65,822 research outputs found

    Core-valence correlations for atoms with open shells

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    We present an efficient method of inclusion of the core-valence correlations into the configuration interaction (CI) calculations. These correlations take place in the core area where the potential of external electrons is approximately constant. A constant potential does not change the core electron wave functions and Green's functions. Therefore, all operators describing interaction of MM valence electrons and NMN-M core electrons (the core part of the Hartree-Fock Hamiltonian VNMV^{N-M}, the correlation potential Σ^1(r,r,E)\hat\Sigma_1({\bf r},{\bf r'},E) and the screening of interaction between valence electrons by the core electrons Σ^2\hat\Sigma_2) may be calculated with all MM valence electrons removed. This allows one to avoid subtraction diagrams which make accurate inclusion of the core-valence correlations for M>2M>2 prohibitively complicated. Then the CI Hamiltonian for MM valence electrons is calculated using orbitals in complete VNV^{N} potential (the mean field produced by all electrons); Σ^1\hat\Sigma_1 + Σ^2\hat\Sigma_2 are added to the CI Hamiltonian to account for the core-valence correlations. We calculate Σ^1\hat\Sigma_1 and Σ^2\hat\Sigma_2 using many-body perturbation theory in which dominating classes of diagrams are included in all orders. We use neutral Xe I and all positive ions up to Xe VIII as a testing ground. We found that the core electron density for all these systems is practically the same. Therefore, we use the same Σ^1\hat\Sigma_1 and Σ^2\hat\Sigma_2 to build the CI Hamiltonian in all these systems (M=1,2,3,4,5,6,7,8M=1,2,3,4,5,6,7,8). Good agreement with experiment for energy levels and Land\'{e} factors is demonstrated for all cases from Xe I to Xe VIII.Comment: 13 pages, 5 figure

    Electron-impact excitation of X 1Sigma<sub>g</sub><sup>+</sup>(v[double-prime]=0) to the a[double-prime] 1Sigma<sub>g</sub><sup>+</sup>, b 1Piu, c3 1Piu, o3 1Piu, b[prime] 1Sigma<sub>u</sub><sup>+</sup>, c<sub>4</sub><sup>[prime]</sup> 1Sigma<sub>u</sub><sup>+</sup>, G 3Piu, and F 3Piu states of molecular nitrogen

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    Measurements of differential cross sections (DCSs) for electron-impact excitation of the a[double-prime] 1Sigmag+, b 1Piu, c3 1Piu, o3 1Piu, b[prime] 1Sigmau+, c4[prime] 1Sigmau+, G 3Piu, and F 3Piu states in N2 from the X 1Sigmag+(v[double-prime]=0) ground level are presented. The DCSs were obtained from energy-loss spectra in the region of 12 to 13.82 eV measured at incident energies of 17.5, 20, 30, 50, and 100 eV and for scattering angles ranging from 2° to 130°. The analysis of the spectra follows a different algorithm from that employed in a previous study of N2 for the valence states [Khakoo et al. Phys. Rev. A 71, 062703 (2005)], since the 1Piu and 1Sigmau+ states form strongly interacting Rydberg-valence series. The results are compared with existing data

    Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium

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    Experiments with acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. Comparison of the determined dispersion relations for guided surface acoustic modes with a theoretical model reveals the dependencies of the elastic moduli of the granular medium on pressure. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing through non-affine motion leads to a peculiar scaling of shear rigidity with pressure near the jamming transition corresponding to zero pressure. Unexpectedly, and in disagreement with the most of the available theories, the bulk modulus depends on pressure in a very similar way to the shear modulus

    Analytic results for NN particles with 1/r21/r^2 interaction in two dimensions and an external magnetic field

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    The 2N2N-dimensional quantum problem of NN particles (e.g. electrons) with interaction β/r2\beta/r^2 in a two-dimensional parabolic potential ω0\omega_0 (e.g. quantum dot) and magnetic field BB, reduces exactly to solving a (2N4)(2N-4)-dimensional problem which is independent of BB and ω0\omega_0. An exact, infinite set of relative mode excitations are obtained for any NN. The N=3N=3 problem reduces to that of a ficticious particle in a two-dimensional, non-linear potential of strength β\beta, subject to a ficticious magnetic field BficJB_{\rm fic}\propto J, the relative angular momentum.Comment: To appear in Physical Review Letters (in press). RevTeX file. Two figures available from [email protected] or [email protected]

    Rabi oscillations of a qubit coupled to a two-level system

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    The problem of Rabi oscillations in a qubit coupled to a fluctuator and in contact with a heath bath is considered. A scheme is developed for taking into account both phase and energy relaxation in a phenomenological way, while taking full account of the quantum dynamics of the four-level system subject to a driving AC field. Significant suppression of the Rabi oscillations is found when the qubit and fluctuator are close to resonance. The effect of the fluctuator state on the read-out signal is discussed. This effect is shown to modify the observed signal significantly. This may be relevant to recent experiments by Simmonds et al. [Phys. Rev. Lett. 93, 077003 (2004)].Comment: 4 pages, 4 figure

    Sampling bias in systems with structural heterogeneity and limited internal diffusion

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    Complex systems research is becomingly increasingly data-driven, particularly in the social and biological domains. Many of the systems from which sample data are collected feature structural heterogeneity at the mesoscopic scale (i.e. communities) and limited inter-community diffusion. Here we show that the interplay between these two features can yield a significant bias in the global characteristics inferred from the data. We present a general framework to quantify this bias, and derive an explicit corrective factor for a wide class of systems. Applying our analysis to a recent high-profile survey of conflict mortality in Iraq suggests a significant overestimate of deaths
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