Diamagnetic Atoms Research Articles

Halide-bridged tetranuclear copper(II) complexes: structural, vibrational and magnetic properties of ( μ4-oxo)-hexakis( μ2-chloro)-tetrakis[(morpholine)-copper(II)

The structure and electronic surrounding of the copper(II) coordination centres of the tetranuclear copper(II) complex [Cu 4OCl 6(mor) 4] (mor = morpholine) have been investigated. The crystal structure of the title compound involving one-third acetone solvate molecule per complex was determined by X-ray diffraction. Vibrational spectroscopy (Raman and IR), as well as UV-Vis spectroscopy, and quantum-chemical calculations on a semi-empirical level (ZINDO/l) as well as on the HF and on the DFT level, were performed on solvent free species. The obtained electron density distribution sheds light on the reactivity of the coordination centres. The temperature-dependent magnetic susceptibility measurements down to 3.5 K exhibit properties related to four paramagnetic (Jahn-Teller active) copper(II) atoms bridged by diamagnetic atoms, i.e. the six μ 2-chlorides and the central μ 4-oxygen. Structural variations due to the presence of acetone in single crystals are discussed.

Wave-packet propagation in diamagnetic Rydberg atoms

By studying the time evolution of wave packets on diamagnetic Rydberg atoms, initially localized on classical periodic hydrogenic trajectories, the influence of core scattering can be shown. Outside the core region the wave packet follows a hydrogenic torus, but is ejected on different hydrogenic tori due to core scattering.

High resolution spectral study of atomic diamagnetism in a cesium cell

A resonantly enhanced two-photon spectroscopic approach to study the atomic diamagnetic effect is proposed and experimentally tested in a cesium cell. It eliminates to a large extent difficulties caused by Doppler and motional Stark broadening as well as the overlap of several sets of spectra. For the first time a spectrum with a 60 MHz linewidth for a single set of magnetic sublevels was recorded in a cell.

The magnetic state of diamagnetically diluted antiferromagnetic cobalt monoxide

Magnetic neutron diffraction measurements have been performed on (Co 1− x Mg x )O solid solutions with x = 0.1, 0.2, 0.3, 0.43, 0.53, 0.63 and 0.7 at T = 4.2 –300 K. It is shown that the concentration dependence of the average magnetic moment per atom does not obey the condition of simple dilution. The diamagnetic atom results in a local canting of the moments and an additional reduction of the average magnetic moment. One can consider this atom as a source of random magnetic field due to the appearance of a new superexchange interaction between magnetic atoms through the diamagnetic impurity. The sign of this interaction is opposite to the sign of the direct exchange interaction in the magnetic sublattice.

Hydrogen atom in very strong magnetic and electric fields.

We solved the three-dimensional Schr\odinger equation for a hydrogen atom in strong magnetic and electric fields of arbitrary mutual orientation, obtaining accurate values for the wavelengths and oscillator strengths of some low-lying bound-bound transitions. The influence of the electric-field strength and its relative orientation to the magnetic field on the calculated spectra is compared with the diamagnetic hydrogen atom. We therefore focus on field strengths relevant to the interpretation of spectra of magnetic white dwarf stars---one of the major applications of these calculations. \textcopyright{} 1996 The American Physical Society.

Initial conditions of closed classical orbits from quantum spectra.

A method is presented for determining the initial conditions of classical orbits from the quantum spectra of the diamagnetic hydrogen atom. Each classical trajectory which is closed at the nucleus produces a sinusoidal fluctuation in the photoabsorption spectrum. The amplitude of each orbit's contribution appears in the Fourier transform of a spectrum computed at constant scaled energy. For a given initial state, closed-orbit theory gives the dependence of this recurrence amplitude on the initial angle of an orbit. By comparing the recurrence amplitudes for different initial states, the initial conditions of closed classical orbits are determined from quantum spectra. (c) 1996 American Institute of Physics.

Hyperfine magnetic fields and Curie temperature in the Heusler alloy Ni2MnSn at high pressure

The ‘‘hyperfine magnetic field’’- Hhpf at the nuclei of the diamagnetic atoms 119Sn was measured in Heusler alloy Ni2MnSn by Mössbauer absorption spectroscopy for pressures up to 10.8 GPa at room temperature. The pressure dependences of HhpfSn does not show hysteresis and can be fitted by a linear function HhpfSn(P)/HhpfSn(0) =1+kH⋅P with the coefficient kH=−0.095±0.015 GPa−1, where HhpfSn(0)=4.60±0.12T. Diamond anvil cells were used to obtain high pressure at room temperature. The Curie temperature (TC) has been measured (up to 5.2 GPa) in the ‘‘toroid’’ high pressure device using thermal ac susceptibility measurements. That pressure dependence was linear with the coefficient dTC/dP=7.44 K/Gpa [TC(0)=341.3 K]. The compressibility of the sample has been measured by means of resistive strain gauges at hydrostatic pressure up to 9 GPa. The equation (V−V0)/V0=−a⋅P+b⋅P2 has been fitted to the experimental data with the coefficients a=8.64⋅10−3 GPa−1, b=1.13⋅10−4 GPa−2. The drop of the HhpfSn in pressure range 0–10.8 GPa can be explained on the basis of the empirical theory developed by Delyagin, Krylov, and Nesterov [JETP 76, 1049(1980)].

Nonhydrogenic Rydberg atoms in a magnetic field: A rigorous semiclassical approach.

Multielectron atoms in external fields are essentially more complicated than hydrogen with regard to theoretical treatments. Experimental spectra of helium as well as R-matrix quantum-defect calculations revealed discrepancies between the diamagnetic hydrogen atom and general Rydberg atoms. They appeared most transparent as novel resonance structures in constant scaled-energy recurrence spectra of nonhydrogenic atoms at positions where no hydrogenic resonances exist. To reveal the physical origin of these resonances we performed a rigorous semiclassical investigation of nonhydrogenic atoms in magnetic fields. The ionic core is introduced into the Hamiltonian via a short-ranged core potential. For this Hamiltonian we analyze in detail the classical dynamics of closed orbits. Classical core-scattering results in the creation of a huge number of new closed orbits. They appear to be composed of a sequence of slightly different hydrogenic orbits, interconnected by the core-scattering, and can be grouped into families accordingly. With a semiclassical closed-orbit theory generalized to arbitrary quantum defects of the ionic core and with the closed orbits at hand we are able to calculate photoabsorption spectra of nonhydrogenic atoms. Although each of the new orbits has a low amplitude, the interference of all members of a family results in clearly visible resonances in the Fourier transform recurrence spectra, in good agreement with experiment and quantum calculations. The novel structures in nonhydrogenic spectra are now identified and semiclassically interpreted in terms of families of core-scattered classical orbits. \textcopyright{} 1996 The American Physical Society.

Photoabsorption of Nonhydrogenic Rydberg Atoms in a Magnetic Field: Effects of Core-Scattered Classical Orbits.

The physics of multielectron atoms in strong external fields is substantially more complex than that of hydrogen. In particular, puzzling new resonances were recently observed in experimental photoabsorption spectra of diamagnetic helium and in quantum mechanical calculations of diamagnetic Rydberg atoms. We compute spectra in the framework of periodic-orbit theory and show that the new resonances can be quantitatively explained by different classes of core-scattered classical orbits.

Mössbauer study of HhpfSn in the Heusler alloy Co2MnSn under pressure

The pressure dependence of the ‘‘hyperfine magnetic field’’- Hhpf at the nuclei of the diamagnetic atoms 119Sn was investigated in the Heusler alloy Co2MnSn using Mössbauer absorption spectroscopy with pressures up to 10 GPa at room temperature. The dependence can be fitted by the linear function HhpfSn(P)/HhpfSn(0)=1+k1⋅P with coefficient k1=−0.023 ±0.002 GPa−1, where HhpfSn(0)=10.5±0.3 T. Diamond anvil cells were used for the high pressure generation. A drop of HhpfSn in the pressure range 0–10 GPa can be explained on the basis of empirical theory developed by Delyagin, Krylov, and Nesterov [JETP 76, 8, 1050 (1980)].

Quantum surfaces of section for the diamagnetic hydrogen atom: Husimi functions versus Wigner functions

We compare quantum phase space distributions of individual quantum states of the diamagnetic hydrogen atom obtained by means of Wigner functions with those given by Husimi functions. The comparison is carried out at effective h(cross) approximately 0.035 and at a fixed scaled energy ( epsilon =-0.316) which corresponds to an especially interesting mixed classical phase-space structure. The object of the comparison is to establish which of the two distributions best correlates with the classical Poincare surface of section for a representative set of single states. As expected, the states investigated display the strongest positive intensity on a single local invariant phase-space structure (such as a scar or torus) and at this level there is little difference between the Husimi and the Wigner function. However the weak structures (fringes of the Wigner function or zeros of the Husimi function) are shown here to be radically different for the Wigner relative to the Husimi representation. In both cases the weak structures permeate all of phase space. In addition they show different character for integrable and chaotic dynamics and so reflect the global structure of phase-space to a much greater extent than the localized strong structure. The Wigner functions of selected states are shown to have additional dynamically significant structures which are not apparent in the Husimi functions. These include negative intensity features seen in the Wigner-but not the Husimi-functions which are very well correlated with structures of the classical Poincare surfaces of section. Despite its complex oscillatory nature the Wigner function delineates better classical features, for example showing the outline of islands of stability avoided by states supported by chaotic regions with greater sharpness than the Husimi function.

Phase space scars and quantization of non-integrable systems: the diamagnetic hydrogen atom

We present here a study of the quantum phase space localization (Wigner functions) in dependence of semiclassical quantization rules for the hydrogen atom in magnetic fields. We consider primarily two energy regions. In the first the corresponding classical system is near-integrable and in the second near fully chaotic. We study phase space localization (scars) close to stable and unstable trajectories, tori and the invariant manifold associated with the almost circular, unstable periodic trajectory. We find that these classical structures are an important element for the structure of the wavefunctions and the semiclassical quantization predictions are in good agreement with the quantal results.

Classical chaos and quantal Wigner distributions for the diamagnetic H atom

Abstract It has turned out that quantum wave functions of chaotic model systems show an enhanced probability of presence along classical periodic orbits. Inspired by this quantum chaological connection, we analyse Wigner distributions for the diamagnetic hydrogen atom. We report on classical and quantal Poincare surfaces-of-section and discuss the strength of localization in dependence of semiclassical quantization conditions.

Wigner functions for the diamagnetic hydrogen atom: quantum fringes

Phase-space distributions (Wigner functions) for eigenstates of the diamagnetic hydrogen atom at fixed scaled energy have been obtained for the intermediate regime in between regularity and full chaos. States localized on the three major fixed points of the classical Poincare surface of section have been considered. While previous numerical work was primarily concerned with phase-space localization on period orbits, here the oscillatory structure (quantum fringes) forms the main subject. The fringes are delocalized relative to the dominant positive structures. Although the latter are strongly localized on fixed points and their associated invariant manifolds, the fringes permeate the whole energy surface. Fringes originating in the ergodic part of phase-space experience an abrupt change in character, in addition to the expected fall in amplitude, within stable islands. As a result, a single quantum state can provide a striking map of the global structure of phase-space. Phase-space is partitioned into relatively strong irregular scar fringes in the ergodic region and weaker regular Airy type fringes inside stable islands. Quantum probability distributions near bifurcations and confluences have also been examined. A comparison with Husimi distributions has been carried out and it is shown that the latter have lost some dynamically interesting structures.

A new ESR spectrum in the Y-Ca-Ba-La-Cu-O high-Tc superconductor system

Electron spin resonance spectra (ESR) of YBa1.5La0.5Cu3O7.21 and Y0.7Ca0.3Ba1.5La0.5Ca3O7.08 high-Tc superconductors (HTSC) were obtained using 3 cm and 2 mm ESR spectrometers. A nearly isotropic Lorentz line with a g factor of 2.0065+or-0.0005 was observed and interpreted as being due to the electron located near a diamagnetic atom in the HTSC lattice.

Magnetic properties of the mixed-valence heteropoly blues with a Keggin structure

A theoretical model is proposed to explain the observed magnetic properties of the twelve-nuclear mixed-valence tungsten complexes with a central diamagnetic or paramagnetic atom. The electronic energy levels of a two-electron twelve-center system are calculated by using the Hubbard Hamiltonian. It is shown that the diamagnetic ground state with a large singlet—triplet gap can arise due to the delocalization of an electron pair over the tungstate framework. The delocalization hides the effects of the antiferromagnetic exchange between the two excess electrons and the central paramagnetic atom.

Study of the photoabsorption spectrum of diamagnetic Rydberg atoms without the need of using full eigenvectors

We present a new method for efficient and accurate determination of the eigenvalues and the photoabsorption spectrum of Rydberg atoms in the presence of uniform magnetic fields. The procedure consists of the following elements: (a) Hamiltonian and basis set based on the SO(4, 2) dynamical group and its SO(2, 1) subgroup; (b) Lanczos algorithm with spectrum transformation for dealing with the “internal” energy spectrum of ultralarge sparse symmetric Hamiltonians; and (c) a new procedure for the calculation of photoabsorption spectra of Rydberg atoms without the need of determining and using the full eigenvectors of very large dimension. The method is applied to the photoabsorption spectrum of diamagnetic Rydberg hydrogen atoms in the energy regime close to the ionization threshold where the corresponding classical behavior is chaotic. Good agreement with experimental data is obtained.

Magnitude of Higgs-boson-exchange CP violation in two-doublet models with large tan beta.

CP violation in neutral Higgs-boson exchange is studied in two-doublet models in an expansion in (1/${\mathrm{tan}}^{2}$\ensuremath{\beta}). The typical magnitude of various CP-violating quantities is found for large tan\ensuremath{\beta}. In particular the electric dipole moment (EDM) of the electron and the coefficient ${\mathit{c}}_{\mathit{S}}$ of the CP-violating electron-nucleon scalar-pseudoscalar operator are examined and it is found that in a simple class of two-doublet models ${\mathit{c}}_{\mathit{S}}$/${\mathit{d}}_{\mathit{e}}$ is typically O(${\mathrm{tan}}^{2}$\ensuremath{\beta}). Therefore ${\mathit{c}}_{\mathit{S}}$ is more important than ${\mathit{d}}_{\mathit{e}}$ for the EDM's of diamagnetic atoms and molecules (Hg, Xe, TlF) typically if tan\ensuremath{\beta}\ensuremath{\gtrsim}5, and for paramagnetic atoms (Cs, Tl) if tan\ensuremath{\beta}\ensuremath{\gtrsim}15. The dependence on tan\ensuremath{\beta} of the various contributions to the neutron EDM including the Weinberg three-gluon operator, and the dependence on tan\ensuremath{\beta} of the top-quark EDM are also discussed. Supersymmetric and three-doublet models are also considered.

Nuclear magnetic resonance of 3He dissolved in vitreous silica

For the first time 3He gas dissolved in solids (pyrex and suprasil glasses) has been studied by NMR. The chemical shifts are mainly determined by interaction with diamagnetic atoms of the glass structure and not by magnetic interaction with Fe 3+ ions. In pyrex the relaxation times at 25°C are: T 1( 3He) = 65±6.5 ms, T 2( 3He) = 1.1±0.1 ms and the activation energy for relaxation is E a( T 1) = E a( T 2) = 3.4±0.3 kJ/mol (−70 to 100°C). In suprasil T 2( 3He) = 1.1±0.1 s (25°C), E a = 18±2 kJ/mol (−40 to 20°C) and T 1( 3He) = 370±40 s (0°C). The relaxation times in both glasses are determined by magnetic dipole-dipole interaction, in pyrex with Fe 3+ ions modulated by spin-flip and in suprasil with unpaired electrons of defects in the glass structure modulated by the fast diffusion of helium atoms. The estimated values of distances of closest approach of diffusing 3He atoms to Fe 3+ ions in pyrex and to defects in suprasil are ∼ 5 and ∼ 3 Å, respectively.

Description of Quantum Irregular Spectra by Soliton-Gas Picture

A soliton-gas model is proposed to describe the orderly energy-level structures in quantum chaos. By diagonalizing the model Hamilton matrix, we show that our model leads to the transition from Poisson to GOE-like level-spacing distribution in the small spacing regime and that this transition depends on both the soliton density and the fluctuation of acceleration induced by collisions of solitons. Fitting of spectral rigidity (what is called Δ-statistics) in the transition regime to a theoretically proposed one is also carried out. In this case, it does not come to fit to the Gaussian orthogonal ensemble prediction. This can be considered to reflect the coherent nature of solitons lying behind the irregular spectra. Reflecting the fact that the number of levels is large, saturation of the rigidity is not observed. In addition, we discuss a possibility of applying our model to the recent experiment on diamagnetic Rydberg atoms.