Synthesis and structures of O-anthrylmethyl-substituted hexahomotrioxacalix[3]arenes

O-Alkylation of 7,15,23-tri-tert-butyl-25,26,27-trihydroxy-2,3,10,11,18,19-hexahomo-3,11,19-trioxacalix[3]arene (1H₃) with 9-chloromethylanthracene 5 was carried out under different reaction conditions. Variation of the number of anthrylmethyl group introduced at the phenolic rim of hexahomotrioxacalix[3]arene 1H₃ was achieved through selective O-alkylation using stoichiometric amounts of 9-chloromethylanthracene 5 in acetone to afford the mono-O-alkylated product 2H₂An, the di-O-alkylated product 3HAn₂ and the tri-O-alkylated product partial-cone-4An₃, respectively. Interestingly, by using an acetone/benzene (1:1 v/v) mixed solvent system, the cone-4An₃ was successfully synthesized. These results suggest that the solvent can also control the conformation of the O-alkylation products. The possible reaction routes of the cone-4An₃ and partial-cone-4An₃ are also discussed

Early Afterglows of Gamma-Ray Bursts in a Stratified Medium with a Power-Law Density Distribution

A long-duration gamma-ray burst (GRB) has been widely thought to arise from the collapse of a massive star, and it has been suggested that its ambient medium is a homogenous interstellar medium (ISM) or a stellar wind. There are two shocks when an ultra-relativistic fireball that has been ejected during the prompt gamma-ray emission phase sweeps up the circumburst medium: a reverse shock that propagates into the fireball, and a forward shock that propagates into the ambient medium. In this paper, we investigate the temporal evolution of the dynamics and emission of these two shocks in an environment with a general density distribution of $n\propto R^{-k}$ (where $R$ is the radius) by considering thick-shell and thin-shell cases. A GRB afterglow with one smooth onset peak at early times is understood to result from such external shocks. Thus, we can determine the medium density distribution by fitting the onset peak appearing in the light curve of an early optical afterglow. We apply our model to 19 GRBs, and find that their $k$ values are in the range of 0.4 - 1.4, with a typical value of $k\sim1$, implying that this environment is neither a homogenous interstellar medium with $k=0$ nor a typical stellar wind with $k=2$. This shows that the progenitors of these GRBs might have undergone a new mass-loss evolution.Comment: 32 pages, 5 figures, 1 table, published in Ap

Analysis on Heavy Quarkonia Transitions with Pion Emission in Terms of the QCD Multipole Expansion and Determination of Mass Spectra of Hybrids

One of the most important tasks in high energy physics is search for the exotic states, such as glueball, hybrid and multi-quark states. The transitions $\psi(ns)\to \psi(ms)+\pi\pi$ and $\Upsilon(ns)\to \Upsilon(ms)+\pi\pi$ attract great attentions because they may reveal characteristics of hybrids. In this work, we analyze those transition modes in terms of the theoretical framework established by Yan and Kuang. It is interesting to notice that the intermediate states between the two gluon-emissions are hybrids, therefore by fitting the data, we are able to determine the mass spectra of hybrids. The ground hybrid states are predicted as 4.23 GeV (for charmonium) and 10.79 GeV (for bottonium) which do not correspond to any states measured in recent experiments, thus it may imply that very possibly, hybrids mix with regular quarkonia to constitute physical states. Comprehensive comparisons of the potentials for hybrids whose parameters are obtained in this scenario with the lattice results are presented.Comment: 16 pages, 2 figur