X-ray absorption spectra at the Ca-L2,3_{2,3}-edge calculated within multi-channel multiple scattering theory

We report a new theoretical method for X-ray absorption spectroscopy (XAS) in condensed matter which is based on the multi-channel multiple scattering theory of Natoli et al. and the eigen-channel R-matrix method. While the highly flexible real-space multiple scattering (RSMS) method guarantees a precise description of the single-electron part of the problem, multiplet-like electron correlation effects between the photo-electron and localized electrons can be taken account for in a configuration interaction scheme. For the case where correlation effects are limited to the absorber atom, a technique for the solution of the equations is devised, which requires only little more computation time than the normal RSMS method for XAS. The new method is described and an application to XAS at the Ca $L_{2,3}$-edge in bulk Ca, CaO and CaF$_2$ is presented.Comment: 10 pages, 4 figures, submitted to Phys. Rev.

Long-range interactions between an atom in its ground S state and an open-shell linear molecule

Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a non-zero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nonadiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown that for the interactions of molecules in excited states that are connected to the ground state by multipolar transition moments additional terms in the long-range induction energy appear. All these theoretical developments are illustrated with the numerical results for systems of interest for the sympathetic cooling experiments: interactions of the ground state Rb($^2$S) atom with CO($^3\Pi$), OH($^2\Pi$), NH($^1\Delta$), and CH($^2\Pi$) and of the ground state Li($^2$S) atom with CH($^2\Pi$).Comment: 30 pages, 3 figure

Effective Hamiltonian for transition-metal compounds. Application to Na_xCoO_2

We describe a simple scheme to construct a low-energy effective Hamiltonian H_eff for highly correlated systems containing non-metals like O, P or As (O in what follows) and a transition-metal (M) as the active part in the electronic structure, eliminating the O degrees of freedom from a starting Hamiltonian that contains all M d orbitals and all non-metal p orbitals. We calculate all interaction terms between d electrons originating from Coulomb repulsion, as a function of three parameters (F_0, F_2 and F_4) and write them in a basis of orbitals appropriate for cubic, tetragonal, tetrahedral or hexagonal symmetry around M. The approach is based on solving exactly (numerically if necessary) a MO_n cluster containing the transition-metal atom and its n nearest O atoms (for example a CoO_6 cluster in the case of the cobaltates, or a CuO_n cluster in the case of the cuprates, in which n depends on the number of apical O atoms), and mapping them into many-body states of the same symmetry containing d holes only. We illustrate the procedure for the case of Na_xCoO_2. The resulting H_eff, including a trigonal distortion D, has been studied recently and its electronic structure agrees well with angle-resolved photoemission spectra [A. Bourgeois, A. A. Aligia, and M. J. Rozenberg, Phys. Rev. Lett. 102, 066402 (2009)]. Although H_eff contains only 3d t_2g holes, the highly correlated states that they represent contain an important amount not only of O 2p holes but also of 3d e_g holes. When more holes are added, a significant redistribution of charge takes place. As a consequence of these facts, the resulting values of the effective interactions between t_2g states are smaller than previously assumed, rendering more important the effect of D in obtaining only one sheet around the center of the Brillouin zone for the Fermi surface (without additional pockets).Comment: 11 pages, 1 figure, accepted for publication in Phys.Rev.

Symmetries and collective excitations in large superconducting circuits

The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into larger networks. It is an open question to what degree modularity also holds for quantum circuits -- circuits made of superconducting material, in which electric voltages and currents are governed by the laws of quantum physics. If realizable, quantum coherence in larger circuit networks has great potential for advances in quantum information processing including topological protection from decoherence. Here, we present theory suitable for quantitative modeling of such large circuits and discuss its application to the fluxonium device. Our approach makes use of approximate symmetries exhibited by the circuit, and enables us to obtain new predictions for the energy spectrum of the fluxonium device which can be tested with current experimental technology

The higher order C_n dispersion coefficients for the alkali atoms

The van der Waals coefficients, from C_11 through to C_16 resulting from 2nd, 3rd and 4th order perturbation theory are estimated for the alkali (Li, Na, K and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali atoms and hydrogen. The parameters are determined from sum-rules after diagonalizing the fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the C_n/r^n potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to C_10/r^10 results in a dispersion interaction that is accurate to better than 1 percent whenever the inter-nuclear spacing is larger than 20 a_0. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive (C_11, C_13, C_15) and attractive (C_12, C_14, C_16) dispersion forces.Comment: 8 pages, 7 figure

SU(3) Clebsch-Gordan Coefficients for Baryon-Meson Coupling at Arbitrary N_c

We present explicit formulae for the SU(3) Clebsch-Gordan coefficients that are relevant for the couplings of large N_c baryons to mesons. In particular, we compute the Clebsch-Gordan series for the coupling of the octet (associated with mesons, and remains the correct representation at large N_c) to the large N_c analogs of the baryon octet and decuplet representations.Comment: 8 pages, no figures, ReVTe

The Development of High Voltage for the Production of Neutrons and Artificial Radioactivity

Author Institution: Associate Director, Westinghouse Research Laboratories, East Pittsburgh, Pa

Coulomb correlation in presence of spin-orbit coupling: application to plutonium

Attempts to go beyond the local density approximation (LDA) of Density Functional Theory (DFT) have been increasingly based on the incorporation of more realistic Coulomb interactions. In their earliest implementations, methods like LDA+$U$, LDA + DMFT (Dynamical Mean Field Theory), and LDA+Gutzwiller used a simple model interaction $U$. In this article we generalize the solution of the full Coulomb matrix involving $F^{(0)}$ to $F^{(6)}$ parameters, which is usually presented in terms of an $\ell m_\ell$ basis, into a $jm_{j}$ basis of the total angular momentum, where we also include spin-orbit coupling; this type of theory is needed for a reliable description of $f$-state elements like plutonium, which we use as an example of our theory. Close attention will be paid to spin-flip terms, which are important in multiplet theory but that have been usually neglected in these kinds of studies. We find that, in a density-density approximation, the $jm_j$ basis results provide a very good approximation to the full Coulomb matrix result, in contrast to the much less accurate results for the more conventional $\ell m_\ell$ basis

Dynamics of Electrons in Graded Semiconductors

I present a theory of electron dynamics in semiconductors with slowly varying composition. I show that the frequency-dependent conductivity, required for the description of transport and optical properties, can be obtained from a knowledge of the band structures and momentum matrix elements of homogeneous semiconductor alloys. New sum rules for the electronic oscillator strengths, which apply within a given energy band or between any two bands, are derived, and a general expression for the width of the intraband absorption peak is given. Finally, the low-frequency dynamics is discussed, and a correspondence with the semiclassical motion is established.Comment: 4 pages, Revte

Alternative Mathematical Technique to Determine LS Spectral Terms

We presented an alternative computational method for determining the permitted LS spectral terms arising from $l^N$ electronic configurations. This method makes the direct calculation of LS terms possible. Using only basic algebra, we derived our theory from LS-coupling scheme and Pauli exclusion principle. As an application, we have performed the most complete set of calculations to date of the spectral terms arising from $l^N$ electronic configurations, and the representative results were shown. As another application on deducing LS-coupling rules, for two equivalent electrons, we deduced the famous Even Rule; for three equivalent electrons, we derived a new simple rule.Comment: Submitted to Phys. Rev.