Phase Shift Differences Research Articles

Small separations and phase shift differences of $\ell$ = 0, 1 p-modes

Aims. We investigate the diagnostic potential of � = 0, 1 p-modes and the origin of the periodicity in their small separations. Methods. We used theoretical analysis, phase-shifts, modelling. and data analysis. Results. The periodicity in the small separations between modes of � = 0, 1 is determined by the acoustic radius of the base of the outer convective envelope. The mean variation is determined primarily by the structure of the inner core. The separations are related to the inner phase shifts differences δ1 − δ0 which we show can be determined directly from the frequencies. The modulation period is shifted slightly by the frequency dependence of the phase shifts and the amplitudes. We present results using data from the BiSON, IRIS, and GOLF experiments, and a solar model, all of which give a modulation period of ∼359 ± 5 μHz corresponding to an acoustic radius ∼1422 ± 20 s.

Minimization of Linear Dependencies Through the Use of Phase Shifters

Two-dimensional scan design with a linear test pattern generator is a practical built-in self-test technique, but it suffers from linear dependencies, which reduce the fault coverage. To alleviate this problem, networks of xor gates known as phase shifters can be employed. Current techniques based on the empirical criterion of imposing large phase shift differences (channel separations) between successive scan chains cannot adequately remove the dependencies. In this paper, we present a method that addresses explicitly the minimization of linear dependencies through appropriate selection of phase shift values. The method is based on the criterion of minimizing the linear dependencies in each cone of the circuit under test, and is applicable to any type of linear test pattern generator, be it linear feedback shift register of the external- xor or internal-xor type, cellular automaton, etc. Experimental results demonstrate the effect of the approach in increasing fault coverage.

Complete experiments in photoionization of atoms and molecules

The general discussion of possible complete experiments in photoionization of atoms and molecules is presented. In atoms the complete experiment must include measurements of the angular distribution and spin polarization of photoelectrons and the alignment or/and orientation of the residual ion. Two relations connecting the spin polarization parameters and the parameters characterizing the ion polarization state are presented. The complete experiments performed for Xe atom demonstrated a good agreement between theory and experiment. The complete experiments in photoionization of diatomic molecules can be performed by measuring photoelectron angular distributions for fixed-in-space molecules with circularly or elliptically polarized light. The use of additional experimental data like the angular asymmetry parameter β and the ratio of π to σ symmetry resolved cross sections made it possible to extract as many as 16 dipole matrix elements and phase shift differences for the C K-shell of CO molecule. Comparison with the recent calculations in the relaxed core Hartree–Fock approximation revealed discrepancies between theory and experiment.

O K-shell photoemission of the CO molecule: comparison between theory and experiment

Photoionization cross sections, dipole matrix elements and phase shifts are calculated for the O K-shell of the CO molecule using two theoretical models. One of them is a new version of the relaxed core Hartree–Fock approximation with a fractional charge. The value of this charge is considered as a fitting parameter. In this paper, the fractional charge 0.7 was used which gives a correct position of the maximum of the σ* shape resonance in the photoionization cross section. The other model is a modification of the multiple scattering method with overlapping atomic spheres. The dipole matrix elements and phase shift differences calculated by these two methods are compared with the corresponding values determined from the complete experiment by Cherepkov et al (2000 J. Phys. B: At. Mol. Opt. Phys. 33 4213).

On a complete experiment on photoionization of atoms

There are seven experimentally measurable parameters characterizing the photoionization of a closed shell atom in the electric dipole approximation, namely, the cross section, four parameters describing the photoelectron angular distribution and spin polarization, and two parameters describing the alignment and orientation of the residual ion. They are defined by five theoretical values, three dipole matrix elements and two phase shift differences. As a consequence, these seven experimental parameters are not mutually independent, and there must be two equations connecting them. One of these equations connecting the photoionization parameters was found earlier, and the second one for the particular case of photoionization of an np3/2 subshell of a closed shell atom is derived here. It connects the photoelectron parameters with the alignment and orientation of the residual ion. We also checked that there are no other independent relations between the parameters. From these facts it follows that a complete photoionization experiment is possible, and it must include the measurements of the parameters of both the photoelectron and the residual ion.

Characterization of σushape resonance in the C 1s ionization continuum of CO2 molecules

Angular distributions of photoelectrons from the carbon K-shell of fixed-in-spaceCO2 molecules have been measured in the region of the σushape resonance with an angle-resolved photoelectron–photoion coincidencetechnique. The detection of the photoions ejected to the parallel directionto the electric vector of the incident synchrotron radiation probesthe contribution of C 1s → εℓσuchannels. From the measured data a set of dipole matrix elementsand phase shift differences has been determined. Though thef-wave dipole matrix element appears to be the largest, the p-and h-wave matrixelements are of the same order of magnitude. This explains the absence of thenodal plane of a single partial wave in the measured angular distribution patterns.

Complete photoionization experiment in the region of the 2σg → σu shape resonanceof the N2molecule

Angular distributions of photoelectrons (ADPs) from the 2σgshell of a fixed-in-space N2 molecule have been measured for left- andright-elliptically polarized, as well as for linearly polarized, light. From these dataa set of dipole matrix elements and phase shift differences characterizing theprocess has been determined taking into account the acceptance angles of bothelectron and ion detectors, i.e. the complete experiment has been performed.Good agreement between the experimental and the relevant theoretical valuescalculated in the random phase approximation is obtained. Based on the results ofthe complete experiment, three-dimensional ADPs and ions are predicted fordifferent light polarizations.

Direct probe of the shape resonance mechanism in 2sigma(g)-shell photoionization of the N2 molecule.

Angular distributions of photoelectrons from a 2sigma(g) shell of fixed-in-space N2 molecules have been measured for left- and right-elliptically polarized and for linearly polarized light at several photon energies in the region of sigma(*) shape resonance. That allowed the determination of a set of dipole matrix elements and phase shift differences characterizing the process. These data clearly show the enhancement of the fsigma(u) partial cross section in the resonance simultaneously with an abrupt increase of the corresponding phase shift by pi, which is the first experimental demonstration of the nature of the sigma(*) shape resonance in homonuclear diatomic molecules.

Circadian phase-delaying effects of bright light alone and combined with exercise in humans

In a within-subjects (n = 18), counterbalanced design, the circadian phase-shifting effects of 3 h of 1) bright light (3,000 lx) alone 2) and bright light combined with vigorous exercise were compared. For each treatment, volunteers spent 3 nights and 2 days in the laboratory, typically receiving the treatment from approximately 2300 to 0200 on night 2. Bedtimes and waketimes were fixed to the volunteers' habits. Illumination was 50 lx during other wake hours and 0 lx during sleep. Bright Light Alone elicited a significant phase delay in rectal temperature minimum (70 min), but not in urinary 6-sulphatoxymelatonin (6-SMT) acrophase (20 min). Bright Light + Exercise elicited a significant phase delay in 6-SMT (68 min), but did not result in a significant difference in shift compared with Bright Light Alone. The study had adequate statistical power (80%) to detect phase-shift differences between treatments of approximately 2-2.5 h. Thus any antagonism of light shifts with exercise could not have been revealed. Within the limited exercise and light parameters of this study, the results suggest that exercise does not reliably modulate phase-shifting effects of late night bright light in humans.

The Kr M4,5N1N2,3 1P1 Auger decay: measurement of the transferred spin polarization and analysis of Auger amplitudes

The angular distribution of the transferred spin polarization ofKr M4,5N1N2,3 1P1 Auger electrons after primaryionization with circularly polarized light has been measuredand the intrinsic parameters δ1 and ξ1 have beendetermined from experimental results. The explicit equationinterconnecting the intrinsic parameters for Auger decay from a(d5/2)-1 core hole has been derived and is used for a detailed analysis of the transitions in terms of Auger amplituderatios and phase shift differences. The results indicate thatthe final ionic state is well described by a 1P symmetry. Additional constraints imposed on the intrinsic parameters forsinglet states prevent unambiguous determination of Augeramplitudes from experiment even in the limiting case of pureLS coupling.

Testing the feasibility of a complete Auger decay experiment by spin- and angle-resolved electron spectroscopy on XeN4O2,3O2,3 3P1

The intrinsic parameters β1 and γ1 weredetermined separately for the first time by explicitmeasurement of the angular distribution of the transferred spinpolarization of Xe N4O2,3O2,3 3P1 Auger electronsafter primary excitation with circularly polarized light fromthe BESSY-II helical undulator UE56/1. The feasibility of acomplete experiment for the Auger decay, i.e. extraction ofCoulomb matrix elements from the experimental data, isdiscussed and reveals a new fundamental equation connecting theintrinsic parameters of Auger decay. An analysis procedure isperformed, yielding a well confined solution space foramplitude ratios and phase shift differences.

Molecular-frame photoelectron angular distributions in inner-valencephotoionization of N2

A full partial-wave analysis of photoionization to two inner-valencestates of N2+ has been achieved on the basis of experimentalmolecular-frame photoelectron angular distributions determined by thevelocity imaging photoionization coincidence (VIPCO) technique. The twostates (2σg)-1 2Σg+ and F2Σg+ are assumed to dissociate rapidly so that theaxial recoil approximation applies. The dipole matrix elements and phaseshift differences show the strong influence of the known shape resonance,and are in reasonable agreement with some existing theoreticalpredictions.

Forced Rayleigh scattering studies of mixtures of amplitude and phase gratings in methyl yellow/alcohol solutions

Forced Rayleigh scattering (FRS) studies have been carried out on methyl yellow/alcohol solutions at two different probe wavelengths (633 and 543 nm). The signal shapes observed at the two wavelengths are quite different: using ethanol and 2-propanol as solvents, we observe at 633 nm a decay–grow–decay (DGD) shape similar to profiles frequently reported in the literature, while at 543 nm we observe a DGD shape in which the signal at the local minimum does not reach the baseline. In principle, the nonzero minimum can be accounted for by a difference (due to amplitude/phase-grating mixtures) in the phase shifts of light scattered from the photoproduct and ground-state molecules. To test this hypothesis, we first show in a straightforward manner that the signal can be approximated as the product of a polynomial and an exponential decay, which allows for data reduction of profiles with zero or nonzero phase-shift differences. Using this approach, the diffusion coefficients measured using the two probe wavelengths are found to be the same to within an uncertainty of 2%–3%. The results provide strong evidence that the difference in signal shapes is caused by amplitude/phase-grating mixtures within the methyl yellow/alcohol system, and imply that diffusion coefficients can be measured without difficulty for other FRS systems characterized by such mixtures.

Laser photoionization of polarized Ar atoms produced by excitation with synchrotron radiation

The laser-synchrotron radiation combination technique has recently been incorporated into an apparatus for two-dimensional photoelectron spectroscopy of atoms and molecules in order to investigate photoionization dynamics of polarized atoms. Ground state Ar atoms are excited with linearly polarized synchrotron radiation to Rydberg states lying below the first ionization potential. The aligned atoms thus formed are ionized by irradiation of a laser which is also linearly polarized. Photoelectrons emitted in the direction of the electric vector of the synchrotron radiation are sampled and energy analysed. The photoelectron angular distribution is measured with respect to the electric vector of the laser. Expressions which correlate the asymmetric coefficients for the angular distribution with theoretical dynamic parameters involving transition dipole matrix elements are derived. The anisotropy of the present angular distribution can be reasonably explained, assuming that the matrix elements and phase shift differences are essentially independent of the total angular momentum quantum number of the final state and that the spin-orbit interaction in the continuous spectrum is small.

Higher multipole and retardation effects in the spin and polarization correlations of polarized photoelectrons ejected from the 2pJ subshell by polarized photons - a nonrelativistic approach

We study spin and polarization correlations in atomic photoionization from npJ subshells, including the first retardation corrections to the dipole approximation. This extends previous work on distributions of unpolarized photoelectrons ejected by polarized photons (Bechler A and Pratt R H 1989 Phys. Rev. A 39 1774, 1990 Phys. Rev. A 42 6400). A nonrelativistic Pauli-Schrödinger approach in a self-consistent central potential is used, neglecting spin-orbit coupling. There are nontrivial correlations, even in this nonrelativistic approximation, and even without taking into account spin-orbit coupling, provided the electron is ejected from a subshell with a definite value J of the total angular momentum. (However, if summation over J is performed, one would have to include the spin-orbit coupling in order to obtain any remaining spin and polarization correlations in the nonrelativistic approach). Explicit formulae are given in terms of dipole and quadrupole radial matrix elements and phase shift differences. Results are compared with exact numerical calculations. Corrections to the dipole approximation are generally small at low energies and low Z, but increase with energy and atomic number. Including the first retardation corrections significantly improves agreement.

Charge dependence of the nucleon-nucleon interaction

Based upon the Bonn meson-exchange-model for the nucleon-nucleon $(\mathrm{NN})$ interaction, we calculate the charge-independence breaking (CIB) of the $\mathrm{NN}$ interaction due to pion-mass splitting. Besides the one-pion exchange (OPE), we take into account the $2\ensuremath{\pi}$-exchange model and contributions from three and four irreducible pion exchanges. We calculate the CIB differences in the ${}^{1}{S}_{0}$ effective range parameters as well as phase-shift differences for partial waves up to total angular momentum $J=4$ and laboratory energies below 300 MeV. We find that the CIB effect from OPE dominates in all partial waves. However, the CIB effects from the $2\ensuremath{\pi}$ model are noticable up to D waves and amount to about 40% of the OPE CIB contribution in some partial waves, at 300 MeV. The effects from $3\ensuremath{\pi}$ and $4\ensuremath{\pi}$ contributions are negligible except in ${}^{1}{S}_{0}$ and ${}^{3}{P}_{2}.$

Charge asymmetry of the nucleon-nucleon interaction

Based upon the Bonn meson-exchange model for the nucleon-nucleon $(\mathrm{NN})$ interaction, we study systematically the charge-symmetry-breaking (CSB) of the $\mathrm{NN}$ interaction due to nucleon mass splitting. Particular attention is paid to CSB generated by the $2\ensuremath{\pi}$-exchange contribution to the $\mathrm{NN}$ interaction, $\ensuremath{\pi}\ensuremath{\rho}$ diagrams, and other multimeson exchanges. We calculate the CSB differences in the ${}^{1}{S}_{0}$ effective range parameters as well as phase shift differences in $S,$ $P,$ and higher partial waves up to 300 MeV laboratory energy. We find a total CSB difference in the singlet scattering length of 1.6 fm which explains the empirical value accurately. The corresponding CSB phase-shift differences are appreciable at low energy in the ${}^{1}{S}_{0}$ state. In the other partial waves, the CSB splitting of the phase shifts is small and increases with energy, with typical values in the order of $0.1\ifmmode^\circ\else\textdegree\fi{}$ at 300 MeV in $P$ and $D$ waves.

Direct Determination of Partial Wave Contributions in theσ*Shape Resonance of CO Molecules

The first complete experiment for the C $K$-shell of CO molecules in the region of the ${\ensuremath{\sigma}}^{*}$ shape resonance has been performed by detecting photoelectrons in coincidence with fragment ions. Four ratios of dipole matrix elements and four phase shift differences have been extracted from the experimental data. Their analyses show that, in the ${\ensuremath{\sigma}}^{*}$ shape resonance due to the $l$ mixing, $d$ and $f$ partial waves give the main contribution to the cross section, and $f$ and $g$ waves give the main contribution to a rapid increase of phase shift by $\ensuremath{\pi}$.

Hydrophone transduction mechanism

A sensing portion for an interferometric planar hydrophone is disclosed which comprises: a support assembly; a plurality of hollow compliant mandrels mounted to the support assembly in a fixed planar relationship with respect to each other to form a planar configuration; a sensing optical fiber sequentially wound around each of the plurality of mandrels to form a single, serial, optical sensing arm or path between an input position on a first one of the plurality of mandrels and an output position on a last one of the plurality of mandrels; and an acoustically transparent material encapsulating the sensing portion to form a sealed compliant planar hydrophone. In an operational system, an interferometric planar hydrophone is disclosed which comprises: the sensing portion in which the sensing arm is operative to measure a predetermined measurand in a preselected environment and which sensing portion further includes a reference optical fiber environmentally isolated from the predetermined measurand; a light source for transmitting coherent light to both of the sensing and reference optical fibers; and circuitry responsive to light received from the sensing and reference optical fibers for developing an output signal indicative of phase shift differences between the sensing and reference optical fibers to determine the predetermined measurand.

Photoionization of an open-shell atom with open-shell final ionic state: A spin-resolved study of photoelectrons above the Tl + (6s6p) 3P 1 limit

Spin-resolved measurements of the dynamic photoionization parameters for photoelectrons from thallium atoms are presented for the Tl + (5d 106s6p) 3P 1 final ionic state in the complex spectral region from 90 to 77 nm. For a complete description of this ionization process more than three transition matrix elements are needed since neither the initial nor the final state has closed-shell configuration. An approximate determination of matrix elements and phase shift differences is carried out. In addition, it is discussed how complete information may in principle be obtained.