Core-valence correlations for atoms with open shells

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 $M$ valence electrons and $N-M$ core electrons (the core part of the Hartree-Fock Hamiltonian $V^{N-M}$, the correlation potential $\hat\Sigma_1({\bf r},{\bf r'},E)$ and the screening of interaction between valence electrons by the core electrons $\hat\Sigma_2$) may be calculated with all $M$ valence electrons removed. This allows one to avoid subtraction diagrams which make accurate inclusion of the core-valence correlations for $M>2$ prohibitively complicated. Then the CI Hamiltonian for $M$ valence electrons is calculated using orbitals in complete $V^{N}$ potential (the mean field produced by all electrons); $\hat\Sigma_1$ + $\hat\Sigma_2$ are added to the CI Hamiltonian to account for the core-valence correlations. We calculate $\hat\Sigma_1$ and $\hat\Sigma_2$ 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 $\hat\Sigma_1$ and $\hat\Sigma_2$ to build the CI Hamiltonian in all these systems ($M=1,2,3,4,5,6,7,8$). 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

Interelectronic-interaction effect on the transition probability in high-Z He-like ions

The interelectronic-interaction effect on the transition probabilities in high-Z He-like ions is investigated within a systematic quantum electrodynamic approach. The calculation formulas for the interelectronic-interaction corrections of first order in 1/Z are derived using the two-time Green function method. These formulas are employed for numerical evaluations of the magnetic transition probabilities in heliumlike ions. The results of the calculations are compared with experimental values and previous calculations

Electron-impact excitation of X 1Sigma_g⁺(v[double-prime]=0) to the a[double-prime] 1Sigma_g⁺, b 1Piu, c3 1Piu, o3 1Piu, b[prime] 1Sigma_u⁺, c₄^[prime] 1Sigma_u⁺, G 3Piu, and F 3Piu states of molecular nitrogen

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

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

String Theory and Water Waves

We uncover a remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain {hat c}<1 string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We observe that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context.Comment: 49 pages, 4 figure

Electron spin resonance investigation of Mn^{2+} ions and their dynamics in manganese doped SrTiO_3

Using electron spin resonance, lattice position and dynamic properties of Mn2+ ions were studied in 0.5 and 2 % manganese doped SrTiO3 ceramics prepared by conventional mixed oxide method. The measurements showed that Mn2+ ions substitute preferably up to 97 % for Sr if the ceramics is prepared with a deficit of Sr ions. Motional narrowing of the Mn2+ ESR spectrum was observed when temperature increases from 120 K to 240-250 K that was explained as a manifestation of off-center position of this ion at the Sr site. From the analysis of the ESR spectra the activation energy Ea = 86 mV and frequency factor 1/?0 ? (2-10)x10^(-14) 1/s for jumping of the impurity between symmetrical off-center positions were determined. Both values are in agreement with those derived previously from dielectric relaxation. This proves the origin of dielectric anomalies in SrTiO3:Mn as those produced by the reorientation dynamics of Mn2+ dipoles.Comment: 16 pages, 6 figure