Spectral Response of a Stochastic Oscillator under Impacts

An approximate analytical procedure is presented to estimate theresponse spectrum of an oscillator with elastic impacts under a Gaussian whitenoise excitation. The proposed approach is based on a perturbation analysis ofthe problem and on the use of the stochastic averaging principle. The basicidea is to replace the initial system by a more regular system obtained byapproximating the nonlinear restoring force by a Chebychev polynomial, and thento construct for this regular system two approximations: one for the flowand one for the stationary distribution of the response amplitude. Ananalytical approximation of the response spectrum can then be derived fromthese results. Predictions from this analytical approximation are compared with corresponding digital simulation estimates and with the ones obtained from theconventional equivalent linearization method.     

X ray spectroscopic intercomparison between hydrogenic ions of different Z as a method for determining Lamb shifts

Novel methods for determining the 1s Lamb shift of hydrogenic ions are outlined. In one method the energy of a 2–1 transition in the hydrogenic ion of nuclear charge Z is compared to a 4–2 transition in the hydrogenic ion of charge 2Z. A second method exploits close coincidences between Lyman series transitions in ions of similar Z. This revised version was published online in August 2006 with corrections to the Cover Date.     

Resonant and near-threshold photoionization cross sections of Fe14+

Photoionization (PI) of Fe14+ in the range from 450 to 1100 eV was measured at the BESSY II storage ring using an electron beam ion trap achieving high target-ion area densities of 10(10) cm(-2). Photoabsorption by this ion is observed in astrophysical spectra and plasmas, but until now cross sections and resonance energies could only be provided by calculations. We reach a resolving power E/ΔE of at least 6500, outstanding in the present energy range, which enables benchmarking and improving the most advanced theories for PI of ions in high charge states.     

Invariant convex subcones of the Tits cone of a linear Coxeter group

We investigate the faces and the face lattices of arbitrary Coxeter group invariant convex subcones of the Tits cone of a linear Coxeter system as introduced by E.B. Vinberg. Particular examples are given by certain Weyl group invariant polyhedral cones, which underlie the theory of normal reductive linear algebraic monoids as developed by M.S. Putcha and L.E. Renner. We determine the faces and the face lattice of the Tits cone and the imaginary cone, generalizing some of the results obtained for linear Coxeter systems with symmetric root bases by M. Dyer, and for linear Coxeter systems with free root bases by E. Looijenga, P. Slodowy, and the author.     

Coupled ab initio potential energy surfaces for the two lowest 2A′ electronic states of the C2H molecule

Realistic two-valued potential energy surfaces for the reaction C(³P) + CH(X²Π) → C₂ + H have been constructed from a set of high level ab initio data describing the first two ²A′ electronic states of the C₂H system. These states have linear equilibrium configurations, known as the X ²Σ⁺ and A²Π states, and are coupled by a conical intersection. They lead to the formation of C₂(X¹Σ⁺ _g) and C₂(a³Π_u) considering an adiabatic dissociation process. The ab initio calculations are of the multireference configuration interaction variety and were carried out using a polarized triple-zeta basis set. Using the ab initio adiabatic energies and the matrix elements of the dipole moment, a 2 × 2 diabatic representation of the electronic Hamiltonian was built. Each element of this Hamiltonian matrix was expressed within the double many-body expansion (DMBE) scheme which is based, in this case, on the extended Hartree-Fock approximate correlation energy model (EHFACE). The analytical adiabatic potential energy surfaces are then obtained as the eigenvalues of this matrix, and display correctly the Σ/Π conical intersection. Moreover, the non-adiabatic couplings given by our analytical model are compared with the ab initio ones, and good qualitative agreement is observed.     

The Cosmological constant problem

Observational evidence seems to indicate that the expansion of the universe is currently accelerating. Such an acceleration strongly suggests that the content of the universe is dominated by a non-clustered form of matter, the so-called dark energy. The cosmological constant, introduced by Einstein to reconcile General Relativity with a closed and static Universe, is the most likely candidate for dark energy although other options such as a weakly interacting field, also known as quintessence, have been proposed. The fact that the dark energy density is some one hundred and twenty orders of magnitude lower than the energy scales present in the early universe constitutes the cosmological constant problem. We review various aspects of the cosmological constant problem and some interesting scenarios using supersymmetry or extra-dimensions attempting to solve one of the most puzzling issues in physics.     

Radiative Electron Capture into the K- and L-Shell of H-, He-, and Li-Like Uranium Ions at Relativistic Energies

Hyperfine Interactions - We report on the experimental study of the angular distributions of photons for the time-reversed photoionization process, i.e., the radiative electron capture (REC), in...     

Dielectronic recombination of lithium-like gold: Towards QED tests

Dielectronic recombination (DR) and radiative recombination (RR) of lithium-like gold in the energy range of 0 to 225 eV have been studied at the Experimental Storage Ring (ESR) of the GSI in Darmstadt. Main objective of the measurements is the precise determination of the 2s_1/2−2p_1/2 energy splitting as an additional QED test. This novel method, developed at the ESR [1], is based on the extrapolation of a multitude of measured resonances Au⁷⁵⁺ (1s²2p_1/2 nl_j) up to the series limit (n = ∞). Furthermore experimental data for the Au⁷⁵⁺ (1s²2p_3/26l_j) resonance manifold are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Evaluation of a new maintenance concept for the preservation of highways

Asphalt roads gradually deteriorate over time and need mendingto remain in a good state. Inspections are performed to obtaininformation about the current state of the road; when the levelof damage reaches the established standards, the road is repairedthrough a maintenance action that is considered most cost-effective.Because of economies of scale, it is to a certain extent economicalto limit the number of maintenance services by integrating neighbouringsegments into a homogeneous section which is completely repaired.In this report we consider the question of whether it is economicallyjustified to adopt a maintenance concept in which the road isoccasionally regenerated from junction to junction with a distanceof several kilometers. The big advantage of junction-to-junctionmaintenance is that it can be done within special road barrierconstructions which reduce the road capacity only slightly,so that the road can be maintained 24 hours a day.     

An absolute measurement of the probability for 1s σ and 2p σ excitation of the leadK shell

Using particle x-ray coincidence techniques, the probability forK shell ionization has been measured absolutely at two impact parameters for collisions of 5.8 MeV/amu²⁰⁸Pb on Ag and Au. In the asymmetric collision system Pb-Ag, the 1sσ excitation probability of the PbK shell is 2.2% at 25 fm impact parameter, and an exponential probability distribution falls off too quickly to account for the measured total cross section. For the symmetric system Pb-Au, the latter conclusion is also made for the 2pσ excitation probability although in this case, the probability is much larger being 29% at 42 fm.