Calculated Phase Shifts Research Articles

Excited states of 4He

The study of the 4He nucleus is important because it is the most basic sub-unit (cluster) in nuclei. We have investigated the structures and the reaction mechanisms in 4He by using the correlated Gaussian basis function with the global vector representation. In order to treat the boundary condition for the ab-initio calculation of the four nucleons, we employ the Microscopic R-matrix Method (MRM) and the Complex Scaling Method (CSM) . Elastic-scattering phase shifts for four-nucleon systems are studied in an ab-initio type cluster model with MRM in order to clarify the role of the tensor force and to investigate cluster distortions in low energy d+d and t+p scattering. For 1S0, the calculated phase shifts show that the t+p and h+n channels are strongly coupled to the d+d channel for the case of the realistic interaction.

On the computation of the magnetic phase shift for magnetic nano-particles of arbitrary shape using a spherical projection model

The magnetic phase shift of an electron wave traveling through a magnetized object is computed by considering the object to be made up of a collection of uniformly magnetized spheres arranged on the nodes of a cubic grid. In the limit of vanishing grid size, this approach becomes equivalent to other numerical approaches. Update equations are derived for the change of the magnetic phase shift when the magnetization of a single object voxel is modified. Example phase shift calculations are presented for a uniformly magnetized sphere, circular disks with an infinitely sharp vortex core and a smooth core, and an oval disk with a pair of vortices and an antivortex.

Studying the convergence of the relativistic J-matrix method in elastic scattering of electron from model potentials

We present a convergence study of the relativistic J-matrix method, applied to elastic scattering of electrons on the various model potentials vanishing faster than Coulomb one. Calculations have been performed using newly developed JMATRIX code. The code have been used to calculate phase shifts for a wide range of energies and to obtain total, differential, momentum transfer and spin-polarization cross-sections, using the partial waves analysis. The results are compared to the other theoretial calcalations.

Infinite-Cutoff Renormalization of the Chiral Nucleon–Nucleon Interaction up to N3LO

Naively, the "best" method of renormalization is the one where a momentum cutoff is taken to infinity while maintaining stable results due to a cutoff-dependent adjustment of counterterms. We have applied this renormalization method in the non-perturbative calculation of phase-shifts for nucleon-nucleon (NN) scattering using chiral NN potentials up to next-to-next-to-next-to-leading order (N3LO). For lower partial waves, we find that there is either no convergence with increasing order or, if convergence occurs, the results do not always converge to the empirical values. For higher partial waves, we always observe convergence to the empirical phase shifts (except for the 3G5 state). Furthermore, no matter what the order is, one can use only one or no counterterm per partial wave, creating a rather erratic scheme of power counting that does not allow for a systematic order-by-order improvement of the predictions. The conclusion is that infinite-cutoff renormalization is inappropriate for chiral NN interactions, which should not come as a surprise, since the chiral effective field theory, these interactions are based upon, is designed for momenta below the chiral-symmetry breaking scale of about 1 GeV. Therefore, this value for the hard scale should also be perceived as the appropriate upper limit for the momentum cutoff.

Laser lock-in thermography for thermal contact characterisation of surface layer

Lock-in thermography was applied to determine the thermal contact conductance of a W-layer (140μm) on a CFC-substrate. A lock-in thermography system together with a pulse repetition rate Nd:YAG laser (1064nm, 1–500Hz pulse repetition rate) for layer heating was applied for phase shift measurements on the W-layer. A numerical model for direct phase shift calculations was developed and applied to rapid determination of the Fourier amplitudes and phases of the temperature. Thermal conductance coefficients were obtained by comparing the experimental and simulation phase shifts.

Two- and Three-Body Coulomb Solution Method in a Momentum Space

We present a method to calculate two- and three-body amplitudes including the Coulomb potential in a momentum space. Our aim is to obtain the exact two-body Coulomb amplitudes used in three-body calculations, which reproduce the analytic phase shifts. For the purpose, our theory is based on the modified Coulomb potential (MCP) whose Fourier transformation is equivalent to the pure Coulomb potential in a configuration space, and the two-potential theory with an auxiliary potential. Moreover, one can analytically determine a decisive range R dec in the MCP. By using the MCP, we obtain the two-body Coulomb modified nuclear amplitude as well as the pure Coulomb amplitude. The calculated phase shift are very good fitting with the experimental data.

Analytical calculation of nonreciprocal phase shifts and comparison analysis of enhanced magneto-optical waveguides on SOI platform

Transfer matrices for one-dimensional (1-D) multi-layered magneto-optical (MO) waveguides are formulated to analytically calculate the nonreciprocal phase shifts (NRPS). The Cauchy contour integration (CCI) method is introduced in detail to calculate the two complex roots of the transcendental equation corresponding to backward and forward waves. By virtue of perturbation theory and the variational principle, we also present the general upper limit of NRPSs in 1-D MO waveguides. These analytical results are applied to compare silicon-on-insulator (SOI) based MO waveguides. First, a three-layered waveguide system with MO medium is briefly examined and discussed to check the validity and efficiency of the above theory. Then we revisited the reported low-index-gap-enhanced NRPSs in MO waveguides and obtained substantially different results. Finally, the potential of common plasmonic waveguides to enhance the nonreciprocal effect is investigated by studying different waveguides composed of Metal, MO medium and dielectrics. Our study shows that the reasonable NRPSs can be optimized to some extent but not as much as claimed in previous publications.

Two Point Correlation Technique for the Measurements of Poloidal Plasma Rotation by Heavy Ion Beam Probe

The paper proposes a method to measure poloidal rotation velocity of toroidal plasma vpol using Heavy Ion Beam Probe (HIBP) with a multi-slit energy analyzer. The method is based on calculation of phase shift between broadband density turbulence measured simultaneously in two sample volumes, located at the same magnetic surface but separated poloidally. Oscillatory component of HIBP beam current is used as a density turbulence characteristic. HIBP is capable to provide the temporal evolution of the vpol in a fixed radial position and also the vpol profile by periodic radial scan. Method was verified in real plasma experiment in ECRH and NBI discharges on the TJ-II stellarator. Result shows that in low density discharges (ne ≈ 0.3-0.5 × 10 19 m −3 ) absolute values of local vpol is about 4-6 km/s, oriented in the ion diamagnetic drift direction. When HIBP operates for radial scans, it is conventionally measuring the plasma potential profile, and so provides the radial electric field Er and velocity of E × B drift (vE×B) at the same time as plasma rotation. Experimental data shows that in low density ECRH plasma the rotation velocity coincides with E × B velocity within achieved experimental accuracy. When the density is increasing, both vE×B and vpol tends to decrease and then change the sign at threshold plasma densities in the range of ne ≈ 0.7-1 × 10 19 m −3 . With this new proposed technique HIBP becomes the new effective tool to study plasma rotation and turbulence characteristics in toroidal plasmas.

Distinct Global Patterns of Strong Positive and Negative Shifts of Seasons over the Last 6 Decades

Alterations of annual temperature cycles have profound implications on how the planet responds to global climate change. In this study, a high resolution global analysis of temperature cycle shifts and their development over time is presented. We show that over the last 63 years, phase shifts in the annual near surface temperature cycle exhibit large spatiotemporal variability. The calculated phase shifts comprise earlier onsets of seasons as well as delays with similar frequencies, depending on location. From 1978 to 2010 Eastern Europe experienced an advanced annual cycle of near-surface temperature of 3.2 days while Eastern Australia shows an opposite shift towards later seasons of 3.5 days in comparison to the preceding 30-year period from 1948 to 1977. The largest phase shifts of –5.5 days toward earlier seasons over land were found in Belarus and Northwest Russia. For the first time the developments of seasonal temperature shifts were generalized for large areas by using self-organizing feature map neural networks resulting into 4 significant global trends. The temperature phase shifts are also shown to have strong correlations with the timing of shrub foliation observed at 57 phenological stations across the USA. The findings have far-reaching, yet regionally distinct consequences on agriculture, animal life cycles, plant phenology, and regional weather phenomena that change with annual temperature cycles.

Four-Nucleon Scattering with a Correlated Gaussian Basis Method

Elastic-scattering phase shifts for four-nucleon systems are studied in an $ab$-$initio$ type cluster model in order to clarify the role of the tensor force and to investigate cluster distortions in low energy $d+d$ and $t+p$ scattering. In the present method, the description of the cluster wave function is extended from a simple (0$s$) harmonic-oscillator shell model to a few-body model with a realistic interaction, in which the wave function of the subsystems are determined with the Stochastic Variational Method. In order to calculate the matrix elements of the four-body system, we have developed a Triple Global Vector Representation method for the correlated Gaussian basis functions. To compare effects of the cluster distortion with realistic and effective interactions, we employ the AV8$^{\prime}$ potential as a realistic interaction and the Minnesota potential as an effective interaction. Especially for $^1S_0$, the calculated phase shifts show that the $t+p$ and $h+n$ channels are strongly coupled to the $d+d$ channel for the case of the realistic interaction. On the contrary, the coupling of these channels plays a relatively minor role for the case of the effective interaction. This difference between both potentials originates from the tensor term in the realistic interaction. Furthermore, the tensor interaction makes the energy splitting of the negative parity states of $^4$He consistent with experiments. No such splitting is however reproduced with the effective interaction.

EXTENDED MICROSCOPIC CLUSTER MODEL STUDY OF FOUR NUCLEON SCATTERING

d+d ( S -wave) elastic scattering phase shifts are studied in an extended microscopic cluster model in order to investigate cluster-breaking effects appearing in the low-energy scattering. The description of the cluster wave function is extended from a simple (0s) harmonic-oscillator shell model to a few-body model, in which the wave function of the sub-system is determined with the Stochastic Variational Method (SVM). To compare the cluster breaking effects with realistic and effective interactions, we employed the G3RS potential as a realistic interaction and the Minnesota (MN) potential as an effective interaction. The calculated phase shifts show that t+p and 3 He +n channels are strongly coupled to the d+d channel for the case of the realistic interaction (G3RS). On the contrary, the coupling of these channels plays a relatively minor role for the case of the effective interaction (MN).

Cluster virial expansion for the equation of state of partially ionized hydrogen plasma

We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-virial expansion. We use the Beth-Uhlenbeck approach to calculate the second virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase shifts and binding energies. Experimental scattering cross-sections as well as phase shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase shift calculation, we generalize the cluster-virial expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the virial expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semiempirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second virial coefficient for the electron-atom interaction represents a benchmark for other, semiempirical approaches.

Phase shift formulas in uniaxial media: an application to waveplates

The calculation of phase shift and optical path difference in birefringent media is related to a wide range of applications and devices. We obtain an explicit formula for the phase shift introduced by an anisotropic uniaxial plane-parallel plate with arbitrary orientation of the optical axis when the incident wave has an arbitrary direction. This allows us to calculate the phase shift introduced by waveplates when considering oblique incidence as well as optical axis misalignments. The expressions were obtained by using Maxwell's equations and boundary conditions without any approximation. They can be applied both to single plane wave and space-limited beams.

Fast array processor for the noiselet reverberation model.

The noiselet reverberation model, instead of transmitting the pulse itself, transmits a superposition of many copies of the pulse, each copy with a random amplitude and phase. This allows the simulation to mimic the point scatterer method without requiring a prohibitively large number of scatterers. It uses the GRAB ray model to introduce the propagation information. It provides a real-time high-fidelity simulation, providing element-level time series as an output for a planar array of receivers. However, it is presently limited by the phase shift calculations required by the frequency-domain beamformer to about 20 receivers without an unacceptable trimming of the number of rays used. Here, an approach is demonstrated that significantly improves the speed of this computation by identifying those receivers requiring the same phase shift to within a given specified error, such that only a single phase shift computation is required. These receivers fall onto a finite width strip, or quasi stave, that is not required to be parallel to element rows or columns. Along with providing a significant speed-up to the calculation, the approach becomes more efficient as the number of receivers increases, thereby allowing real time simulations using receiver arrays of over 100 elements.

Accurate calculation of phase shifts for three-body reactions with the adiabatic expansion method

In this work we describe a new efficient method to compute accurate scattering phase shifts. The method is based on the Kohn Variational Principle. When applied to three-body reactions described through the adiabatic expansion method, a fast convergence of the phase shift (similar to the convergence of the energy for bound states) is found.

Series of doubly excited states 3Se of Li+ below the N = 2 threshold of Li2+**Research work supported by the NSERC of Canada.

We use a numerical procedure developed earlier, based on the Harris–Nesbet variational calculation of phase shifts for elastic scattering of electron from Li2+ (Gien 2003 J. Phys. B: At. Mol. Opt. Phys. 36 2291), to determine the series of doubly excited states 3Se of Li+ at energies below the N = 2 threshold of Li2+. Our results of position and width for the low-lying doubly excited states are to be compared with those obtained by other research groups employing various different numerical methods for their calculations. This work provides a new set of higher lying doubly excited state resonances 3Se of Li+ to be compared with those determined with a completely different numerical method by Chung and Lin (1998 At. Data and Nucl. Data Tables 69 101). In addition, we are also able to determine five more of these doubly excited states, 3Se(2,11a), 3Se(2,12a), 3Se(2,10b), 3Se(2,11b) and 3Se(2,12b), which lie very close to the N = 2 excitation threshold of Li2+. We discuss the results of our work in comparison with those of other research groups, stressing the significant accuracy of our method and its relevant research perspective.

Use of stabilization by uniformly charged sphere for the resonance states calculations

The possibility of using the uniformly charged sphere with the variable charge and constant radius for accurate phase shift and resonance states parameters calculations is investigated. It is demonstrated on the example of the Hazy-Taylor model problem that the proposed numerical technique provides the relative errors about 1% for the phase shift function and resonance state parameters (energy and width). The choice of the optimal basis set for such calculations is discussed also.

Structural Interpretation of J Coupling Constants in Guanosine and Deoxyguanosine: Modeling the Effects of Sugar Pucker, Backbone Conformation, and Base Pairing

The (3)J(C8-H1'), (3)J(C4-H1'), (1)J(C8-H8), (1)J(C1'-H1'), (1)J(C2'-H2'), and (1)J(C2'-H2'2) indirect scalar coupling constants were calculated with the density functional theory in the deoxyguanosine and riboguanosine molecules. The following geometry descriptors were considered in analysis of the structural dependence of the six J couplings: the glycosidic torsion angle chi and conformation of the hydroxymethyl group at the C4' carbon of sugar mimicking the backbone residue and the sugar pucker (C2'-, C3'-endo). The (3)J(C8-H1') and (3)J(C4-H1') couplings, which are typically assigned to the chi torsion, also depended on the sugar pucker, although the calculated dependence of the latter coupling on sugar pucker was nearly negligible. New parametrization of the Karplus equations, taking into account the stereoinversion effect at the glycosidic nitrogen atom and solvent effects, was calculated for the (3)J(C8-H1') and (3)J(C4-H1') coupling assigned to the chi torsion. The calculated phase shift of chi torsion angle in these new Karplus equations was larger by approximately 10 degrees compared to its commonly accepted value of 60 degrees (Wijmenga, S. S.; van Buuren, B. N. M. Prog. NMR Spectrosc. 1998, 32, 287.). The calculated (1)J(C2'-H2') and (1)J(C2'-H2'2) coupling dominantly depended on the sugar type (deoxyribose or ribose) and its pucker, while the (1)J(C1'-H1') and (1)J(C8-H8) coupling dominantly depended on the glycosidic torsion angle, although quantitatively, all four (1)J couplings depended on both geometry parameters. The dependences of j-couplings on the torsion angle chi calculated in isolated nucleosides were compared with those taking into account the effect of base pairing occurring in the WC/SE RNA base pair family, which appeared to be minor. The calculated (3)J couplings agreed well with available experimental data similarly as the (1)J couplings, although lack of experimental data diminished more reliable validation of the later couplings.

Electron-induced bond breaking at low energies in HCOOH and glycine: The role of very short-livedσ∗anion states

Cross sections for dissociative electron attachment (DEA) to formic acid and glycine are calculated by the resonant $R$-matrix theory. A model with one effective reaction coordinate close to the O-H stretch motion is employed. The choice of the anion $R$-matrix pole and the surface amplitude as functions of the reaction coordinate for formic acid are based on scattering phase-shift calculations using the finite element discrete model. For glycine the input parameters are adjusted to reproduce experimental data. The results show that the mechanism of DEA in these molecules is similar to that for the hydrogen halides and involves electron capture into a ${\ensuremath{\sigma}}^{\ensuremath{\ast}}(\text{OH})$ orbital so that no ${\ensuremath{\sigma}}^{\ensuremath{\ast}}/{\ensuremath{\pi}}^{\ensuremath{\ast}}$ coupling is required. Nonlocal effects play an important role for both molecules. In particular, pronounced steps and cusps are seen at the vibrational excitation thresholds. A sharp threshold peak in glycine is interpreted as a vibrational Feshbach resonance.

Variable toroidal ferrite phase shifter

Careful design of the magnetic bias circuit used in ferrite phase shifters can help to reduce space, weight and energy consumption. Low reluctance circuits must avoid air-gaps and this can be achieved using toroidal-shaped ferrite inserts positioned inside a rectangular waveguide. Here, these ferrite inserts are fabricated using a viscous plastic processing method that avoids machining and produces a continuous magnetic circuit. Finite-element methods are used to initially model the magnetostatic solution for the bias circuit before being used to analyse the microwave performance of a double toroid phase shifter. A closed-form technique is introduced to model the dielectric slab waveguide impedance transformer. The final insertion loss was < 1 < dB over the 9.5 < 10.3 <GHz band and return loss of 20 < dB was achievable. The phase shift calculation agrees to within 10< of the measured values.