Calculated Phase Shifts Research Articles

Anomaly-free singularities in the generalized Kohn variational method

We have carried out an analysis of singularities in Kohn variational calculations for low-energy (e+–H2) elastic scattering. Provided that a sufficiently accurate trial wavefunction is used, we argue that our implementation of the Kohn variational principle necessarily gives rise to singularities which are not spurious. We propose two approaches for optimizing a free parameter of the trial wavefunction in order to avoid anomalous behavior in scattering phase shift calculations, the first of which is based on the existence of such singularities. The second approach is a more conventional optimization of the generalized Kohn method. Close agreement is observed between the results of the two optimization schemes; further, they give results which are seen to be effectively equivalent to those obtained with the complex Kohn method. The advantage of the first optimization scheme is that it does not require an explicit solution of the Kohn equations to be found. We give examples of anomalies which cannot be avoided using either optimization scheme but show that it is possible to avoid these anomalies by considering variations in the nonlinear parameters of the trial function.

Scaling functions applied to three-body recombination ofCs133atoms

We demonstrate the implications of Efimov physics in the recently measured recombination rate of Cesium-133 atoms. By employing previously calculated results for the energy dependence of the recombination rate of Helium-4 atoms, we obtain three independent scaling functions that are capable of describing the recombination rates over a large energy range for identical bosons with large scattering length. We benchmark these and previously obtained scaling functions by successfully comparing their predictions with full atom-dimer phase shift calculations with artificial Helium-4 potentials yielding large scattering lengths. Exploiting universality, we finally use these functions to determine the 3-body recombination rate of Cesium-133 atoms with large positive scattering length, compare our results to experimental data obtained by the Innsbruck group and find excellent agreement.

Contribution of the Gouy phase to two-pathway coherent control of the photoionization and photodissociation of vinyl chloride

The electric field of a light wave accumulates a pi phase shift as it passes through a focus. We show here how this effect, known as the Gouy phase, may be used to control the branching ratio of a unimolecular reaction when the products are formed with different numbers of photons. We demonstrate this control method for the ionization and dissociation of vinyl chloride, using absorption of 177 and 532 nm photons to induce a pair of interfering paths. Excellent agreement between the observed and calculated phase shift as a function of the axial coordinate of the laser focus indicates that fragmentation occurs via a ladder switching mechanism. The axial dependence of the modulation depth is evidence of loss of coherence at higher internal temperatures of the molecule.

Modelling dissociative dynamics of biosystems after metastable electron attachment: the sugar backbones

The damage induced by radiation in cells is currently described via low-energy attachment of electrons produced in the biological medium by the primary radiation. Therefore the corresponding metastable anionic states are obtained in this work from multichannel quantum calculations which, in the present study, involve β-D-ribose and β-D-deoxyribose molecular fragments from RNA and DNA structures. The scattering attributes associated with the resonant processes are derived from the computed total, elastic cross sections by means of a high-level Breit-Wigner analysis of the calculated phase shifts. The present procedure is shown to provide a powerful tool for extracting the resonance parameters from the scattering data even in the presence of broad, overlapping resonances which typically occur in the resonant dynamics of complicated biosystems after electron attachment effects.

Amplitude-phase methods for analyzing the radial Dirac equation: calculation of scattering phase shifts

Approaches inspired by a recent amplitude-phase method for analyzing the radial Dirac equation are presented to calculate phase shifts. Regarding the spin- and pseudo-spin symmetries of relativistic spectra, the coupled first-order and the decoupled second-order differential forms of the radial Dirac equation are investigated by using a novel and the ‘classical’ amplitude-phase methods, respectively. The quasi non-relativistic limit of the amplitude-phase formulae is discussed for both positive and negative energies. In the positive (E> mc2) low-energy region, the relativistic effects of scattering phase shifts are discussed based on two scattering potential models. Results are compared with those of non-relativistic calculations. In particular, the numerical results obtained from a rational approximation of the Thomas–Fermi potential are discussed in some detail.

Nonlinear phase conjugate ultrasonic waves in moving media

The basic principle of acoustic wave phase conjugation provides compensation of phase incursions during back propagation of the phase conjugate waves (PCW) towards the source of the primary emission. This feature of PCW results from time reversal invariance of acoustic field in a stationary medium. In moving media or in the presence of flows the time reversal invariance is broken resulting in essential modification of PCW properties. The incident wave spatial distribution is not reproduced completely by the phase conjugate wave and the phase incursions are not compensated any more. In the present paper the general theory of PCW propagation in moving nonlinear media is developed. The theory is applied for description of PCW acoustic rays and calculation of noncompensated phase shift of PCW on the source of the primary probing wave. The treatment of the phase shift of the PCW is developed as a new method of diagnostics and imaging of flow velocity distributions in liquid. The method is approved experimentally on examples of laminar and vortex flows and immersed fluid jet in water. Improvement of quality of the images of flows using nonlinear modes of propagation and interaction of phase conjugate waves is demonstrated.

Influence of Spin–Orbit Force on Nucleon–Nucleon Scattering in the Quark Delocalization Colour Screening Model

The symmetric spin–orbit interactions of one-gluon-exchange and confinement are included in the nucleon—nucleon phase shift calculation in the framework of quark delocalization colour screening model. The spin–orbit interaction has little influence on D wave phase shift. For the triplet P waves, 3PT is in good agreement with the experimental data and 3PLS is attractive but not strong enough, whereas 3PC is too strongly repulsive. Our results indicate that the symmetric spin–orbit interaction of one-gluon-exchange and confinement potential cannot give a good description of the triplet P wave phase shifts. More sophisticated considerations, the delocalization depending on the relative orientation between two cluster, might be needed to improve the description of P-wave NN interaction.

Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser

Knowledge about the temperature distribution inside solid-state laser crystals is essential for calculation of thermal phase shift, thermal lensing, thermally induced birefringence, and heat-induced crystal bending. Solutions for the temperature distribution for the case of steady-state heat loading have appeared in the literature only for simple cylindrical crystal shapes and are usually based on numerical techniques. For the first time, to our knowledge, a full analytical solution of the heat equation for an anisotropic cubic cross-section solid-state crystal is presented. The crystal is assumed to be longitudinally pumped by a Gaussian pump profile. The pump power attenuation along the crystal and the real cooling mechanisms, such as convection, are considered in detail. A comparison between our analytical solutions and its numerical counterparts shows excellent agreement when just a few terms are employed in the series solutions.

Doubly excited states 1De and 3De of He below the N = 2 threshold of He+**Research work supported by the NSERC of Canada.

The positions and widths of the three series of doubly excited-state singlet and triplet resonances 1De and 3De of He at energies below the N = 2 excitation threshold of He+ were determined through an accurate calculation of phase shifts employing a numerical procedure developed earlier by us for electron–hydrogenlike-ion scattering within the Harris–Nesbet variational method. Our results can be used to resolve the discrepancy existing among those obtained by various research groups for the middle-lying resonances of these series. Due to the high accuracy of our method, we were able to determine, for the first time, the positions and widths of several high-lying resonances very close to the threshold, and hence to confirm the definite existence of the c series of doubly excited states of the extremely narrow width for both singlet and triplet D waves as predicted by theory for He. We discuss our results in comparison with those obtained by other groups who employed completely different numerical methods for their calculations, stressing the significant accuracy of our method and its possible relevant future research perspective.

Calculations for very low energy scattering of positrons by molecular hydrogen

We give a progress report on ongoing calculations of phase shifts for very low energy elastic scattering of positrons by molecular hydrogen, using the generalised Kohn variational method. Further, provisional calculations of Zeff for molecular hydrogen at low energies are presented and discussed. The preliminary nature of the work is emphasised throughout.

The Coulomb scattering in momentum space for few-body systems

A new boundary condition method for Coulomb scattering in momentum space is applied to the two-, three- and four-nuclear charged-particle systems. The method is based on the two-potential theory with the short range potential and the rest auxiliary potential which can be handled numerically. We applied the method to obtain the Coulomb phase shifts for the two-body case. Our calculated phase shift is in very good agreement with the analytic one. The extended method to the three- and four-body systems is also discussed.

Erratum: Renormalization of theNNinteraction with a chiral two-pion exchange potential. II. Noncentral phases [Phys. Rev. C74, 064004 (2006)

We extend the renormalization of the NN interaction with Chiral Two Pion Exchange Potential to the calculation of non-central partial wave phase shifts with total angular momentum j<=5 . The short distance singularity structure of the potential as well as the requirement of orthogonality conditions on the wave functions determines exactly the number of undetermined parameters after renormalization.

Misregistration artifacts in image‐derived arterial input function in non‐echo‐planar imaging‐based dynamic contrast‐enhanced MRI

To characterize misregistration artifact in arterial input function (AIF) pixels in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) using a two-dimensional non-echo-planar imaging (EPI)-based gradient-recalled echo (GRE) sequence. Dynamic gadopentetate-enhanced MRI was acquired in the rat using a semikeyhole acquisition scheme. The AIF was obtained from abdominal aorta pixels. Different sliding-window reconstruction techniques were applied to determine which lines in a series of the semikeyhole acquisition were associated with the misregistration artifacts. The misregistration along the phase-encoding direction arose when k-space lines were acquired during the rise-time of the aortic gadolinium concentration. The maximum blood concentration of gadolinium estimated from the phase shift calculation agreed with that estimated from dosage. AIF misregistration results from a phase shift due to increasing gadolinium concentration in the aorta, and may need to be considered in small animal DCE-MRI studies with a high rate of rise in the AIF in high-field MR applications.

The Potential-Density Phase-Shift Method for Determining the Corotation Radii in Spiral and Barred Galaxies

We have developed a new method for determining the corotation radii of density waves in disk galaxies, which makes use of the calculated radial distribution of an azimuthal phase shift between the potential and density wave patterns. The approach originated from improved theoretical understanding of the relation between the morphology and kinematics of galaxies and of the dynamical interaction between density waves and the basic-state disk stars, which results in the secular evolution of disk galaxies. In this paper we present the rationales behind the method and the first application of it to several representative barred and grand-design spiral galaxies, using near-infrared images to trace the mass distributions, as well as to calculate the potential distributions used in the phase-shift calculations. We compare our results with those from other existing methods for locating the corotations and show that the new method both confirms the previously established trends of bar-length dependence on galaxy morphological types and provides new insights into the possible extent of bars in disk galaxies. The method also facilitates the estimation of mass accretion/excretion rates due to bar and spiral density waves, providing an alternative way of quantifying the importance of these features in disk galaxies. A preliminary analysis of a larger sample shows that the phase-shift method is likely to be a generally applicable, accurate, and essentially model-independent method for determining the pattern speeds and corotation radii of single or nested density wave patterns in galaxies. Other implications of the results of this work include that most of the nearby bright disk galaxies appear to possess quasi-stationary spiral modes; that these density wave modes, as well as the associated basic states of the galactic disks, slowly transform over the time span of a Hubble time due to a collective dissipation process directly related to the presence of the phase shift between the potential and density patterns; and that self-consistent N-particle systems contain physics not revealed by the passive orbit analysis approaches.

Blind phase shift estimation in phase-shifting interferometry

A blind phase shift estimation algorithm that allows simultaneous calculation of phases and phase shifts from three or more interferograms is presented. In phase-shifting interferometry, the phase shift errors introduce specific correlations between the calculated background intensity distribution and the fringe component. These correlations can be measured with a cross-power spectrum. By minimization of an objective function based on this cross-power spectrum, the actual phase shifts are estimated and used for phase recovery. The validity of this algorithm is verified by both the numerical simulation and the experiment results.

Renormalization of theNNinteraction with a chiral two-pion exchange potential. II. Noncentral phases

We extend the renormalization of the NN interaction with chiral two-pion exchange potential to the calculation of noncentral partial wave phase shifts with total angular momentum j{<=}5. The short distance singularity structure of the potential, as well as the requirement of orthogonality conditions on the wave functions, determines exactly the number of undetermined parameters after renormalization.

Alpha–alpha potential up to 47.3 MeV bombarding energy

Experimental differential cross sections for elastic scattering of two α particles have been fitted with an l-independent non-monotonic real potential up to 34.2 MeV (lab) and a complex potential with non-monotonic real part from 35.1 to 47.3 MeV (lab). The calculated phase shifts, in general, agree with those derived from the phase shift analyses of the experimental cross sections. In particular, the s- and d-wave phase shifts tend to zero in the limit of zero energy implying the absence of any bound state. Thus, 8Be is unbound in the potential and the calculated decay width of about 6 eV agrees with the observed one. This potential has its roots in the energy-density functional (EDF) theory with the sudden approximation. In fact, the calculated angular distributions using the derived EDF potential are in reasonable agreement with the experimental data at some energies up to 15.2 MeV (lab). Modifying the Buck, Friedrich and Wheatley (BFW) potential by adding a small repulsive core leads to about the same quality of fits. The modified BFW potential, however, binds 8Be in Pauli forbidden states, and s- and d-wave phase shifts in it tend to 2 π and π, respectively, in the limit of zero energy.

Quantum corrections to the second virial coefficient in one dimension

The semiclassical limit of the quantum mechanical second virial coefficient in one dimension is examined using using realistic interatomic potentials for $^{4}\mathrm{He}$, ${\mathrm{H}}_{2}$, and $^{20}\mathrm{Ne}$. A direct transcription from three dimensions of the quantum correction series through ${\ensuremath{\hbar}}^{4}$ gives results for ${B}_{2}$ within 0.5% of those from the phase shift calculations for $^{4}\mathrm{He}$ at $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $^{20}\mathrm{Ne}$ at $30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

High accuracy ultrasonic air temperature measurement using multi-frequency continuous wave

This article describes a highly accurate and instant-response ultrasonic system for measuring air temperature using multi-frequency continuous waves (MFCW). The proposed system uses a method heretofore applied only to radio frequency distance measurement but not to air-based ultrasonic systems. The method presented here is based upon the comparative phase shifts generated by three continuous ultrasonic waves of different but closely spaced frequencies. It uses the ultrasonic measurement of the changes in the speed of sound in the air to determine the temperature of bulk air. The changes in the speed of sound are calculated from phase shift of multi-frequency continuous wave. In our experiment, in a temperature-controlled chamber, we placed two 40 kHz ultrasonic transducers face to face with a constant distance in between. We use MFCW of 40/41.8/42 kHz. A single-chip microprocessor-based signal generator and phase detector are used to record and calculate phase shift and temperature. In a proof-of-concept experiment, it is accurate to ±0.4 °C from 0 to 80 °C with 0.05% resolution and temperature changes are instantly reflected within 100 ms.

The overall phase shift and lens effect calculation using Gaussian boundary conditions and paraxial ray approximation for an end-pumped solid-state laser

In this work, the inhomogeneous equation of heat conduction was exactly solved by applying inhomogeneous boundary conditions for laser crystals of aspect ratio=1 (aspect ratio=radius of the laser rod/length of the laser rod). We have shown that the paraxial ray approximation leads the solution to be a function ofr2, that is, the approximation is equivalent to a situation in which a homogeneous pump source is used. The solution was then used to derive expressions for the overall phase shift, focal length of the thermal lens and the end effect induced curvature of the end face. The expressions were then applied to Nd:YAG laser medium. The result shows a meaningful correction of the order of 0.001 cm to the focal length of Nd:YAG rod for 3 W source power and beam waist of 100 μm.