Invariant tensors inSU (3)

The construction of independentSU (3) tensors out of octets of fields is considered by investigating numerically invariantSU (3) tensors. A method of obtaining independent sets of these to any rank is discussed and also independent sets are explicitly displayed up to fifth rank. It is shown that this approach allows us to obtain relations among the invariant tensors, and useful new identities involving thed _ijk andf _ijk tensors are exhibited.     

Double and single electron capture and loss in 0.5–2.5 MeV/uO q+ −Ne (q=5, 7, 8) collisions

Cross sections for single and double electron capture and loss in 8–40 MeVO ^q+ ?Ne (q=5, 7, 8) collisions have been measured. The results are compared with theoretical calculations.     

Efficient global optimization of reactive force‐field parameters

Reactive force fields make low‐cost simulations of chemical reactions possible. However, optimizing them for a given chemical system is difficult and time‐consuming. We present a high‐performance implementation of global force‐field parameter optimization, which delivers parameter sets of the same quality with much less effort and in far less time than before, and also offers excellent parallel scaling. We demonstrate these features with example applications targeting the ReaxFF force field. © 2015 Wiley Periodicals, Inc.     

First results of electron cooling experiments at LEAR

The first results are presented of electron cooling experiments in the Low-Energy Antiproton Ring (LEAR) at CERN, performed with a proton beam of about 50 and 21 MeV. The number of stored protons ranged from 10⁷ to 3 × 10⁹. Cooling times of the order 1 s and proton drag rates of up to 0.7 MeV/s were obtained. The capture of cooling electrons by protons producing hydrogen atoms was used to derive an effective electron temperature (0.25 eV). From the angular profile of the neutral hydrogen beam an upper limit of 3π mm.mrad could be deduced for the horizontal equilibrium proton-beam emittance. The lowest equilibrium momentum spread was 2 × 10⁵ (FWHM), as derived from the analysis of the longitudinal Schottky signal. This Schottky signal exhibited an unusual behaviour with beam intensity and under certain conditions showed a doublepeak structure which was associated with collective beam noise. For very cold beams transverse instabilities were observed, which resulted in a rapid spill-off of protons and a stabilization at lower intensities. The threshold of these instabilities was raised by heating the proton or the electron beam. The cooling of a bunched proton beam was investigated. The reduction of the proton momentum spread led to bunch lengths of about 2 m, containing 3 × 10⁸ protons.     

Invariant tensors inSU(3). II

InvariantSU(3) octet tensors are constructed in terms of matrices and applied to the problem of forming tensors from a single octet used repeatedly. Next a similar problem but with two octets is considered which demonstrates that different outer products of invariant tensors may be related. Finally, a theorem is proved which shows that the number of invariant tensors is essentially finite, and that relations of ranks greater than six exist on outer products of these tensors.