Low-lying isovector monopole resonances

The mass difference between the even-even isobaric nuclei having the valence nucleons on the same degenerate level is attributed to a Josephson-type interaction between pairs of protons and pairs of neutrons. This interaction can be understood as an isospin symmetry-breaking mean field for a four-particle interaction separable in the two particles-two holes channel. The strength of this mean field is estimated within an o(5) algebraic model, by using the experimental value of the inertial parameter for the collective isorotation induced by the breaking of the isospin symmetry. In superfluid nuclei, the presumed interaction between the proton and neutron condensates leads to coupled oscillations of the BCS gauge angles, which should appear in the excitation spectrum as low-lying isovector monopole resonances.Comment: 16 pages/LaTex + 1 PostScript figure; related to cond-mat/9904242, math-ph/000500

New results for the missing quantum numbers labeling the quadrupole and octupole boson basis

The many $2^k$-pole boson states, $|N_kv_k\alpha_k I_kM_k>$ with $k=2,3$, realize the irreducible representation (IR) for the group reduction chains $SU(2k+1)\supset R_{2k+1}\supset R_3\supset R_2$. They have been analytically studied and widely used for the description of nuclear systems. However, no analytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$'s IR, determined by the reduction $R_{2k+1}\supset R_3$, is available. Thus, the number of distinct values taken by $\alpha_k$ has been so far obtained by solving some complex equations. Here we derive analytical expressions for the degeneracy $d_v(I)$ characterizing the octupole and quadrupole boson states, respectively. The merit of this work consists of the fact that it completes the analytical expressions for the $2^k$-pole boson basis.Comment: 10page

X-ray absorption spectroscopy systematics at the tungsten L-edge

A series of mononuclear six-coordinate tungsten compounds spanning formal oxidation states from 0 to +VI, largely in a ligand environment of inert chloride and/or phosphine, has been interrogated by tungsten L-edge X-ray absorption spectroscopy. The L-edge spectra of this compound set, comprised of [W<sup>0</sup>(PMe<sub>3</sub>)<sub>6</sub>], [W<sup>II</sup>Cl<sub>2</sub>(PMePh<sub>2</sub>)<sub>4</sub>], [W<sup>III</sup>Cl<sub>2</sub>(dppe)<sub>2</sub>][PF<sub>6</sub>] (dppe = 1,2-bis(diphenylphosphino)ethane), [W<sup>IV</sup>Cl<sub>4</sub>(PMePh<sub>2</sub>)<sub>2</sub>], [W<sup>V</sup>(NPh)Cl<sub>3</sub>(PMe<sub>3</sub>)<sub>2</sub>], and [W<sup>VI</sup>Cl<sub>6</sub>] correlate with formal oxidation state and have usefulness as references for the interpretation of the L-edge spectra of tungsten compounds with redox-active ligands and ambiguous electronic structure descriptions. The utility of these spectra arises from the combined correlation of the estimated branching ratio (EBR) of the L<sub>3,2</sub>-edges and the L<sub>1</sub> rising-edge energy with metal Z<sub>eff</sub>, thereby permitting an assessment of effective metal oxidation state. An application of these reference spectra is illustrated by their use as backdrop for the L-edge X-ray absorption spectra of [W<sup>IV</sup>(mdt)<sub>2</sub>(CO)<sub>2</sub>] and [W<sup>IV</sup>(mdt)<sub>2</sub>(CN)<sub>2</sub>]<sup>2–</sup> (mdt<sup>2–</sup> = 1,2-dimethylethene-1,2-dithiolate), which shows that both compounds are effectively W<sup>IV</sup> species. Use of metal L-edge XAS to assess a compound of uncertain formulation requires: 1) Placement of that data within the context of spectra offered by unambiguous calibrant compounds, preferably with the same coordination number and similar metal ligand distances. Such spectra assist in defining upper and/or lower limits for metal Z<sub>eff</sub> in the species of interest; 2) Evaluation of that data in conjunction with information from other physical methods, especially ligand K-edge XAS; 3) Increased care in interpretation if strong π-acceptor ligands, particularly CO, or π-donor ligands are present. The electron-withdrawing/donating nature of these ligand types, combined with relatively short metal-ligand distances, exaggerate the difference between formal oxidation state and metal Z<sub>eff</sub> or, as in the case of [W<sup>IV</sup>(mdt)<sub>2</sub>(CO)<sub>2</sub>], add other subtlety by modulating the redox level of other ligands in the coordination sphere