4p States and X-Ray Spectroscopy

Abstract

Novel integrable systems of coupled first-order autonomous PDEs in 1 + 1 dimensions (space x and time t) are presented. Integrable covariant 2-vector and 3-vector PDEs, as well as higher-order integrable PDEs for a single, or a couple, of scalar-dependent variables (including an extension of the sine-Gordon equation and a remarkably neat, highly nonlinear third-order PDE), are also obtained by appropriate reductions of the basic matrix equations. The Lax pairs that characterize the integrable character of the basic matrix PDEs are also exhibited, as well as their single-soliton solutions. These solitons generally exhibit the boomeronic (and, less generically, the trapponic) phenomenology, namely they do not move uniformly, but rather (in an appropriate reference system) come in from one end in the remote past and boomerang back to that same end in the remote future (boomerons), or are trapped to oscillate around a value fixed by the initial data (trappons).

Electric quadrupole contribution to resonant x-ray scattering: Application to multipole ordering phases inCe1−xLaxB6

“…Actually, for most of transition-metal compounds, both experimental studies and theoretical studies based on electronic structure calculations have revealed that the RXS intensities are brought about by the hybridization between the 4p band and the 2p band of the neighboring anions rather than the direct Coulomb interaction between the electron in the 4p band and electrons in the 3d band. 3,4 This result is reasonable because of the extended nature of the 4p state.…”

“…We have demonstrated the usefulness of the derived formula by calculating the E2 RXS spectra in Ce 1−x La x B 6 . Phase II is believed to be an AFQ order of O xy type, and our formula dictates that the energy dependence is given by a combination of α (2) E2 (ω) and α (4) E2 (ω). We have obtained the RXS intensity in the same order of intensity as obtained by assuming the AFO order.…”

Relativistic configuration interaction calculations on the Kα x-ray spectra of sulfur

“…It is well known that the radiative decay of atoms ionized to different degrees in the inner and outer shells gives rise to a complex x-ray spectrum consisting of a large number of closely spaced fine structure lines and the complexities of the x-ray spectrum depend on the initial multiple vacancy states and also on the numerous possible transitions. The studies for atomic x-ray spectra [1,2] as well as molecular x-ray spectra [3][4][5] have attracted much interest in recent years. Spin-forbidden electric dipole transitions are of great importance as diagnostics for different astrophysical sources, laboratory-induced fusion plasmas and also in the study of atomic collisions [6].…”