Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms

Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schr\"odinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wavefunctions, and use of Slater-type orbitals (STO's). The required Coulomb integrals for STO's are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular we reproduce the anomalous magnetic moment and orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.Comment: 14 pages, 1 figur

Exchange-assisted tunneling in the classical limit

The exchange interaction and correlations may produce a power-law decay instead of the usual exponential decrease of the wave function under potential barrier. The exchange-assisted tunneling vanishes in the classical limit, however, the dependence on the Planck constant h is different from that for a conventional single-particle tunneling

Magnetism in purple bronze Li0.9_{0.9}Mo6_6O17_{17}

Muon spin relaxation measurements around the 25 K metal-insulator transition in Li$_{0.9}$Mo$_6$O$_{17}$ elucidate a profound role of disorder as a possible mechanism for this transition. The relaxation rate $1/T_1$ and the muon Knight shift are incompatible with the transition to a SDW state and thus exclude it.Comment: pages 2, fig 2, The conf. on strongly correlated electron systems, SCES 2004, German

Implementation of screened hybrid functionals based on the Yukawa potential within the LAPW basis set

The implementation of screened hybrid functionals into the WIEN2k code, which is based on the LAPW basis set, is reported. The Hartree-Fock exchange energy and potential are screened by means of the Yukawa potential as proposed by Bylander and Kleinman [Phys. Rev. B 41, 7868 (1990)] for the calculation of the electronic structure of solids with the screened-exchange local density approximation. Details of the formalism, which is based on the method of Massidda, Posternak, and Baldereschi [Phys. Rev. B 48, 5058 (1993)] for the unscreened Hartree-Fock exchange are given. The results for the transition-energy and structural properties of several test cases are presented. Results of calculations of the Cu electric-field gradient in Cu2O are also presented, and it is shown that the hybrid functionals are much more accurate than the standard local-density or generalized gradient approximations

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

Anisotropic fragmentation in low-energy dissociative recombination

On a dense energy grid reaching up to 75 meV electron collision energy the fragmentation angle and the kinetic energy release of neutral dissociative recombination fragments have been studied in a twin merged beam experiment. The anisotropy described by Legendre polynomials and the extracted rotational state contributions were found to vary on a likewise narrow energy scale as the rotationally averaged rate coefficient. For the first time angular dependences higher than 2$^{nd}$ order could be deduced. Moreover, a slight anisotropy at zero collision energy was observed which is caused by the flattened velocity distribution of the electron beam.Comment: 8 pages, 4 figures; The Article will be published in the proceedings of DR 2007, a symposium on Dissociative Recombination held in Ameland, The Netherlands (18.-23. July 2008); Reference 19 has been published meanwhile in S. Novotny, PRL 100, 193201 (2008

Positronic lithium, an electronically stable Li-e+^+ ground state

Calculations of the positron-Li system were performed using the Stochastic Variational Method and yielded a minimum energy of -7.53208 Hartree for the L=0 ground state. Unlike previous calculations of this system, the system was found to be stable against dissociation into the Ps + Li$^+$ channel with a binding energy of 0.00217 Hartree and is therefore electronically stable. This is the first instance of a rigorous calculation predicting that it is possible to combine a positron with a neutral atom and form an electronically stable bound state.Comment: 11 pages, 2 tables. To be published in Phys.Rev.Let

On the secondly quantized theory of many-electron atom

Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial integrals appearing in the expressions of matrix elements of arbitrary physical operators of atomic quantities has two main disadvantages: (i) The numerical codes for the calculation of spin-angular coefficients are usually very time-consuming; (ii) f-shells are often omitted from programs for matrix element calculation since the tables for their coefficients of fractional parentage are very extensive. The authors suppose that a series of difficulties persisting in the traditional approach to the calculation of spin-angular parts of matrix elements could be avoided by using this secondly quantized methodology, based on angular momentum theory, on the concept of the irreducible tensorial sets, on a generalized graphical method, on quasispin and on the reduced coefficients of fractional parentage