Radiative rates for E1, E2, M1, and M2 transitions in the Br-like ions Sr IV, Y V, Zr VI, Nb VII, and Mo VIII

Energies and lifetimes are reported for the lowest 375 levels of five Br-like ions, namely Sr~IV, Y~V, Zr~VI, Nb~VII, and Mo~VIII, mostly belonging to the 4s$^2$4p$^5$, 4s$^2$4p$^4$4$\ell$, 4s4p$^6$, 4s$^2$4p$^4$5$\ell$, 4s$^2$4p$^3$4d$^2$, 4s4p$^5$4$\ell$, and 4s4p$^5$5$\ell$ configurations. Extensive configuration interaction has been included and the general-purpose relativistic atomic structure package ({\sc grasp}) has been adopted for the calculations. Additionally, radiative rates are listed among these levels for all E1, E2, M1, and M2 transitions. From a comparison with the measurements, the majority of our energy levels are assessed to be accurate to better than 2\%, although discrepancies between theory and experiment for a few are up to 6\%. An accuracy assessment of the calculated radiative rates (and lifetimes) is more difficult, because no prior results exist for these ions.Comment: 112 pages including 10 Tables, will appear in ADND

Orbital Ordering and Resonant X-ray Scattering in Layered Manganites

In layered manganites with orbital and charge orderings, the degeneracy of the Mn $4p$ orbitals as well as the $3d$ ones is lifted by the effects of the $4p$ bands and the local Coulomb interactions. We formulate the atomic scattering factor for the resonant x-ray scattering in the memory function method by taking into account these effects on an equal footing. It is shown that the polarization dependences of the scattering intensities at the orbital and charge superlattice reflections observed in LaSr$_{2}$Mn$_2$O$_7$ are caused by the local and itinerant characters of $4p$ electrons, respectively. We examine the type of the orbital ordered state.Comment: 4 pages, 3 figure

Resonant X-Ray Magnetic Scattering from CoO

We analyze the recent experiment [W. Neubeck {\em et al.}, Phys. Rev. B \vol(60,1999,R9912)] for the resonant x-ray magnetic scattering (RXMS) around the K edge of Co in the antiferromagnet CoO. We propose a mechanism of the RXMS to make the $4p$ states couple to the magnetic order: the intraatomic exchange interaction between the $4p$ and the $3d$ states and the $p$-$d$ mixing to the $3d$ states of neighboring Co atoms. These couplings induce the orbital moment in the $4p$ states and make the scattering tensor antisymmetric. Using a cluster model, we demonstrate that this modification gives rise to a large RXMS intensity in the dipole process, in good agreement with the experiment. We also find that the pre-edge peak is generated by the transition to the $3d$ states in the quadrupole process, with negligible contribution of the dipole process. We also discuss the azimuthal angle dependence of the intensity.Comment: 15 pages, 8 figure

Photodetachment study of He^- quartet resonances below the He(n=3) thresholds

The photodetachment cross section of He^- has been measured in the photon energy range 2.9 eV to 3.3 eV in order to investigate doubly excited states. Measurements were made channel specific by selectively detecting the residual He atoms left in a particular excited state following detachment. Three Feshbach resonances were found in the He(1s2p ^3P)+e^-(epsilon p) partial cross section: a ^4S resonance below the He(1s3s ^3S) threshold and two ^4P resonances below the He(1s3p ^3P) threshold. The measured energies of these doubly excited states are 2.959260(6) eV, 3.072(7) eV and 3.26487(4) eV. The corresponding widths are found to be 0.20(2) meV, 50(5) meV and 0.61(5) meV. The measured energies agree well with recent theoretical predictions for the 1s3s4s ^4S, 1s3p^2 ^4P and 1s3p4p ^4P states, respectively, but the widths deviate noticeably from calculations for 1s3p^2 ^4P and 1s3p4p ^4P states.Comment: 10 pages, 3 figures, LaTeX2e scrartcl, amsmath. Accepted by Journal of Physics B; minor changes after referee repor

4p states and X-Ray Spectroscopy

The 4p states in transition metals and their compounds usually play minor roles on their physical quantities. Recent development of resonant x-ray scattering (RXS) at the K-edge of transition metals, however, casts light on the 4p states, because the signals on orbital and magnetic superlattice spots are brought about by the modulation in the 4p states. The 4p states are extending in solids and thereby sensitive to electronic states at neighboring sites. This characteristic determines the mechanism of RXS that the intensity on the orbital superlattice spots are mainly generated by the lattice distortion and those on magnetic superlattice spots by the coupling of the 4p states with the orbital polarization in the 3d states at neighboring sites. Taking up typical examples for orbital and magnetic RXS, we demonstrate these mechanisms on the basis of the band structure calculation. Finally, we study the MCD spectra at the K-edge, demonstrating that the same mechanism as the magnetic RXS is working.Comment: 9 pages, 9 figures, submitted to Physica Scripta (comment

Loewy lengths of centers of blocks II

Let ZB be the center of a p-block B of a finite group with defect group D. We show that the Loewy length LL(ZB) of ZB is bounded by $\frac{|D|}{p}+p-1$ provided D is not cyclic. If D is non-abelian, we prove the stronger bound $LL(ZB)<\min\{p^{d-1},4p^{d-2}\}$ where $|D|=p^d$. Conversely, we classify the blocks B with $LL(ZB)\ge\min\{p^{d-1},4p^{d-2}\}$. This extends some results previously obtained by the present authors. Moreover, we characterize blocks with uniserial center.Comment: 9 pages, this paper incorporates arXiv:1611.0605

Theory of Anomalous X-ray Scattering in Orbital Ordered Manganites

We study theoretically the anomalous X-ray scattering as a new probe to observe the orbital orderings and excitations in perovskite manganites. The scattering matrix is given by the virtual electronic excitations from Mn $1s$ level to unoccupied Mn $4p$ level. We find that orbital dependence of the Coulomb interaction between Mn $3d$ and Mn $4p$ electrons is essential to bring about the anisotropy of the scattering factor near the K edge. The calculated results in $MnO_6$ clusters explain the forbidden reflections observed in $La_{0.5}Sr_{1.5}MnO_4$ and $LaMnO_3$. A possibility of the observation of the orbital waves by the X-ray scattering is discussed.Comment: 4 pages, 2 figure