Spectrum of $^7$Li and elastic scattering reaction $^4$He($^3$H, $^3$H)$^4$He are studied using the unified description of the Gamow shell model in the coupled-channel formulation (GSMCC). The reaction channels are constructed using the cluster expansion with the two mass partitions [$^4$He + $^3$H], [$^6$Li + n].

J. P. Linares Fernández M. Płoszajczak N. Michel

Two dimensional concordance plots involving the baryon-to-photon ratio, $\eta$, and an effective number of light neutrinos, $N_{\nu}$, are used to discuss the overall consistency of standard big-bang nucleosynthesis in light of recent determinations of the primordial deuterium ($^2$H) abundance. Observations of high-redshift Ly-$\alpha$ clouds have provided discordant $^2$H/H determinations: one cloud with $^2$H/H high compared with the previously accepted upper limit on ($^2$H + $^3$He)/H; and one system with a significantly lower upper bound on $^2$H/H than those previously obtained. The high value of $^2$H/H agrees well with the current observationally-inferred primordial abundances of $^4$He and $^7$Li for $N_{\nu}=3$. The low value of $^2$H/H does not fit well with the current observationally-inferred primordial abundance of $^4$He for $N_{\nu}=3$. In addition, if the low value of $^2$H/H is indicative of the primordial deuterium abundance, then significant depletion of $^7$Li in old, hot Pop II halo stars is probably required to obtain a concordant range of $\eta$, for {\em any} effective number of neutrino flavors. The use of conservative ranges for the primordial abundances of $^2$H, $^4$He, and $^7$Li allow success of the standard picture for $N_{\nu}=3$.

Christian Y. Cardall George M. Fuller

C$_4$H and $c$-C$_3$H$_2$, as unsaturated hydrocarbon molecules, are important for forming large organic molecules in the interstellar medium. We present mapping observations of C$_4$H ($N$=9$-8$) lines, $c$-C$_3$H$_2$ ($J_{Ka,Kb}$=2$_{1,2}$-1$_{0,1}$) %at 85338.894 MHz and H$^{13}$CO$^+$ ($J$=1$-0$) %at 86754.2884 MHz toward 19 nearby cold molecular cores in the Milky Way with the IRAM 30m telescope. C$_4$H 9--8 was detected in 13 sources, while $c$-C$_3$H$_2$ was detected in 18 sources. The widely existing C$_4$H and $c$-C$_3$H$_2$ molecules in cold cores provide material to form large organic molecules. Different spatial distributions between C$_4$H 9--8 and $c$-C$_3$H$_2$ 2--1 were found. The relative abundances of these three molecules were obtained under the assumption of local thermodynamic equilibrium conditions with a fixed excitation temperature. The abundance ratio of C$_4$H to $c$-C$_3$H$_2$ ranged from 0.34 $\pm$ 0.09 in G032.93+02 to 4.65 $\pm$ 0.50 in G008.67+22. A weak correlation between C$_4$H/H$^{13}$CO$^+$ and $c$-C$_3$H$_2$/H$^{13}$CO$^+$ abundance ratios was found, with a correlation coefficient of 0.46, which indicates that there is no tight astrochemical connection between C$_4$H and $c$-C$_3$H$_2$ molecules.

Yijia Liu Junzhi Wang Shu Liu Ningyu Tang Yan Gong Yuqiang Li Juan LI Rui Luo Yani Xu

The stability of different stoichiometric H$_n$Br ($n$=1-7) compounds under pressure are extensively studied using density functional theory calculations. Five new energetically stable stoichiometries of H$_2$Br, H$_3$Br, H$_4$Br, H$_5$Br, and H$_7$Br were uncovered at high pressure. The results show that HBr is stable below 64 GPa, then decomposes into new compound H$_2$Br and Br$_2$ molecular crystal. For H$_2$Br and H$_3$Br compounds, they were found to become stable above 30 GPa and 8 GPa, respectively. In addition, we accidentally discovered the triangular H$_3^+$ species in H$_5$Br compounds at 100 GPa. Further electron-phonon coupling calculations predicted that hydrogen-rich H$_2$Br and H$_4$Br compounds are superconductors with critical temperature of superconductivity $T_c$ of 12.1 K and 2.4 K at 240 GPa, respectively.

Defang Duan Fubo Tian Xiaoli Huang Da Li Hongyu Yu Yunxian Liu Yanbin Ma Bingbing Liu Tian Cui

We present high-resolution and high-quality UVES spectroscopic data of the metal-poor double-lined spectroscopic binary CS 22876--032 ([Fe/H] $\sim -3.7$ dex), with the goal to derive the $^6$Li/$^7$Li isotopic ratio by analysing the \ion{Li}{i} $\lambda$~670.8~nm doublet. We coadd all 28 useful spectra normalised and corrected for radial velocity to the rest frame of the primary star. We fit the Li profile with a grid of the 3D-NLTE synthetic spectra, to take into account the line profile asymmetries induced by stellar convection, and perform Monte Carlo simulations to evaluate the uncertainty of the fit of the Li line profile. We check that the veiling factor does not affect the derived isotopic ratio, $^6$Li/$^7$Li, and only modifies the Li abundance, A(Li), by about 0.15~dex. The best fit of the Li profile of the primary star provides A(Li)~$ = 2.17 \pm 0.01$~dex and $^6$Li/$^7$Li~$=8^{+2}_{-5}$\% at 68\% confidence level. In addition, we improve the Li abundance of the secondary star at A(Li)~$= 1.55 \pm 0.04$~dex, which is about 0.6~dex lower than that of the primary star. The analysis of the Li profile of the primary star is consistent with no detection of $^6$Li and provides an upper-limit to the isotopic ratio of $^6$Li/$^7$Li~$< 10$\% at this very low metallicity, about 0.5~dex lower in metallicity than previous attempts for detection of $^6$Li in extremely metal poor stars. These results do not solve or worsen the cosmological $^7$Li problem, nor support the need for non standard $^6$Li production in the early Universe.

J. I. González Hernández P. Bonifacio E. Caffau H. G. Ludwig M. Steffen L. Monaco R. Cayrel

The Tur\'{a}n number of a graph $H$, denoted $\mbox{ex}(n,H)$, is the maximum number of edges in an $n$-vertex graph with no subgraph isomorphic to $H$. Solymosi conjectured that if $H$ is any graph and $\mbox{ex}(n,H) = O(n^{\alpha})$ where $\alpha > 1$, then any $n$-vertex graph with the property that each edge lies in exactly one copy of $H$ has $o(n^{\alpha})$ edges. This can be viewed as conjecturing a possible extension of the removal lemma to sparse graphs, and is well-known to be true when $H$ is a non-bipartite graph, in particular when $H$ is a triangle, due to Ruzsa and Szemer\'{e}di. Using Sidon sets we exhibit infinitely many bipartite graphs $H$ for which the conjecture is false.

Craig Timmons Jacques Verstraete

Evolutionary crystal structure prediction searches have been employed to explore the ternary Li-F-H system at 300 GPa. Metastable phases were uncovered within the static lattice approximation, with LiF$_3$H$_2$, LiF$_2$H, Li$_3$F$_4$H, LiF$_4$H$_4$, Li$_2$F$_3$H and LiF$_3$H lying within 50 meV/atom of the 0 K convex hull. All of these phases contain H$_n$F$_{n+1}^-$ ($n$ = 1; 2) anions, and Li$^+$ cations. Other structural motifs such as LiF slabs, H$_3^+$ molecules, and F$^{\delta -}$ ions are present in some of the low enthalpy Li-F-H structures. The bonding within the H$_n$F$_{n+1}^-$ molecules, which may be bent or linear, symmetric or asymmetric, is analyzed. The five phases closest to the hull are insulators, while LiF$_3$H is metallic and predicted to have a vanishingly small superconducting critical temperature. This study lays the foundation for future investigations of the role of temperature and anharmonicity on the stability and properties of compounds and alloys in the Li-F-H ternary system.

Tiange Bi Andrew Shamp Tyson Terpstra Russell J. Hemley Eva Zurek

Lithium abundances have been determined in more than 100 metal-poor halo stars both in the field and in clusters. From these data we find trends of Li with both temperature and metallicity and a real dispersion in Li abundances in the Spite Li plateau. We attribute this dispersion primarily to Li depletion (presumably due to extra mixing induced by stellar rotation) and to Galactic chemical evolution. We derive a primordial Li of 2.44 $\pm$0.18 for A(Li)$_p$ = log N(Li/H) + 12.00. This agrees with the Li abundances predicted by the $WMAP$ results. For stars cooler than the Li plateau we have evidence that Li depletion sets in at hotter temperatures for the higher metallicity stars than for the low-metal stars. This is the opposite sense of predictions from stellar models. The smooth transition of the Li content from the Li plateau stars to the cool stars adds weight to the inference of Li depletion in the plateau stars.

Ann Merchant Boesgaard Megan C. Novicki Alex Stephens

High-dispersion spectra in the Li 6708 Angstrom region have been obtained and analyzed in the old, metal-deficient cluster, NGC 2243. From Hydra spectra for 29 astrometric and radial-velocity members, we derive rotational velocities, as well as [Fe/H], [Ca/H], [Si/H], and [Ni/H] based on 17, 1, 1, and 3 lines, respectively. Using ROBOSPECT, an automatic equivalent width measurement program, we derive [Fe/H] = -0.54 +/- 0.11 (MAD), for an internal precision for the cluster [Fe/H] below 0.03 dex. Given the more restricted line set, comparable values for [Ca/H], [Si/H], and [Ni/H] are -0.48 +/- 0.19, -0.44 +/- 0.11, and -0.61 +/- 0.06, respectively. With E(B-V) = 0.055, appropriate isochrones imply (m-M) = 13.2 +/- 0.1 and an age of 3.6 +/- 0.2 Gyr. Using available VLT spectra and published Li abundances, we construct a Li sample of over 100 stars extending from the tip of the giant branch to 0.5 mag below the Li-dip. The Li-dip is well populated and, when combined with results for NGC 6819 and Hyades/Praesepe, implies a mass/metallicity slope of 0.4 solar-mass/dex for the high mass edge of the Li-dip. The A(Li) distribution among giants reflects the degree of Li variation among the turnoff stars above the Li-dip, itself a function of stellar mass and metallicity and strongly anticorrelated with a v_rot distribution that dramatically narrows with age. Potential implications of these patterns for the interpretation of Li among dwarf and giant field populations, especially selection biases tied to age and metallicity, are discussed.

B. J. Anthony-Twarog C. P. Deliyannis . B. A. Twarog

Let $H$ be a subgroup of a group $G$. $H$ is said satisfying $\Pi$-property in $G$, if $|G/K:N_{G/K}(HK/K\cap L/K)|$ is a $\pi(HK/K\cap L/K))$-number for any chief factor $L/K$ of $G$, and, if there is a subnormal supplement $T$ of $H$ in $G$ such that $H\cap T\le I\le H$ for some subgroup $I$ satisfying $\Pi$-property in $G$, then $H$ is said $\Pi$-normal in $G$. By these properties of some subgroups, we obtain some new criterions of $p$-nilpotency of finite groups.

Baojun Li Tuval Foguel