Perturbation of the angular correlation of γ-rays by molecular motion

The time dependent angular correlation of successive gamma rays emitted by a nucleus coupled by a quadrupolar field to a randomly reorienting molecule is calculated for a complete range of rates of molecular motion using a strong collision model. The results in the fast and slow motion limits are similar to those previously obtained using a diffusional model. Calculated curves of G ₂₂(t) are given in the intermediate range of rates of motion and the results compared with published experimental observations.     

Spin diffusion effects on E.S.R. linewidths in the quasi-two-dimensional magnetic system bis[1,2-bis(2-methoxyethoxy)ethane] sodium biphenylide

The electron spin resonance absorption line of a single crystal of the quasi-two-dimensional system bis[1,2-bis(2-methoxyethoxy)ethane] sodium biphenylide has been investigated. Experiments are performed at 9·4 GHz (X-band) and at 0·0332 GHz (B ₀ ≈ 1·1 mT). Only at X-band does the linewidth have a (3 cos² ? - 1)² angular dependence (? is the angle between the magnetic field and the normal to the two-dimensional magnetic plane). The linewidth is frequency dependent especially at the magic angle (? = 54° 44′). The results are interpreted with the linewidth theory of Richards and Salamon. For both frequencies good agreement exists between experimental and theoretical results, proving the importance of spin diffusion in the long time behaviour of the spin correlation functions.     

Quantum HeisenbergS=1 spin glass: Effect of anisotropy and ferromagnetic interaction

A complete analysis of the transfer dynamics in an asymmetric nonlinear dimer model with different cubic site polarizations is given. The analysis is performed for both the dynamics of the full density matrix on the Bloch sphere (location of fixed points, bifurcation in dependence on the polarization strength) and of the reduced space of the occupation difference using a potential function. For a time dependent harmonic perturbation the appearance of chaotic transfer regimes near a homoclinic structure on the Bloch sphere is demonstrated. A comparison with spin models is performed. It is shown that the chaotic regime corresponds to chaotic motion in a classical spin model witha–S _z ² nonlinearity and an external magnetic field having its constant and time dependent parts in the same direction.     

Electron spin polarization in a rotating triplet

The triplet model of electron spin polarization in fluid media is evaluated. The model consists of an initial singlet molecule rotating in a static, externally applied magnetic field. Intersystem crossing into different zero-field states is represented by a rate matrix diagonal in the molecular frame, and this matrix is expressed as an effective spin operator. The triplet rotates, and the motion affects the polarization in the laboratory frame, and also causes spin relaxation in the triplet manifold. The triplet is chemically quenched, and the polarization appears in the doublet fragments. The model is treated in a density matrix formalism and on the basis of anisotropic rotational diffusion of the triplet molecule. Explicit expressions are obtained in terms of the molecular parameters, the various rate constants, and the rotational correlation time.     

Ergodic theorem for an impurity spin subsystem in a paramagnet

A model for verifying and developing the fundamental ideas underlying the ergodic hypothesis is proposed. The model describes the dynamics of the spin subsystem formed by impurity charges with spin I and a small g factor in a crystal immersed in a strong constant external magnetic field under conditions where the spin system of the nuclei in the crystal is isolated from the other degrees of freedom. The additive integral of motion is the projection of the total spin of the subsystem onto the external field. Attention is focused mainly on the case of I=1/2. It is shown that the ergodic hypothesis holds if the correlation radius is finite in the initial state and that the ergodic hypothesis is violated if the initial state is sharply localized or has global correlation. The nonergodicity of the ⁸Li− ⁶Li spin subsystem, which is a convenient object for experimental investigations of spin dynamics, is revealed. An estimate is obtained for the time for transition from a sharply localized disturbance of the canonical distribution to a quasiequilibrium state. Zh. éksp. Teor. Fiz. 116, 1398–1418 (October 1999)     

Manifestation of liquid-state and solid-state properties in electron relaxation of paramagnetic ions in solutions: Non-Markovian processes

The linewidth δH and the spin-spin relaxation time T ₂ for Gd³⁺, Mn²⁺, and Cr³⁺ ions in aqueous, water-glycerol, and water-poly(ethylene glycol) solutions at paramagnetic ion concentrations providing the dipole-dipole mechanism of spin relaxation are measured using two independent methods, namely, electron paramagnetic resonance (EPR) and nonresonance paramagnetic absorption in parallel fields. Analysis of the experimental results indicates a gradual crossover from pure liquid-state (diffusion) to quasi-solid-state (rigid lattice) spin relaxation. It is demonstrated that the limiting cases are adequately described by standard, universally accepted formulas for dipole-dipole interactions in the liquid-state (the correlation time of translational motion satisfies the condition τ _c ?τ₂) and solid-state (τ _c ?τ₂) approximations. A complete theoretical treatment of the experimental dependences (including the observed gradual crossover of spin relaxation) is performed in the framework of the non-Markovian theory of spin relaxation in disordered media, which is proposed by one of the authors. Within this approach, the collective memory effects for spin and molecular (lattice) variables are taken into account using the first-order and second-order memory functions for spin-spin and spin-lattice interactions. A correlation between the spin magnitude and the temperature-viscosity conditions corresponding to the crossover to non-Markovian relaxation is revealed, and the situations in which structural transformations occurring in the solutions favor the crossover to solid-state spin relaxation are analyzed.     

Spin-other-orbit interaction in highly excited configurations with p and g electrons in outer shells

The matrix of the operator of the spin-other-orbit interaction energy is constructed for npn’g and np ⁵ n’g configurations. The matrix elements of this operator are calculated in the single-configuration approximation with wave functions in the LSJM representation and in the representation of uncoupled angular momenta using the known general formulas. The spin-other-orbit interaction is represented by three direct and three exchange radial Marvin spin interaction integrals.     

A mixed basis approach in the SGP-limit

A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s²) time, where s denotes the number of boundary elements. Several approximate eigenvalues and eigenfunctions to the diffusion operator are retrieved. The method is applied to 1D and 2D systems with Neumann boundary conditions.     

Biased motion about the long molecular axis in ‘ordered’ smectic phases as studied by deuterium NMR relaxation

Spectral densities of motion were determined by deuteron NMR relaxation measurements in the ‘ordered’ smectic-B and -G phases of 4-n-pentyloxybenzylidene-d ₁-4′-heptylaniline and 4-n-pentyloxybenzylidene-4′-heptylaniline-2,3,5,6-d ₄ at two different Larmor frequencies. Different forms of motional behaviour are involved in these phases in comparison with those in the high temperature ‘disordered’ phases. Specifically, internal ring rotation and direction fluctuation are not effective in the ordered smectic phases. In addition, the fast rotation of the molecule about its long molecular axis is now strongly hindered to give a libration motion of angular amplitudes of about 100°. The third-rate model is again used to describe the molecular reorientation, taking the restricted γ motion into account. The effects of phase biaxiality on spin relaxation in the smectic-G phase are also discussed.     

The properties of liquid nitrogen

Measurements are reported of the nitrogen-nucleus spin-lattice relaxation time, T ₁, in liquid nitrogen ¹⁴N₂ and liquid nitrogen ¹⁵N₂ along the liquid-vapour coexistence line from 77·3 K up to the critical temperature and for the fluid at the critical density up to 145 K. Values of the molecular reorientational correlation time, τ _Q , and the molecular angular momentum correlation time, τ _sr , are determined. The values of τ _Q and τ _sr and the relation between them are discussed in terms of various theories of molecular reorientation in molecular liquids. The values of τ _Q and τ _sr are also compared with those predicted by computer simulation methods. It is concluded that the molecular reorientation in liquid nitrogen is not by classical reorientational diffusion except possibly at temperatures near the triple point. It is suggested that at higher temperatures the reorientation is on average by rather large angles and that the process may be quantum mechanical to some extent. (For paper I in this series see reference [8].)     

14N spin relaxation study in the hexagonal phase of a lyotropic liquid crystal

¹⁴N quadrupolar splitting and spin-lattice relaxation times T _IZ and T _IQ were measured in the hexagonal phase of a binary mixture of dodecyltrimethylammonium chloride and water. The derived spectral densities of motion at seven temperatures together with their corresponding quadrupolar splittings were analysed based on a simple model of ‘classical’ aggregates. Both fast local motion and slower surface self-diffusion about the cylindrical aggregate axis were required to account for the ¹⁴N spin relaxation in this phase. The azimuthal correlation time was found to be tens of nanoseconds.     

Hubbard relations for linear molecules

The Hubbard relations for linear molecules in the cases of the extended diffusion model (EDM) and Ivanov's theory are derived. The M-diffusion variant of the EDM leads to an unphysical result as the dielectric and Raman correlation times approach infinity and it is suggested that M-diffusion is not a realistic model. The J-diffusion is almost the same as for spherical molecules. When the reduced angular momentum correlation time, τ _J *, is very much less than unity both EDM and Ivanov theory give a relation similar to the friction model [2], i.e. the original Hubbard relations [14] with the coefficient 6^-1, instead of 2^-1 as obtained by O'Reilly [3]. For τ _J * > 1 the various versions of Hubbard's relations are different enough to be distinguished experimentally.     

Solution Structure of Proline Pentapeptide. Analysis of the NOESY Spectra by Means of Spectrum Simulation

In this paper the NOESY spectra of proline pentapeptide are analyzed, and computer-simulated NOESY spectra are compared with the experimental spectra themselves. In simulating the spectra, the full relaxation matrix method is applied without assuming slow- or fast-motion limits. The calculated spectra are fitted to the experimental one in the following four steps: (1) determination of the proton-proton distance constraints from the experimental NOESY spectrum; (2) calculation of a rough 3D molecular structure by means of a distance geometry algorithm (DISGEO); (3) refinement of the structure; (4) adjustment of the correlation time of the overall tumbling motion of the molecule. The obtained proline pentapeptide structure in solution is close to the all-trans configuration of poly-L-prolines and the correlation time of the overall tumbling motion of the molecule is 0.4 ns; i.e. the isotropic rotational diffusion constant is D = 4.2 × 10⁸ s⁻¹.     

Photoinduced dynamics to photoluminescence in Ln3+ (Ln = Ce,Pr) doped β-NaYF4 nanocrystals computed in basis of non-collinear spin DFT with spin-orbit coupling

ABSTRACT

In this work, non-collinear spin DFT + U approaches with spin-orbit coupling (SOC) are applied to Ln³⁺ doped β-NaYF₄ (Ln = Ce, Pr) nanocrystals in Vienna ab initio Simulation Package taking into account unpaired spin configurations using the Perdew–Burke–Ernzerhof functional in a plane wave basis set. The calculated absorption spectra from non-collinear spin DFT + U approaches are compared with that from spin-polarised DFT + U approaches. The spectral difference indicates the importance of spin–flip transitions of Ln³⁺ ions. Suite of codes for nonadiabatic dynamics has been developed for 2-component spinor orbitals. On-the-fly nonadiabatic coupling calculations provide transition probabilities facilitated by nuclear motion. Relaxation rates of electrons and holes are calculated using Redfield theory in the reduced density matrix formalism cast in the basis of non-collinear spin DFT + U with SOC. The emission spectra are calculated using the time-integrated method along the excited state trajectories based on nonadiabatic couplings.     

Theg-factor of the 659 keV level in117In

We have measured theg-factor of the 659 keV, 3/2⁺, state in¹¹⁷In, using time differential perturbed angular correlation technique. The spin precession of this state was measured in an external field of 20·2 kG. The values of the Larmor precession frequencyω and theg-factor are obtained to be (60·1±0·3)10⁶ rads/sec and 0·625±0·007 respectively.     

On the calculation of <H 2> molecular integrals

The density matrix equations of motion arising in the triplet mechanism of chemically induced electron spin polarization are solved exactly without the imposition of the Redfield approximation. It is shown that the triplet spin relaxation time occurring in the final expression is not the true relaxation time because the spectral density involved depends both on the rotational correlation time and on the quenching rate. The effective spin relaxation time differs only slightly from the true time. The equations are extended to the case where the initial triplet passes on its polarization to the secondary triplet and exact solutions for the polarizations of the latter's doublets are obtained in the form Π_B = cΠ_A; an explicit expression for c is presented. The consequences of the secondary triplet being able to pass back its polarization to the initial triplet are explored and a ‘coherence effect’ on the polarization on the first triplet's doublets is analysed.     

Spin States of Iron(III) in Highly Saddled Dodecaphenylporphyrin Complexes

The alignment correlation term in the β-decay angular distribution from purely nuclear spin aligned ²⁰Na has been measured for the first time. The final objective is to test the G parity symmetry, one of the fundamental symmetry in the weak nucleon current. For artificial creation of the alignment, the knowledge of the hyperfine interaction of ²⁰Na implanted in a single-crystal ZnO was utilized. *Research Abroad, Japan Society for the Promotion of Science     

Nuclear magnetic moments for J~π=2_1~+ state of ~(10)Be with ab initio Monte Carlo shell model calculation

The magnetic moment of 2+1 state for 10Be are calculated and investigated in terms of single particle orbits for protons and neutrons under the framework of ab initio Monte Carlo shell model method in an emax = 3 model space. The reduced matrix elements of orbital and spin angular momentum are evaluated. It is found that the orientations of orbital angular momentum in diferent single particle orbits are consistent. Conversely,the orientations of spin in diferent single particle orbits tend to be chaotic. The nuclear magnetic moment of 2+1 state for 10Be is obtained as 1.006N and is discussed in regards to the contribution of orbital and spin angular momentum both for protons and neutrons. The corresponding g-factor is also given.