A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added, to appear in CM

Dielectronic Recombination (via N=2 --> N'=2 Core Excitations) and Radiative Recombination of Fe XX: Laboratory Measurements and Theoretical Calculations

We have measured the resonance strengths and energies for dielectronic recombination (DR) of Fe XX forming Fe XIX via N=2 --> N'=2 (Delta_N=0) core excitations. We have also calculated the DR resonance strengths and energies using AUTOSTRUCTURE, HULLAC, MCDF, and R-matrix methods, four different state-of-the-art theoretical techniques. On average the theoretical resonance strengths agree to within <~10% with experiment. However, the 1 sigma standard deviation for the ratios of the theoretical-to-experimental resonance strengths is >~30% which is significantly larger than the estimated relative experimental uncertainty of <~10%. This suggests that similar errors exist in the calculated level populations and line emission spectrum of the recombined ion. We confirm that theoretical methods based on inverse-photoionization calculations (e.g., undamped R-matrix methods) will severely overestimate the strength of the DR process unless they include the effects of radiation damping. We also find that the coupling between the DR and radiative recombination (RR) channels is small. We have used our experimental and theoretical results to produce Maxwellian-averaged rate coefficients for Delta_N=0 DR of Fe XX. For kT>~1 eV, which includes the predicted formation temperatures for Fe XX in an optically thin, low-density photoionized plasma with cosmic abundances, our experimental and theoretical results are in good agreement. We have also used our R-matrix results, topped off using AUTOSTRUCTURE for RR into J>=25 levels, to calculate the rate coefficient for RR of Fe XX. Our RR results are in good agreement with previously published calculations.Comment: To be published in ApJS. 65 pages with 4 tables and lots of figure

Enhanced dielectronic recombination of lithium-like Ti19+ ions in external ExB fields

Dielectronic recombination(DR) of lithium-like Ti19+(1s2 2s) ions via 2s->2p core excitations has been measured at the Heidelberg heavy ion storage ring TSR. We find that not only external electric fields (0 <= Ey <= 280 V/cm) but also crossed magnetic fields (30 mT <= Bz <= 80 mT) influence the DR via high-n (2p_j nl)-Rydberg resonances. This result confirms our previous finding for isoelectronic Cl14+ ions [Bartsch T et al, PRL 82, 3779 (1999)] that experimentally established the sensitivity of DR to ExB fields. In the present investigation the larger 2p_{1/2}-2p_{3/2} fine structure splitting of Ti19+ allowed us to study separately the influence of external fields via the two series of Rydberg DR resonances attached to the 2s -> 2p_{1/2} and 2s -> 2p_{3/2} excitations of the Li-like core, extracting initial slopes and saturation fields of the enhancement. We find that for Ey > 80 V/cm the field induced enhancement is about 1.8 times stronger for the 2p_{3/2} series than for the 2p_{1/2} series.Comment: 10 pages, 3 figures, to be published in Journal of Physics B, see also http://www.strz.uni-giessen.de/~k

New Collisional Ionization Equilibrium Calculations for Optically Thin Plasmas

Reliably interpreting spectra from electron-ionized laboratory and cosmic plasmas requires accurate ionization balance calculations for the plasma in question. However, much of the atomic data needed for these calculations have not been generated using modern theoretical methods and their reliability are often highly suspect. We have carried out state-of-the-art calculations of dielectronic recombination (DR) rate coefficients for the hydrogenic through Mg-like ions of all elements from He to Zn as well as for Al- like to Ar-like ions of Fe. We have also carried out state-of-the-art radiative recombination (RR) rate coefficient calculations for the bare through Na-like ions of all elements from H to Zn. Using our data and the most recently recommended electron impact ionization data, we present improved collisional ionization equilibrium (CIE) calculations. Here, as an example, we present our calculated fractional ionic abundances for iron using these data and compare them with those from the previously recommended CIE calculations

Dielectronic Recombination in Photoionized Gas. II. Laboratory Measurements for Fe XVIII and Fe XIX

In photoionized gases with cosmic abundances, dielectronic recombination (DR) proceeds primarily via nlj --> nl'j' core excitations (Dn=0 DR). We have measured the resonance strengths and energies for Fe XVIII to Fe XVII and Fe XIX to Fe XVIII Dn=0 DR. Using our measurements, we have calculated the Fe XVIII and Fe XIX Dn=0 DR DR rate coefficients. Significant discrepancies exist between our inferred rates and those of published calculations. These calculations overestimate the DR rates by factors of ~2 or underestimate it by factors of ~2 to orders of magnitude, but none are in good agreement with our results. Almost all published DR rates for modeling cosmic plasmas are computed using the same theoretical techniques as the above-mentioned calculations. Hence, our measurements call into question all theoretical Dn=0 DR rates used for ionization balance calculations of cosmic plasmas. At temperatures where the Fe XVIII and Fe XIX fractional abundances are predicted to peak in photoionized gases of cosmic abundances, the theoretical rates underestimate the Fe XVIII DR rate by a factor of ~2 and overestimate the Fe XIX DR rate by a factor of ~1.6. We have carried out new multiconfiguration Dirac-Fock and multiconfiguration Breit-Pauli calculations which agree with our measured resonance strengths and rate coefficients to within typically better than <~30%. We provide a fit to our inferred rate coefficients for use in plasma modeling. Using our DR measurements, we infer a factor of ~2 error in the Fe XX through Fe XXIV Dn=0 DR rates. We investigate the effects of this estimated error for the well-known thermal instability of photoionized gas. We find that errors in these rates cannot remove the instability, but they do dramatically affect the range in parameter space over which it forms.Comment: To appear in ApJS, 44 pages with 13 figures, AASTeX with postsript figure

Tests of relativity using a microwave resonator

The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are compared to set new constraints on a possible violation of Lorentz invariance. We determine the variation of the oscillator frequency as a function of its orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike test) with respect to a preferred frame candidate. We constrain the corresponding parameters of the Mansouri and Sexl test theory to $\delta - \beta + 1/2 = (1.5\pm 4.2) \times 10^{-9}$ and $\beta - \alpha - 1 = (-3.1\pm 6.9) \times 10^{-7}$ which is equivalent to the best previous result for the former and represents a 30 fold improvement for the latter.Comment: 8 pages, 2 figures, submitted to Physical Review Letters (October 3, 2002

Spectroscopy and dissociative recombination of the lowest rotational states of H3+

The dissociative recombination of the lowest rotational states of H3+ has been investigated at the storage ring TSR using a cryogenic 22-pole radiofrequency ion trap as injector. The H3+ was cooled with buffer gas at ~15 K to the lowest rotational levels, (J,G)=(1,0) and (1,1), which belong to the ortho and para proton-spin symmetry, respectively. The rate coefficients and dissociation dynamics of H3+(J,G) populations produced with normal- and para-H2 were measured and compared to the rate and dynamics of a hot H3+ beam from a Penning source. The production of cold H3+ rotational populations was separately studied by rovibrational laser spectroscopy using chemical probing with argon around 55 K. First results indicate a ~20% relative increase of the para contribution when using para-H2 as parent gas. The H3+ rate coefficient observed for the para-H2 source gas, however, is quite similar to the H3+ rate for the normal-H2 source gas. The recombination dynamics confirm that for both source gases, only small populations of rotationally excited levels are present. The distribution of 3-body fragmentation geometries displays a broad part of various triangular shapes with an enhancement of ~12% for events with symmetric near-linear configurations. No large dependences on internal state or collision energy are found.Comment: 10 pages, 9 figures, to be published in Journal of Physics: Conference Proceeding

Dielectronic Recombination of Ground-State and Metastable Li+ Ions

Dielectronic recombination has been investigated for Delta-n = 1 resonances of ground-state Li+(1s^2) and for Delta-n = 0 resonances of metastable Li+(1s2s ^3S). The ground-state spectrum shows three prominent transitions between 53 and 64 eV, while the metastable spectrum exhibits many transitions with energies < 3.2 eV. Reasonably good agreement of R-matrix, LS coupling calculations with the measured recombination rate coefficient is obtained. The time dependence of the recombination rate yields a radiative lifetime of 52.2 +- 5.0 s for the 2 ^3S level of Li+.Comment: Submitted to Phys. Rev. A; REVTeX, 4 pages, 3 figure