Formation of H3+ in Collisions of H2+ with H2 Studied in a Guided Ion Beam Instrument

In order to study collisions between ions and neutrals, a new Guided Ion Beam (GIB) apparatus, called NOVion, has been assembled and tested. The primary purpose of this instrument is to measure absolute cross sections at energies relevant for technical or inter- and circumstellar plasmas. New and improved results are presented for forming H₃⁺ in collisions of H₂⁺ with H₂. Between 0.1 eV and 2 eV, our measured effective cross sections are in good overall agreement with most previous measurements. However, at higher energies, our results do not show the steep decline, recommended in the standard literature. After critical evaluation of all experimental and theoretical data, a new analytical function is proposed, describing properly the dependence of the title reaction on the collision energy up to 10 eV.     

Growth and Spectral Properties of Yb^3＋-doped Ba3Gd（BO3）3 Crystal

Crystal of Yb3+-doped Ba3Gd(BO3)3 has been grown by the Czochralski method. The spectroscopic characterizations have been investigated at room temperature. The Yb3+:Ba3Gd(BO3)3 crystal exhibits broad absorption at 976nm with FWHM of 7nm and large overall spitting of 2F7/2 manifold (823cm-1). The absorption and emission cross sections are 5.09×10-21cm2 at 976nm and 0.97×10-21cm2 at 1040nm,respectively. The fluorescence lifetime is 2.84 ms.     

Stimulated Raman scattering measurements of H2 vibration–vibration transfer

We present a new set of V–V rate coefficients for vibrational levels 0–5 in H₂ at 300 K, measured using a stimulated Raman–spontaneous Raman pump/probe apparatus. The measured rate of the non-resonant process, H₂(v = 1) + H₂(v = 1) → H₂(v = 0) + H₂(v = 2), is consistent with the previously reported experimental value of Kreutz et al. However, semi-classical predictions of such non-resonant processes, using the identical inter-molecular potential and methodology to that given by Cacciatore and Billing, results in rates which are too slow, by a factor of approximately 3. For the “resonant” V–V process, H₂(v = 1) + H₂(v = 0) → H₂(v = 0) + H₂(v = 1), the semi-classical rate is found to be too slow by an even larger factor, of approximately 30, compared to the experimental rate, but consistent with the previously reported experimental result of Farrow and Chandler. Further, unlike the semi-classical model prediction in which the (1, 1 → 2, 0) process rate is predicted to exceed that of the (1, 0 → 0, 1) process, the experimental data shows it to be a factor of approximately 2.5 less, suggesting that semi-classical methods that treat the rotational motion classically are unsuitable for the highly anharmonic H₂ molecule. The ratio of pure rotation and rotation–vibration Raman cross sections for scattering from levels 0 and 1 is also determined, with results which agree with calculations of Schwartz and LeRoy, but are somewhat larger than previous experimental results of Cureton.     

Computation of cross sections for the F+H2(v=0,j=0) → FH(v′j)+H reaction by the hyperspherical method

Summary A quantum mechanical calculation of cross sections for the reaction F+H₂(v=0,j=0) FH(vj)+H has been performed on the T5A semiempirical potential surface using hyperspherical coordinates. State-to-state integral and differential cross sections converge rapidly with the number of components of the total angular momentum projection onto the axis of least inertia. Thev=3 differential cross section has a forward peak whose magnitude increases with energy whereas thev=2 differential cross section has a backward maximum, in qualitative agreement with cross-beam experiments. Thev=2 andv=3 rotational distributions are in rather good agreement with experiment, but not the vibrational branching ratios.     

Calculation of Ionization,Excitation and Electron Capture Cross Sections for Be4++H(2s, 2p) Collisions

A computational study of Be⁴⁺+H(2s, 2p) collisions has been carried out employing the Classical Trajectory Monte Carlo (CTMC) method for the impact energy range from 20 keV/u to 1000 keV/u. The integral n partial cross sections for H(n) excitation and Be³⁺(n) electron capture and, the total ionization and electron capture cross sections are calculated and compared to recent semiclassical results. A general good agreement is observed for the n partial and total electron capture and ionization cross sections. The comparative study of the three inelastic processes show no significant differences between both excited targets.     

Non-vanishing of the twisted cohomology on the complement of hypersurfaces

Generically, the cohomology with coefficients in a local system of rank one on the complement in of the union of a finite number of hypersurfaces vanishes except in the highest dimension. We study the non-generic case, in which the cohomology in other dimensions does not vanish. When the hypersurfaces are hyperplanes, many examples of this kind are known. In this paper, we consider the case in which the hypersurfaces need not be hyperplanes. We prove that the hypersurfaces given by some particular linear systems have non-vanishing local system cohomologies.

     

On a Family of Hyperplane Arrangements Related to the Affine Weyl Groups

Let be an irreducible crystallographic rootsystem in a Euclidean space V, with ⁺ theset of positive roots. For , , let be the hyperplane . We define a set of hyperplanes . This hyperplane arrangement is significant inthe study of the affine Weyl groups. In this paper it is shown that thePoincaré polynomial of is , where n is the rank of and h is the Coxeter number of the finiteCoxeter group corresponding to .     

Central quotients of biautomatic groups

The quotient of a biautomatic group by a subgroup of the center is shown to be biautomatic. The main tool used is the Neumann-Shapiro triangulation of S ^n-1, associated to a biautomatic structure on . Among other applications, a question of Gersten and Short is settled by showing that direct factors of biautomatic groups are biautomatic. Received: October 4, 1994     

Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.