A-Nd2O3 is a layer structure built on the (NdO)n+n cation. Data for the 4.2 K optical spectrum and the strongly anisotropic parallel and perpendicular paramagnetic susceptibilities between 4 and 1000 K measured on single crystals, are reproduced using a Hamiltonian, that involves 12 free atom parameters (three Racah’s parameters, the spin–orbit coupling constant, Trees’ parameters α and β, and Judd’s six Tk operators) and six C3v crystal field parameters. The Hamiltonian operates on the 364 kets in 4f3, that is including J mixing. 88 Stark levels (from 0 to 34 000 cm−1) were fitted to a mean square deviation of 17 cm−1. The crystal field parameters (Wybourne’s formalism) are B20=−836 cm−1, B40=634 cm−1, B43=−1606 cm−1, B60=752 cm−1, B63=237 cm−1, B66=672 cm−1. The spectrum is strongly displaced to the red with respect to Nd3+ in LaCl3 and this is due to a lowering of Slater’s integrals F2 and F4 by 2% to 3%. The F6 integral is unchanged. The spin–orbit coupling constant is also lowered by 2%. The interaction parameters are slightly affected.
We test whether or not the orbital poles of the systems in the solar neighbourhood are isotropically distributed on the celestial sphere. The problem is plagued by the ambiguity on the position of the ascending node. Of the 95 systems closer than 18 pc from the Sun with an orbit in the 6th Catalogue of Orbits of Visual Binaries, the pole ambiguity could be resolved for 51 systems using radial velocity collected in the literature and CORAVEL database or acquired with the HERMES/Mercator spectrograph. For several systems, we can correct the erroneous nodes in the 6th Catalogue of Orbits and obtain new combined spectroscopic/astrometric orbits for seven systems [WDS 01083+5455Aa,Ab; 01418+4237AB; 02278+0426AB (SB2); 09006+4147AB (SB2); 16413+3136AB; 17121+4540AB; 18070+3034AB]. We used of spherical statistics to test for possible anisotropy. After ordering the binary systems by increasing distance from the Sun, we computed the false-alarm probability for subsamples of increasing sizes, from N = 1 up to the full sample of 51 systems. Rayleigh-Watson and Beran tests deliver a false-alarm probability of 0.5% for the 20 systems closer than 8.1 pc. To evaluate the robustness of this conclusion, we used a jackknife approach, for which we repeated this procedure after removing one system at a time from the full sample. The false-alarm probability was then found to vary between 1.5% and 0.1%, depending on which system is removed. The reality of the deviation from isotropy can thus not be assessed with certainty at this stage, because only so few systems are available, despite our efforts to increase the sample. However, when considering the full sample of 51 systems, the concentration of poles toward the Galactic position l = 46.0• , b = 37• , as observed in the 8.1 pc sphere, totally vanishes (the Rayleigh-Watson false-alarm probability then rises to 18%).
In many instances, the deduction of spectroscopic parameters from electron paramagnetic resonance spectra depends on spectrum simulation and parameter optimization. We have developed two software packages based on the approximate formulae of Iwasaki for the calculation of line positions and on the Levenberg-Marquardt algorithm for nonlinear least-squares optimization. Our software applies to systems having an anisotropicg-tensor and an arbitrary number of hyperfine interactions with nuclei. They are written in the FORTRAN 77 programming language. At present, neither the nuclear quadrupolar interaction nor the nuclear Zeeman interaction terms are handled. The programs CRISAJU and EPRPOWDERFIT apply to the cases of single crystals and powders, respectively. For use in the latter, thanks to the software ODYSSEE which implements automatic differentiation of algorithms, an ancillary subroutine, which contributes to the performance of the optimization, was created automatically
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