Interaction of elemental mercury with selenium surfaces: model experiments for investigations of superheavy elements copernicium and flerovium

The adsorption behavior of ¹⁹⁷Hg and ^183–185Hg on red amorphous selenium (red a-Se) and trigonal selenium (t-Se) was investigated experimentally by off-line and on-line gas chromatographic methods, in preparation of a sensitive chemical separation and characterization of the transactinides copernicium (Cn, Z = 112) and flerovium (Fl, Z = 114). Monte-Carlo simulations of a diffusion controlled deposition were in good agreement with the experimental results, assuming as interaction limits ?ΔH _ads ^red a-Se (Hg) > 85 kJ/mol, and ?ΔH _ads ^t-Se (Hg) < 60 kJ/mol. Both Se allotropes can be used as stationary surfaces in comparative gas-chromatographic chemical investigations of Cn and Fl.     

Optimization of an isothermal gas-chromatographic setup for the chemical exploration of dubnium (Db,Z = 105) oxychlorides

An isothermal gas-chromatographic (IGC) device has been developed and tested for on-line gas phase studies of volatile oxychlorides of short-lived group-5 transition metals. Radioisotopes of niobium and tantalum, produced in nuclear fusion evaporation reactions, are directly flushed into the IGC setup by an inert gas-jet. Oxychloride compounds are formed by the addition of SOCl₂ and O₂. Parameters influencing the formation and transport of NbOCl₃ and TaOCl₃ are discussed. For nuclides with half-lives (t_1/2) of about 30 s, an overall efficiency of 7% is obtained, rendering the IGC setup suitable for the chemical exploration of ²⁶²Db (t_1/2?=?34 s).

     

On singular modular forms for principal congruence subgroups

We show that spaces of vector–valued singular modular forms for principal congruence subgroups of the symplectic group Sp(n,ℤ) of integral weight are generated by suitable finite dimensional families of Siegel theta series. This is obtained as an application of some results concerning the action of trace operators on non–homogeneous theta series.     

Petersson Products of Singular and Almost Singular Theta Series

We evaluate Petersson products of pairs of Siegel theta series of degree n attached to even lattices of rank mn. This allows us to get nice expressions, involving Dirichlet series and standard L-functions, for Petersson products of Siegel modular forms that are linear combinations of such theta series. Some applications to the theory of theta-liftings are also discussed.Mathematics Subject Classification (2000): 11E45, 11E10, 11F27, 11F46