Energy-dependent Phase Shifts Research Articles

Electronic confining effects in Sierpiński triangle fractals

Electron confinement in fractal Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski triangles (STs) on Ag(111) is investigated using scanning tunneling spectroscopy and theoretically simulated by employing an improved two-dimensional (2D) multiple scattering theory in which the energy-dependent phase shifts are explicitly calculated from the electrostatic potentials of the molecular building block of STs. Well-defined bound surface states are observed in three kinds of triangular cavities with their sides changing at a scale factor of 2. The decrease in length of the cavities results in an upshift of the resonances that deviates from an expected inverse quadratic dependence on the cavity length due to the less efficient confinement of smaller triangular cavities. Differential conductance maps at some specific biases present a series of alternative bright and dark rounded triangles preserving the symmetry of the boundary. Our improved 2D multiple scattering model reproduces the characteristics of the standing wave patterns and all features in the differential conductance spectra measured in experiments, illustrating that the elastic loss boundary scattering dominates the resonance broadening in these ST quantum corrals. Moreover, the self-similar structure of STs, that a larger central cavity is surrounded by three smaller ones with a half side length, gives rise to interactions of surface states confined in neighboring cavities, which are helpful for the suppression of the linewidth in differential conductance spectra.

Temperature- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystals.

This paper reports temperature- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystals, involving forbidden (002) and weak (222) reflections. Phase determination based on multiple-beam diffraction is employed to estimate phase shifts from (002)-based {(002)(375)(373̅)} four-beam cases and (222)-based { (222)(5̅33̅)} three-beam cases in the vicinity of the Ge K edge for temperatures from 20 K up to 300 K. The forbidden/weak reflections enhance the sensitivity of measuring phases at resonance. At room temperature, the resonance triplet phases reach a maximum of 8° for the four-beam cases and -19° for the three-beam cases. It is found that the peak intensities and triplet phases obtained from the (002) four-beam diffraction are related to thermal motion induced anisotropy and anomalous dispersion, while the (222) three-beam diffraction depends on the aspherical covalent electron distribution and anomalous dispersion. However, the electron-phonon interaction usually affects the forbidden reflections with increasing temperatures and seems to have less effect on the resonance triplet phase shifts measured from the (002) four-beam diffraction. The resonance triplet phase shifts of the (222) three-beam diffraction versus temperature are also small.

Effect of the magnetism of manganese on the resistivity of liquid manganese–zinc alloys

The electrical resistivity of liquid MnxZn1−x alloys has been measured as a function of temperature between the liquidus and 850°C for a manganese concentration x from 0 to 0.3. The electrical resistivity results has been interpreted within the extended Faber–Ziman formalism taking into account energy dependent phase shifts. Spin-dependent scattering of the conduction electrons has been considered and shows a better agreement with the experimental values than the classical spin-independent approach.

Imaging ofsanddPartial-Wave Interference in Quantum Scattering of Identical Bosonic Atoms

We report on the direct imaging of s and d partial-wave interference in cold collisions of atoms. Two ultracold clouds of 87Rb atoms were accelerated by magnetic fields to collide at energies near a d-wave shape resonance. The resulting halos of scattered particles were imaged using laser absorption. By scanning across the resonance we observed a marked evolution of the scattering patterns due to the energy dependent phase shifts for the interfering s and d waves. Since only two partial-wave states are involved in the collision process the scattering yield and angular distributions have a simple interpretation in terms of a theoretical model.

Effects of the substrate on quantum well states: A first-principles study for Ag/Fe(100)

We have studied the properties of quantum well states in supported Ag(100) films on the Fe substrate by first-principles density-functional calculations. The energies of these quantum well states as a function of thickness N are examined in terms of the characteristic phase shift of the electronic wave function at the interface. These energy-dependent phase shifts are determined numerically for both the film-substrate and film-vacuum interfaces. It is also found that the substrate has a major effect on film stability, enhancing the stability of the N = 5 film and reversing that of the N = 2 film.

QPO sources observed from ginga

Ginga observations of the quasi-periodic oscillations of three low-mass binary X-ray sources, GX5-1 (centroid frequency: 5.5 Hz), X1820-303 (7.5 Hz) and Cyg X-2 (5.2 Hz) are presented. All these low-frequency QPO's were detected when the spectral hardness of the X-ray was positively correlated with the X-ray intensity. The centroid frequency and FWHM of these QPO's are consistent with being constant for all the three sources respectively. The relative amplitude of QPO increases with increasing X-ray energy in a energy range 5–18 keV for all the sources. For Cyg X-2, however, the relative amplitude below 5 keV is larger than that around 5 keV. Furthermore, energy dependent phase shifts as large as 70 m sec were found in the QPO of this source. Both the energy dependent phase shifts and QPO amplitude of Cyg X-2 can be reproduced if we introduce two oscillating parameters with a phase difference of 150 degrees.

Interaction of Si, Ge, and Be solutes with vacancies and interstitials in Ni

The solute-vacancy and the solute-interstitial binding energies for Si, Ge, and Be solutes in Ni matrix have been calculated, using the results of an augmented-plane-wave calculation of the electronic structure of the solute and the solvent atoms. The electronic wave function of the solute is expressed in terms of the wave functions of the unperturbed host lattice. This allows the partial densities of states (DOS) of different angular momentum type at the solute site to be written in terms of those at the solvent atom site and their energy-dependent phase shifts. It is found that the $d$ electron DOS which is large and dominant at the Ni site is rather small at the solute site for all the solutes studied here. At the Si and Ge sites the $p$ DOS is dominant while at the Be site both $s$ and $p$ components are important. The excess charge density displaced by the solute and the potential associated with it show the oscillatory behavior. The $3s$ and $4s$ electrons of Si and Ge, respectively, form bound states below the bottom of the Ni conduction band. These states influence in a profound manner the interaction of these solutes with both vacancies and interstitials. No bound state is formed in the case of Be, where the scattering states in the conduction band are the sole contributors to the interaction energy. We have found that Ge, even though oversized, has a positive binding energy of 0.28 eV with the interstitial in the mixed dumbbell configuration. The undersized Si and Be form mixed dumbbells with binding energies of 0.90 and 0.58 eV, respectively. Contrary to usual expectations the vacancy-solute binding is calculated to be rather strong, 0.73 and 0.55 eV, respectively, for Si and Ge in the nearest-neighbor vacancy-solute configuration. The corresponding interaction with Be is found to be repulsive with a binding energy of -0.32 eV.

Polarization transfer in the (p, n) reaction on light nuclei and nucleon-nucleon phase shifts at 30 and 50 MeV

The polarization transfer coefficient α t , for neutrons emitted in the forward direction in the charge exchange (p, n) reactions on 2H, 6Li and 7Li target nuclei for incident proton energies of 25–100 MeV has been calculated in the impulse approximation. The energy-dependent and energy-independent nucleon-nucleon phase shifts of Arndt and McGregor and the Yale phase shifts were used. Experimental values of α t, recently obtained at proton energies of 30 and 50 MeV are in disagreement with the results of our calculation based on the Yale phase shifts, but show a preference for the Arndt-McGregor phase shifts.

Modified Born Approximation and the Elastic Scattering of Electrons from Helium

We discuss the elastic scattering of electrons from helium atoms in terms of an energy-dependent central-potential model having the form $V(r)=2Zlimit of\text{}\left(\frac{\ensuremath{-}{\ensuremath{\Lambda}}^{2}}{{\ensuremath{\Lambda}}^{2}\ensuremath{-}{\ensuremath{\mu}}^{2}}\frac{{e}^{\ensuremath{-}\ensuremath{\mu}r}}{r}+\frac{{\ensuremath{\mu}}^{2}}{{\ensuremath{\Lambda}}^{2}\ensuremath{-}{\ensuremath{\mu}}^{2}}\frac{{e}^{\ensuremath{-}\ensuremath{\Lambda}r}}{r}\right)\ensuremath{-}\frac{\ensuremath{\alpha}}{{({r}^{2}+{d}^{2})}^{2}}\text{as}\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\mu},$ where $\ensuremath{\mu},\ensuremath{\alpha}$ are fixed constants (for He, $\ensuremath{\mu}=3.375$ and $\ensuremath{\alpha}=1.39$), and $d$ is an energy-dependent phenomenological parameter. The method of partial waves is adapted for a generalized Yukawa potential and a polarization potential. Phase shifts and scattering cross sections are calculated from our potential model using the first Born approximation and a modified form of it. We develop an effective-range theory for a generalized Yukawa and a polarization potential, and apply it to generate a set of energy-dependent electron-helium phase shifts in the region 0-500 eV. Recent experimental angular distribution data in the region 100-500 eV are rather satisfactorily accounted for by our potential model. Our results compare favorably with those of LaBahn and Callaway.

Effective range theory for multi-channel scattering

By considering a simple model for alpha-alpha scattering, the effects on the S-wave phase shift resulting from the first excited state of the alpha particle are investigated. Assuming that each channel contains a Coulomb repulsive field together with a hard core, effective range formulae for the multi-channel scattering problem are derived. From the results, the formulae for no hard core and/or no Coulomb field are written down. Special attention is given to the two-channel problem. The importance of these formulae is that the strongly energy-dependent phase shifts can be expressed in terms of slowly varying functions of energy, the M-matrix elements.

Pion-Nucleon Phase-Shift Analysis: 0-350 MeV

Several sets of energy-dependent pion-nucleon phase shifts have been obtained in the 0-350-MeV energy range. These solutions differ near the end of the energy range and in the signs and magnitudes of some of the small phases. There is very little difference among these solutions in their prediction of the observables, including the spin-rotation parameters. Some very difficult experiments are suggested to distinguish among the solutions.