μ4-4,6-dimethyl-5-nitro­benzene-1,3-dicarboxyl­ato-κ2 O 1:O 1′:O 3:O 3′)bis­(pyridine-κN)dizinc]

In the title complex, [Zn2(C10H7NO6)2(C5H5N)2]n, the repeat unit is a centrosymmetic tetra-carboxyl­ato-O,O’-bridged dimer in which each ZnII atom is five-coordinated by four O atoms from different dianionic 4,6-dimethyl-5-nitro­iso­phthalate ligands [Zn—O = 2.0283 (18)–2.0540 (19) Å] and one N atom from a pyridine mol­ecule [Zn—N = 2.030 (2) Å] in the axial site of a slightly distorted square-pyramidal coordination sphere. The Zn⋯Zn separation is 2.9750 (6) Å. The complex dimers are extended into a two-dimensional polymeric structure parallel to (100) through bridges provided by the second carboxyl­ate group of the ligand