Phase Shift Differences Research Articles

Elastic energy losses of ions and atoms in atomic collisions

An expression for the elastic energy loss of ions and atoms in atomic collisions has been obtained by making use of the Thomas-Fermi potential. It is shown that the phase shift differences the energy loss depends on may be found accurately enough in the quasiclassical approximation and the infinite series comprising the summation over all the impact parameters may be converted into a compact formula. In a broad energy range the elastic energy losses prove to be a universal function of the reduced energy ε. The values of this function are tabulated. In the limiting cases of small, ε≤1, and large, ε⪢ ka, energies (where k is the particle momentum in the center of mass system and a is the Thomas-Fermi-Firsov screening radius) the expression obtained reduces to the result of Lindhard et al. and to that found in the Born approximation, respectively. It is shown that the charge state of the projectile, as a rule, weakly affects the elastic stopping power.

Experimental verification of a spin effect in photoemission: Polarized electrons due to phase-shift differences in the normal emission from Pt(100) by unpolarized radiation.

A theoretical prediction of Tamura and Feder has been experimentally verified: Photoelectrons from the fourfold-symmetric surface of a centrosymmetric crystal, Pt(100), can be polarized even if the incident radiation is unpolarized and the electrons are emitted normal to the surface. For 21.2- and 16.9-eV photon energies, a spin-polarization component ${\mathit{P}}_{\mathit{y}}$ perpendicular to the reaction plane is found. The degree of polarization is up to 15% and does not change when the crystal is rotated about its surface normal. This supports strongly the prediction that the effect is due to phase-shift differences.

Scattering phases in low energy electron diffraction from spot profile analysis and from multiple scattering theory

Spot Profile Analysis Low Energy Electron Diffraction (SPA-LEED) on pseudomorphic submonolayers of Fe(110) on W(110) provides experimental access to phase shift differences between wavelets scattered from Fe top-layer terraces and from the uncovered W-surface, respectively. These phase shifts are alternatively determined within a dynamical LEED calculation and agree surprisingly well with the experimental results.

Hg 5dand 6s: Multichannel quantum-defect analysis of experimental data

Experimental spin-polarization data for the Hg 6s Cooper minimum and dipole-transition amplitudes and phase-shift differences for photoionization of the Hg 5d and 6s shells (eight channels) in the photon-energy region from the $^{2}$${\mathit{D}}_{3/2}$ threshold up to 35 eV (kinetic energies from 0 to 20 eV) are presented and compared with new relativistic random-phase approximation calculations. The data were evaluated from an experimental data set, quantum mechanically ``complete,'' consisting of cross-section and photoelectron spin-polarization data. For the 5d subshells the results show strong interchannel coupling between the outgoing p and f continuum channels. The results for Hg 6s could be used for an independent determination of the photoelectron angular distribution parameter \ensuremath{\beta} in the Cooper-minimum region. This region is shown to be perturbed by numerous two-electron excitations, which might be a possible explanation for the controversy on its location.

Angle- and spin-resolved photoelectron spectroscopy in the region of the 6s6p2 autoionisation of Tl

An angle-, energy- and spin-resolved photoionisation experiment was performed in the region of the 6s6p2 autoionisation resonances of thallium. Using monochromatic circularly polarised synchrotron radiation the energy dependence of the spin-polarisation parameters A, xi and alpha and the angular asymmetry parameter beta of the differential cross section were determined. In the wavelength region investigated these dynamical parameters show a pronounced variation which agrees well with the results of the random phase approximation with exchange' calculation by Cherepkov (1980). A detailed discussion of the resonance behaviour for the autoionising states is given in terms of dipole-matrix elements and phaseshift differences which are extracted from the experimental data.

Photoelectron spin-polarisation spectroscopy in the 5s5p2-autoionisation region of indium

Photoelectron spin-polarisation measurements of In(5s25p) 2P1/2 were performed in the autoionisation region of the 5s5p2-configuration using monochromatic circularly polarised synchrotron radiation at the electron storage ring BESSY. The autoionising levels are analysed in terms of partial cross section, dipole matrix elements and phase-shift differences. In addition the measured photoelectron spin-polarisation data were used for an independent check for the assignments of the autoionising levels.

Magnetic analysis of some large seamounts in the North Atlantic

An analysis of the magnetic structure of Plato and Atlantis seamounts in the North Atlantic was made using the phase-shifting technique of Schouten [9]. The possibility of distinguishing the age of the seamounts from the age of their adjacent seafloor using magnetic data was investigated. The method described proved simple and effective, but showed that age determinations cannot reliably be made from magnetics for the seamounts in question, since the variation of the position of the palaeomagnetic poles during the Cainozoic is not large enough to produce appreciable phase-shift differences in this part of the Atlantic. The polarization is normal. Since smaller seamounts also show a predominance of normal magnetization, this may mean that viscous remanent magnetization (VRM) dating from the present normal period, the Brunhes, is involved. VRM may lead to strong magnetizations in coarse-grained rock as shown by DSDP results. This may result into a general overprinting of thermoremanence (TRM) by VRM, thus glossing over reversed thermoremanent polarizations. Large seamounts thus may appear as normally polarized bodies. The statistics of reversely versus normally polarized seamounts may be explained by the same effect. This implies that palaeomagnetic pole and age determinations based on apparent magnetization directions modelled from the magnetic anomaly pattern over seamounts may be inaccurate.

Implications of anomalous isospin violation for the low energy nucleon-nucleon interaction

Quark mass differences are used to derive an anomalous (i.e., due to the strong interactions) isospin violating potential. The potential includes the effects of pseudoscalar ($\ensuremath{\pi}\ensuremath{-}\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$) and vector meson ($\ensuremath{\rho}\ensuremath{-}\ensuremath{\omega}$) mixing. The finite $\ensuremath{\rho}$ width is included. Low energy $\mathrm{nn}$, $\mathrm{pp}$, and $\mathrm{np}$ phase shift differences are calculated in terms of the fundamental coupling constants. Despite considerable uncertainty in the coupling constants, it is possible to understand the very small $\mathrm{nn}$ and $\mathrm{pp}$ scattering length differences. Furthermore, it appears that effects in the $l>0$ partial waves at finite energies are large enough to be observable in the next few years. Estimates of effects in bound nuclei are presented. These include calculations of the contributions to mirror nuclei binding energy differences and to isospin mixing for a few characteristic cases. In most of those cases the anomalous isospin breaking contributions are of roughly the same size as observed discrepancies. However, inclusion of short range correlations substantially reduces the calculated effects in these cases.NUCLEAR REACTIONS $\mathrm{pp}$, $\mathrm{pn}$, and $\mathrm{nn}$ elastic scattering, $E=0\ensuremath{-}350$ MeV, calculated phase shift differences due to anomalous isospin breaking. Effects in finite nuclei estimated.

Theory of spin polarisation phenomena in molecular photoionisation processes

The angular distribution of molecular photoelectrons with defined spin orientation ejected by polarised or unpolarised light from unoriented diatomic or linear polyatomic molecules is derived in the dipole approximation. Its general structure is the same as in atoms and is defined by five independent parameters. Expressions for these parameters in terms of dipole matrix elements and phaseshift differences are presented. The influence of the spin-orbit interaction both in bound states and in the continuous spectrum is discussed. The degree of polarisation of molecular photoelectrons is expected to be lower than atomic photoelectrons due to the greater number of allowed transitions in molecules.

Angular distribution of molecular photoelectrons with defined spin orientation

The angular distribution of photoelectrons with defined spin orientation is derived for unoriented diatomic molecules exposed to polarised or unpolarised light. Its general structure is the same as in atoms and is defined by five independent parameters. Expressions for these parameters in terms of dipole matrix elements and phaseshift differences are presented.

Microscopic calculations for the two 5/2 − resonances of the nuclei 7Li and 7Be

Calculations for the two 5/2 − resonances of the mirror nuclei 7Li and 7Be are performed within the framework of cluster representations of nuclei. Using the same microscopic forces for both nuclei, their phase-shift and resonance width differences in the energy region of the 5/2 − resonances are shown to be mainly due to effects produced by the Coulomb interaction.

Generalized Wronskian theorem and integral representations for phase shift differences

A generalized Wronskian theorem is proved and applied to the partial wave equations of quantum scattering theory. Integral representations for phase shift differences are derived.

Reflection, Transmission, and Phase Shift of Light at Imbedded Optical Films

Reflectance and transmittance of polarized light at imbedded optical films are measured for films of different compositions and thicknesses. The reflectance/transmittance ratio of plane-polarized light from such films, whose reflectance equals the transmittance at normal incidence, can be varied from approximately 13 to 4 by rotating the plane of polarization. A method is described that permits measurement of differences of phase shift, between reflected and transmitted light, for optical films imbedded in dielectric media that are approximately homogeneous. Phase-shift differences were obtained for two different aluminum films. Whereas values approximately π/2 rad were expected, values of 106° and 74°, respectively, were found for light polarized parallel and perpendicular to the plane of incidence. The two interferograms, produced by light of these two polarizations, appear to be complementary. However, the two interferograms produced by either polarization and observed from opposite sides of the film are not complementary—thus indicating a variation of absorption of the film with optical-path difference.

Theoretical Study ofKl4Decay

${K}_{l4}$ decay is formulated in a way which allows the extraction of form factors and $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ phase-shift differences from data with limited statistics. The only assumptions required are $T$ invariance and a restriction to $S$ and $P$ waves in the final state, no other dynamical assumptions being required. It is shown that the assumption of the $\ensuremath{\Delta}I=\frac{1}{2}$ rule is not necessary if all ${K}_{l4}$ decays are taken into account. When the existing available data are analyzed in the simple extension of the Cabibbo-Maksymowicz approach in which all $P$-wave contributions are taken into account, there is a sign ambiguity in the $S$-wave $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ phase shift. This ambiguity is fundamental to this approach and can be solved only by means of another angular distribution. Such a distribution could be obtained from the existing data.