Angular Coupling Research Articles

Nonadiabatic coupling in cold collisions of spin-polarized metastable hydrogen atoms

Previous calculations of low-temperature cross sections for collisions between spin-polarized metastable hydrogen atoms are improved to include nonadiabatic radial and angular coupling at large interatomic separations. The electrostatic dipole-quadrupole interaction produces nonadiabatic radial coupling between (2s,2p) and (2p,2p) states, while the Coriolis interaction produces nonadiabatic angular coupling. Both of these long-range contributions are handled in a space-fixed atomic gauge that is particularly convenient for a spin-polarized system. The improved theoretical results are compared with an existing experiment.

Electromagnetic Coulomb gas with vector charges and “elastic” potentials: Renormalization group equations

We present a detailed derivation of the renormalization group equations for two-dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between the charges involve both angular couplings and a new electromagnetic potential. This motivates the denomination of “elastic” Coulomb gas. Such elastic Coulomb gases arise naturally in the study of the continuous melting transition of two-dimensional solids coupled to a substrate, either commensurate or with quenched disorder.

Photoionization-induced dynamics of the ammonia cation studied by wave packet calculations using curvilinear coordinates

The determination of the photoelectron spectrum of NH 3 and of the internal conversion dynamics of NH 3 + recently published [A. Viel, W. Eisfeld, S. Neumann, W. Domcke, U. Manthe, J. Chem. Phys. 124 (2006) 214306] is complemented by the investigation of the effect of the vibrational angular momenta couplings on the dynamics. The multi-configurational time-dependent Hartree method is used to propagate a wave packet on the analytical anharmonic six-dimensional three-sheeted potential energy surface for the ground and first excited states of the ammonia cation. Curvilinear coordinates and the associated quasi-exact kinetic energy operator suitable for the multi-configurational time-dependent Hartree scheme are employed. A non-negligible effect of the use of Cartesian normal modes instead of the curvilinear coordinates is observed on the low energy part of the photoelectron spectrum. However, the three different time scales found in the dynamical calculations for the second absorption band are very similar regardless of the use of either normal modes or curvilinear coordinates.

Coupling of Monte Carlo and Discrete‐Ordinates Transport for Ads Calculation

Accelerator‐driven subcritical systems (ADSs) are under investigation worldwide, because the unique feature of subcriticality provides new capabilities in the transmutation of long‐lived radioactive waste. The design of a future ADS requires fast and flexible transport calculation methods. As is shown in the article, coupled Monte Carlo and deterministic calculation methods fulfills this requirement. The paper describes the methodology of an energy‐based volumetric and angular coupling. A new type of Monte Carlo estimator has been developed for the determination of the source term. Test calculations with modified MCNPX and XSDRNPM codes are presented to prove the feasibility of the method.

Light injection in SOI microwaveguides using high-efficiency grating couplers

An experimental characterization of the grating couplers for sub-micrometer silicon-on-insulator (SOI) waveguides is presented. The grating couplers have been designed, realized, and characterized for the +1 diffraction order at an operating wavelength of 1.31 mum for TE polarization. At the resonant angle, a coupling efficiency higher than 55% has been measured. The angular coupling range and the wavelength tolerance have been evaluated to 3deg and 20 nm, respectively. The grating coupler is followed by a taper, and about 50% of the input power at 1.31 mum is coupled into sub-micrometer rib and strip SOI waveguides. The ration between light power decoupled toward the cladding and light power decoupled toward the substrate is about three

Theoretical spectroscopy of the calcium dimer in the AΣu+1, cΠu3, and aΣu+3 manifolds: An ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the AΣu+1(1S1+1D1), cΠu3(1P3+1S1), and aΣu+3(1P3+1S1) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the AΣu+1←XΣg+1 transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca2 spectrum in the AΣu+1(1S1+1D1), cΠu3(1P3+1S1), and aΣu+3(1P3+1S1) manifolds of states.

The evolution of inner-shell multielectronic X-ray spectra from threshold to saturation for low- to high-Z atoms

Inter- and intra-shell electronic correlations in an atom are manifested in, and can be studied through, the X-ray emission spectra of multielectronic transitions. We have measured the spectra of K hα 1,2 hypersatellites (HS), Kα 3,4 satellites (S), and the 3d electron shake-up satellites (D) accompanying the Kα 1,2 diagram lines, and their evolution from the double-ionization threshold, for selected 4- and 5-row elements of the periodic table. These spectra originate in the [1 s] −1, [2p] −1, and [3d] −1 spectator two-electron transitions [1 s] −2→[1s2p] −1, [1s2p] −1→[2p] −2, and [1s3d] −1→[2p3d] −1 respectively. Photoexcitation by monochromatized synchrotron radiation together with high-resolution crystal spectrometers were employed. Ab initio relativistic multiconfigurational Dirac–Fock (RMCDF) calculations reproduce the spectra very well for all transitions, with the HS spectra showing a strong dependence on QED effects. The excitation thresholds were determined accurately. The threshold-to-saturation energy range of the intensity was found to depend strongly on the principal quantum number n of the spectator hole. For example, for Cu, ranges of 2%, 10%, and 60% of the threshold energy are found for the D, S and HS spectra, respectively. Only the D spectrum's evolution conforms to the Thomas model, indicating a dominant shake up/off process. The S and HS spectra seem to be dominated by the knockout (“two-step-one”) process near threshold. The S spectra show a two-regime behavior. Near threshold both shape and intensity vary with excitation energy, and above that only intensity changes are observed. The lower-than-expected K hα 1/K hα 2 intensity ratio found for Z=23–30 and 39–46 indicates that the angular momenta coupling scheme at the regime intermediate between the LS coupling at low-Z and the jj coupling at high-Z may not be fully accounted for by the prevailing theory.

Significant Enhancement of the Optical Second Harmonic Generation in a Poled Azopolymer Thin Grating

Nonlinear optical properties of an electrically poled surface relief grating inscribed on a thin film of azopolymer have been investigated. The linear and nonlinear optical far-field diffraction patterns of the grating are compared, and they show a clear angular separation of the fundamental (lambda = 1.064 mum) and second harmonic generated beams that are diffracted at different angles. The intensity of the zero order transmitted second harmonic generation (SHG) beam from inscribed surface relief grating (SRG) areas has been recorded using the Maker fringe technique and compared to the response from flat areas that were only poled. Poled gratings exhibit a sharp second harmonic generation enhancement for coupling angles of theta(i) = +/-52 degrees due to a quasi-phase matching process. A simple phenomenological model allows one to explain both the second harmonic intensity generated from the thin polar film and the dispersion curve observed under "pp" polarization due to the mismatch of the angular coupling condition: this gives us a good indication of the intensity enhancement of the SHG beam in the forward direction.

Experimental and theoretical studies of Λ doublings and permanent electric dipoles in the low-lying Π1 states of NaCs

We present experimental data on the electric permanent dipole moments d(v',J') and lambda splittings (q factors) in the quasidegenerate (3) 1pi(e/f) state of the NaCs molecule over a wide range of the vibrational (v') and rotational (J') quantum numbers by using the combination of dc Stark mixing and electric radio frequency-optical double resonance methods. Within the experimental (3) 1pi state v' ranged from v' = 0 to 34, q values exhibited a pronounced decrease from 7.91x10(-6) to 0.47x10(-6) cm(-1), while absolute value(d) values varied between 8.0 and 5.0 D. Experimental evaluation yielded small d values about 1 D for D2 1pi state v' < 3 levels. The experiment is supported by ab initio electronic structure calculations performed for the (1-3) 1pi states of NaCs by means of the many-body multipartitioning perturbation theory of potential energy curves, permanent dipole, and angular coupling matrix elements for the lowest singlet states. The predicted d values reproduce their experimental counterparts within the measurement errors while theoretical q factors reproduce the measured v' dependence being, however, systematically overestimated by ca. 1x10(-6) cm(-1). The present NaCs data are compared with those of the NaK and NaRb molecules.

Direct deperturbation analysis of the AΠ2∼BΣ+2 complex of LiAr7,6 isotopomers

Direct deperturbation analysis of the highly accurate experimental rovibronic term values of the A (2)Pi approximately B (2)Sigma(+) complex of LiAr [R. Bruhl and D. Zimmermann, J. Chem. Phys. 114, 3035 (2001)] has been performed in the framework of inverted close-coupling approach implicitly adjusted to the unified treatment of the overall A approximately B coupling effect without reducing the rovibrational dimensionality. The nonlinear fitting procedure was supported by the ab initio calculations on the spin-orbit and angular coupling matrix elements between the lowest X (2)Sigma(+), A (2)Pi, and B (2)Sigma(+) states. The analytical grid mapping based on the reduced variable representation of the radial coordinate r was used to improve the efficiency of the solution of the close-coupling radial equations near the dissociation limit. The mutual A approximately X perturbation effect on the A (2)Pi term values and spin-rotation splitting of the ground state were evaluated for both (7,6)LiAr isotopomers. The resulting empirical potential-energy curves for the adiabatic A (2)Pi and B (2)Sigma(+) states, along with the refined r-dependent nonadiabatic matrix elements, reproduce the total rovibronic structure of the (7)LiAr complex with the standard deviation of 0.003 cm(-1). The mass invariance of the deperturbed electronic parameters was confirmed by the calculation of the rovibronic term values of the (6)LiAr isotopomer which coincided with their experimental counterparts within 0.004 cm(-1).

Free paper: A trial of the early mobilisation of unhealed transtibial amputees

Design and fitting of artificial limbs to lower limb amputees are largely based on the subjective judgement of the prosthetist. Understanding the science of three-dimensional (3D) dynamic coupling at the residuum/socket interface could potentially aid the design and fitting of the socket.A new method has been developed to characterise the 3D dynamic coupling at the residuum/socket interface using 3D motion capture based on a single case study of a trans-femoral amputee. The new model incorporated a Virtual Residuum Segment (VRS) and a Socket Segment (SS) which combined to form the residuum/socket interface. Angular and axial couplings between the two segments were subsequently determined. Results indicated a non-rigid angular coupling in excess of 10° in the quasi-sagittal plane and an axial coupling of between 21 and 35 mm. The corresponding angular couplings of less than 4° and 2° were estimated in the quasi-coronal and quasi-transverse plane, respectively.We propose that the combined experimental and analytical approach adopted in this case study could aid the iterative socket fitting process and could potentially lead to a new socket design.

Localization of structural zones producing hypersensitive behavior: finite element approach

On the basis of our previous works [J. Sound Vib. 260 (1) (2003) 83], one present here a FEM application of a method that allows one to detect structural zones producing hypersensitive behavior. The concept is quite simple, and is cheaper than Monte Carlo simulations. The complete resolution of the problem is done only once, using nominal parameters of the structure, in order to obtain the displacement field. Then, considering another structure, built using variable parameters, chosen in a random way in the acceptable manufacturing range, the finite element assembly procedure is performed. These matrices are finally used to define an indicator in which the displacement field of the nominal solution permits to detect structural zones responsible for hypersensitive behavior. It is based on the computation of energy of a residual displacement field. After a presentation of the basis of this tool, numerical results are presented on a finite element model of a hypersensitive plates network, in which sensitivity problems are linked to angular coupling, and on a cross member beam, which is made up of three spot-welded layers.

Development of Torsional Damper with Crowds of Solid Balls Simulation of Damping Mechanism.

It has been clarified experimentally that newly developed torsional damper can effectively reduce the torsional vibration of crankshaft system by adjusting the weight of balls of the experimental damper. The purpose of this study is to quantify the damping mechanism as the basis for its optimum design. First, the modeling and the computer simulation on the torsional vibration of testing crankshaft system with the damper are carried out. Then, by examining their results in comparison with the experimental results, it is made clear its primary damping mechanism is constituted by not only the friction torque between crowds of solid balls and damper mass but also the fluctuation of the natural frequency caused by alternating between angular displacement and coupling of damper mass to damper case every period of torsional vibration.

An experimental and theoretical study of electronic excitation and charge transfer processes in collisions between Cs( [formula omitted]) atoms and [formula omitted] ions in the 0.30–4.00 keV energy range

The collisional system Cs + Na + with both species in their ground electronic state, has been studied using the crossed molecular beams technique and measuring the resulting fluorescent decay. Emissions from electronically excited Cs( 6 2 P 3/2 ) and Cs( 7 2 P 1/2,3/2 ) atoms have been detected as well as those from excited Na( 3 2 P 1/2,3/2 ) and Na( 4 2 D 3/2,5/2 ) produced by electron transfer. Cross-section values in the 0.30–4.00 keV energy range have been measured for the four different collision channels as well as the branching ratio between the resolved J-states for Cs( 7 2 P 1/2,3/2 ). A qualitative interpretation for some of the measured emission cross-sections as a function of the collision energy has been performed using ab initio one-electron calculations done for the (CsNa) + quasimolecule. Hemiquantal dynamical calculations have been carried out at selected collision energies including radial and angular non-adiabatic couplings, comparing the calculated cross-sections with the experimental data.

Superconductivity with angular dependent coupling: stripes, Coulomb repulsion and enhanced Tc

We have analysed a simple analytically solvable model with an angular dependent coupling λ( ϕ) represented by a square-well form. We have found that the introduction of the Coulomb repulsion λ C, increasing the “contrast” | λ|+| λ C|, or the depth of the angular modulation of λ( ϕ), leads to a remarkable enhancement of the superconducting critical temperature T c. This effect can be optimized by combining attractive ( λ<0) and repulsive ( λ>0) interactions appearing, for example, along stripes and perpendicular to them in high- T c superconductors.

Exact solutions for chemical bond orientations from residual dipolar couplings.

New methods for determining chemical structures from residual dipolar couplings are presented. The fundamental dipolar coupling equation is converted to an elliptical equation in the principal alignment frame. This elliptical equation is then combined with other angular or dipolar coupling constraints to form simple polynomial equations that define discrete solutions for the unit vector(s). The methods are illustrated with residual dipolar coupling data on ubiquitin taken in a single anisotropic medium. The protein backbone is divided into its rigid groups (namely, its peptide planes and Calpha frames), which may be solved for independently. A simple procedure for recombining these independent solutions results in backbone dihedral angles phi and psi that resemble those of the known native structure. Subsequent refinement of these phi-psi angles by the ROSETTA program produces a structure of ubiquitin that agrees with the known native structure to 1.1 A Calpha rmsd.

Superconductivity with Angular Dependent Coupling: Stripes, Coulomb Repulsion and Enhanced T&lt;sub&gt;c&lt;/sub&gt;

Superconductivity with Angular Dependent Coupling: Stripes, Coulomb Repulsion and Enhanced T&lt;sub&gt;c&lt;/sub&gt;

Canonical Three-Body Angular Basis

Three-body problems are basic for the quantum mechanics of molecular, atomic, or nuclear systems. We demonstrate that their variational solution for rotational states can be greatly simplified. A special choice of coordinates (hyperspherical) and of the kinematics (body-fixed coordinate frame) allows one to choose basis functions in a form that makes the angular coupling trivial.

Ro-vibronic states of the NCS radical in the X2Π state

Renner–Teller calculations were performed for the X2Π state of the NCS radical using modified multi-reference configuration interaction (MRCI) three-dimensional potential energy functions (PEFs). For the refinements of the PEFs, existing experimental data were used. In the variational calculations of the ro-vibronic levels for Jtotal⩽7/2 the full anharmonicity and all angular momenta couplings were considered. NCS has about 260 ro-vibronic states (J=P, J⩽7/2) for energies up to 4000 cm-1. Due to a large spin–orbit constant, small bending wavenumber, presence of strong anharmonic resonances, high density of interacting states, and strong variation of the spin–orbit coupling with geometry, the Renner–Teller problem is found to be more complex than in other 15 valence electrons ABC molecules. The standard notation for the linear–linear Renner–Teller case was augmented. It allows a qualitative description of various perturbations existing in the ro-vibronic states of NCS. The close lying A2Π and B2Σ+ states cross near the equilibrium geometry of the B-state and form a conical intersection in bent structures.

A stratified model for ultrasonic propagation in cancellous bone

A new model for ultrasonic wave propagation in cancellous bone is presented here. The model treats cancellous bone as a stratified medium of periodically alternating solid–fluid layers, and considers propagation of two compressional modes, analogous to the fast and slow waves of Biot theory, in terms of slowness surfaces. The behavior of the two modes is examined in vitro using bovine bone samples over a range of incidence angles. Two modes are seen when the cancellous structure is parallel to the propagation direction, but only one mode propagates normal to the structure, and the velocity of the fast wave increases with angle of incidence away from the normal. This behavior can be explained in terms of an angular dependent inertial coupling effect, in keeping with the theory of propagation in stratified media of periodically alternating fluid–solid layers. Quantitative agreement with theory is good. Although the structure being analyzed is essentially an oversimplification of the structure of cancellous bone, the agreement with theory suggests the stratified model offers potential for future research.