Is [ReCl4(CN)2]2− a good Building Block for Single Molecule Magnets? A Theoretical Investigation.

Building blocks containing $5d$ spin centres are promising for constructing single molecule magnets due to their large spin-orbit interaction, but experimental and computational results obtained so far indicate that this might not be the case for Re$^\textrm{IV}$ centres in an octahedral environment. Density functional results obtained in this work for [ReCl$_4$(CN)$_2$]$^{2-}$ and trinuclear complexes formed by attaching Mn$^\textrm{II}$ centres to the cyano ligands indicate that zero field splitting in such complexes exhibits large rhombicity (which leads to fast relaxation of the magnetisation) even if there are only small distortions from an ideal geometry with a four-fold symmetry axis. This is already apparent if second-order spin-orbit perturbation theory is applied but even more pronounced if higher-order spin-orbit effects are included as well, as demonstrated by wavefunction based calculations. Computational results are cast into a ligand field model and these simulations show that especially a distortion which is not along the $C_4/C_2$ axeshas a large effect on the rhombicity. Quantum simulations on these complexes are difficult because the zero field splitting strongly depends on the energetic position of the low-lying doublets from the $t_{2g}^3$ configuration.

Polarization control in spin-transparent hadron colliders by weak-field navigators involving lattice enhancement effect

Hadron polarization control schemes for Spin Transparent (ST) synchrotrons are analyzed. The spin dynamics and beam polarization in such synchrotrons are controlled by spin navigators (SN) which are special small insertions of weak magnetic fields. An SN stabilizes the beam polarization and allows for setting any desirable spin orientation at an interaction point in the operational regime, including a frequent spin flip. We present a general approach to design of SNs. We distinguish different types of SNs, namely, those not causing closed orbit perturbation as well as those producing local and global orbit distortions. In the second case, the concept of the spin response function in an ST synchrotron is applied and expanded to reveal the effect of the SN strength enhancement by magnetic lattice of the synchrotron. We provide conceptual schemes for SN designs using longitudinal and transverse magnetic fields allowing for polarization control at low as well as high energies. We also develop the ST concept for ultra-high energies. This development may enable and stimulate interest in polarized beam experiments in possible polarized collider projects such as Large Hadron Collider (LHC), Future Circular Collider (FCC) and Super Proton Proton Collider (SPPC).

Examination and Enhancement of solar radiation pressure model for BDS-3 satellites

<p>With the successful launch of the last Geostationary Earth Orbit (GEO) satellite in June 2020, China has completed the construction of the third generation BeiDou navigation satellites system (BDS-3). BDS-3 global services have been initiated in July 2020 with the constellation of 3 GEO, 3 Inclined Geosynchronous Orbit (IGSO) and 24 Medium Earth Orbit (MEO) satellites. In order to further improve the performance of BDS-3 services, the quality of BDS-3 precise orbit product needs further enhancements.</p><p>       The solar radiation pressure (SRP) is the main non-conservative orbit perturbation for GNSS satellites and is the key to improve BDS-3 precise orbit determination. In this study, we focus on the SRP models for BDS-3 satellites. Firstly, the widely used Extended CODE Orbit Model with five parameters (ECOM-5) is assessed. With one-year observations of 2020 from both iGMAS and MGEX networks, the five parameters of ECOM model (D0, Y0, B0, Bc and Bs) are estimated for each BDS-3 satellite. The D0 estimates show an obvious dependency on the elevation angle of the Sun above the satellite orbital plane (denoted as β). In addition, large variations can be noticed in eclipse seasons, which indicate the dramatic changes of SRP. The Y0 estimates vary from -0.6 nm/s<sup>2</sup> to 0.6 nm/s<sup>2</sup> for MEO, -1.0 to 1.0 nm/s<sup>2</sup> for IGSO and -1.0 to 1.5 nm/s<sup>2</sup> for GEO satellites. The B0 estimates of several satellites exhibit a clear dependency on the β angle. The largest variation of B0 appears at C45 and C46, changing from 1.0 nm/s<sup>2</sup> at 15 deg to 8.3 nm/s<sup>2</sup> at 64 deg, which implies that the solar panels of these two satellites may have an obvious rotation lag. To compensate the deficiencies of BDS-3 SRP modeling, we introduce several additional parameters into ECOM-5 model (e.g. introducing higher harmonic terms). The POD performances can be improved by about 10% and 40% for BDS-3 MEO/IGSO and GEO satellites, respectively.</p><p>       Except for the empirical model, we also study the semi-empirical SRP model such as the a priori box-wing model. Since the geometrical and optical properties from BDS-3 metadata are general and rough, we apply more detailed geometrical and optical coefficients for BDS-3 satellites. The POD performance can be improved by about 10% compared to empirical SRP models. Furthermore, considering Earth radiation pressure will have an impact of about 1.3 cm in radial component for MEO satellites.</p>

Spin response function technique in spin-transparent synchrotrons

Small perturbative fields in a synchrotron influence both the spin and orbital motion of a stored beam. Their effect on the beam polarization consists of two contributions, a direct kick and an effect of the ring lattice due to orbit perturbation. Spin response function is an analytic technique to account for both contributions. We develop such a technique for the spin-transparent synchrotrons where the design spin motion is degenerate. Several perspective applications are illustrated or discussed. In particular, we consider the questions of the influence of lattice imperfections on the spin dynamics and spin manipulation during an experiment. The presented results are of a direct relevance to NICA (JINR), RHIC (BNL), EIC (BNL) and other existing and future colliders when they arranged with polarization control in the spin-transparent mode.

How the spin-orbit interaction appears with the same order of a non-commutative change of framework for relativistic fermions

In this research, in a difficult but absolutely precise way of calculation, we show how a very tiny amount of a non-commutative change of quantum space would appear almost as big as a normal physical interaction, namely the Rashba spin-orbit interaction, for relativistic fermions. Hence, in order to show that, we firstly solve a relativistic equation of motion of a Dirac particle, influenced by a typical harmonic energy-dependent interaction for commutative and non-commutative frameworks via the Nikiforov–Uvarov exact approach. Then to study perturbation effects of a spin-orbit interaction, we apply it for both mentioned frameworks, obtaining their energy polynomial relations and discriminant formula to precisely extract all physical-admissible roots of their quartic equations. In this step, we analyze the behaviors of their quartic eigenvalue polynomials in four sections and accurately compare them one by one. Finally, we distinctly show that the magnitude of the physical spin-orbit perturbation appears, almost of the same order of imposing a non-commutative geometry change of framework, as an outstanding result.

Orbit Plan Method for General Rendezvous Problems

The orbit plan method of rendezvous mission was studied in this paper. We are concerned with the general rendezvous problem between two satellites which may be in non-coplanar, eccentric orbits, considering orbit perturbation and rendezvous time limitation. The planning problem was modeled as a nonlinear optimization problem, and the adaptive simulated annealing method was used to get the global solution. The Lambert algorithm was used to compute the transfer orbit, so that the endpoint constraint of rendezvous was eliminated. A shooting technique was used to solve the perturbed lambert problem. The method was validated by simulation results.