Theory Of Angular Correlations Research Articles

Crossed-beam experiment for the scattering of low- and intermediate-energy electrons from BF3: A comparative study with XF3 (X = C, N, and CH) molecules.

Absolute differential cross sections (DCSs) for electron interaction with BF3 molecules have been measured in the impact energy range of 1.5-200 eV and recorded over a scattering angle range of 15°-150°. These angular distributions have been normalized by reference to the elastic DCSs of the He atom and integrated by employing a modified phase shift analysis procedure to generate integral cross sections (ICSs) and momentum transfer cross sections (MTCSs). The calculations of DCSs and ICSs have been carried out using an independent atom model under the screening corrected additivity rule (IAM-SCAR). The present elastic DCSs have been found to agree well with the results of IAM-SCAR calculation above 20 eV, and also with a recent Schwinger multichannel calculation below 30 eV. Furthermore, in the comparison with the XF3 (X = B, C, N, and CH) molecules, the elastic DCSs reveal a similar angular distribution which are approximately equal in magnitude from 30 to 200 eV. This feature suggests that the elastic scattering is dominated virtually by the 3-outer fluorine atoms surrounding the XF3 molecules. The vibrational DCSs have also been obtained in the energy range of 1.5-15 eV and vibrational analysis based on the angular correlation theory has been carried out to explain the nature of the shape resonances. Limited experiments on vibrational inelastic scattering confirmed the existence of a shape resonance with a peak at 3.8 eV, which is also observed in the vibrational ICS. Finally, the estimated elastic ICSs, MTCSs, as well as total cross sections are compared with the previous cross section data available.

Time-Dependent Theory of Angular Correlations in Sequential Double Ionization

In this work, we emphasize the importance of the bound-state dynamics to the two-electron ejection in double ionization processes. The conclusions of the present study are pertinent to all excitation or decay processes that proceed via well-defined intermediate states. A general strong-field time-dependent density matrix theory is established and applied to the case of neon, allowing us to analyze the role of the ionizing field in the interpretation of reported angular patterns [M. Kurka et al., J. Phys. B 42, 141002 (2009); A. S. Kheifets, J. Phys. B 42, 134016 (2009)] and in the dynamic ionic alignment. The present analysis reveals that short-pulse coherent excitation of the neon ionic doublet 2P(1/2,3/2) leads to quantum beats in the two-electron angular correlation patterns.

Vibrational excitation of triatomic molecules near the shape resonance region

In this study we have measured angular distributions of differential cross sections (DCS) for vibrational excitation and superelastic scattering from vibrationally excited N2O. The results are analyzed and interpreted using the angular correlation theory by Read.

Angular correlations in the decays of two unstable identical particles with close momenta

For the decay of two identical particles with close momenta, the angular correlations between the directions of emission of decay products are considered on the basis of the model of independent single-particle sources emitting unstable unpolarized particles of nonzero spin. These correlations reflect spin correlations that are caused by quantum-statistics and final-state-interaction effects. A general theory of angular correlations in the decays of two arbitrarily polarized particles (resonances) is constructed.

Angular correlation theory for double photoionization in a rare-gas atom: Ionization by polarized photons

This is a sequel to an earlier article on the theory of angular correlation for double photoionization. Here we consider the two-step double photoionization of a rare gas atom under the influence of a polarized photon beam described by appropriate Stokes parameters. Cylindrical mirror analysers (CMA) are used to detect the outgoing electrons. Theoretical values of the correlation functions are obtained for linearly polarized light. Two different situations is handled. Once, the value of the correlation function is obtained keeping the photo-electron in a fixed direction. The other case the direction of the Auger electron is kept fixed. Comparison with experiments on xenon shows excellent agreement for the case of (4d_{5/2}) photoionization followed by a subsequent (N_{5}-O_{23}O_{23} ^{1}S_{0}) Auger decay for a polarized incident photon of energy (94.5eV) {[}J. Phys.B,

Statistical theory of angular momentum polarization in chemical reactions

A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directions [kcirc] and [kcirc]′ and the product rotational angular momentum j′ are treated in detail, including both pairwise and triple correlations. Explicit formulae are given for three choices of the quantization axis: along [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.

Angular correlation theory for double photoionization in a rare-gas atom

We consider the process of double photoionization (DPI) in a rare-gas atom as a two-step process, namely, (i) photoionization in an inner shell followed by (ii) the emission of an Auger electron from an outer shell. An angular correlation function for the two emitted electrons is defined by analogy with the theory of angular correlation in nuclear physics. An expression is obtained for this angular correlation function by a statistical method that makes use of the density and efficiency operators. The latter takes care of the attenuation of the probability of detection of an electron due to the geometrical properties of the detector. Theoretical values of the angular correlation function are obtained for DPI in xenon and these are shown to be in good agreement with the experimental results given by K\"ammerling and Schmidt [J. Phys. B 26, 1141 (1993)].

Positron Annihilation in Superconducting 123 Compounds

After a brief review of the theory of angular correlation of positron annihilation radiation (ACAR), we illustrate experimental principles and give examples of successful determination of electron momentum density (EMD) and of positron lifetime in solids. The central question which we try to answer concerns the contribution of positron spectroscopy to the knowledge and understanding of the new high temperature superconducting oxides. We find that in these oxides also, partially filled bands exist and we can observe parts of their Fermi surface and measure lifetimes in accordance with band theoretical calculations. There are characteristic differences, however. The intensity of the anisotropy of the ACAR signal is below theoretical expectation and signals depend on sample preparation. Recent studies by the Geneva group have concerned dependence of the signals on impurities, on oxygen content and on the thermal history of preparation. Of particular interest are correlations between the variations of these signals and between the variations of structural and transport properties in these substances. Besides deliberate additions of impurities, the Geneva group also reports progress in the preparations of samples of highest purity (barium zirconate crucibles). The alloy series Pr x Y 1-x Ba2Cu3O 7-δ is of special interest because of exceptional transport properties. The recent positron results on these materials will be presented and commented in the light of theoretical models and in the light of the reported superconductivity of the Pr-compound.

Elastic scattering and vibrational excitation cross sections for electron collisions with C2F6

Absolute elastic cross sections for e-C2F6 collisions have been measured for impact energies of 2 to 100 eV and scattering angles from 10 to 130 degrees . From these, the integrated and momentum transfer cross sections were obtained by extrapolation and numerical integration. Energy loss spectra were measured for vibrational excitation. The vibrational excitation functions show resonances at 4.3 eV and 8.5 eV. By decomposition of the loss spectra and symmetry analysis according to angular correlation theory, the resonances have been assigned to a temporary trapping of the electrons in the a2u (4.3 eV) and eu (8.5 eV) antibonding orbitals of the molecule.

Computation of correlation characteristics of nuclear reactions induced by semi-heavy ions

The present paper suggests a consistent approach to the calculation of different characteristics of nuclear reactions with the production of high-lying quasistationary states of nuclei induced by light and semi-heavy ions with an incident energy up to 10 MeV/nucleon. To investigate this subject it is expedient to analyze the angular correlations of nuclear reaction products. The approach is based on some basic theoretical statements, namely, the general theory of angular correlations in terms of the density matrix and its spin-tensors, two supplementary nuclear reaction models — direct and statistical reaction models — on some methods of computation of quasistationary state characteristics such as the cluster wave functions, width, spectroscopic factors, and, the experimentally observable quantities — differential cross-sections, spin-tensors of the density matrix of the final nuclear state, particle-particle and particle-γ-quantum angular correlation functions and populations of magnetic sublevels of the final nucleus. The approach has been implemented as a package of FORTRAN programs, applied to the analysis of concrete nuclear reactions.

Resonance phenomena observed in electron scattering from acetylene

Electron scattering from acetylene has been studied at low energies by means of an electron impact spectrometer. The 2.5 eV Pi g resonance was seen to lead to appreciable excitation of the nu 4 bending mode and the observed angular dependences of the scattered electrons could only be reconciled with angular correlation theory by assuming a bent geometry for this resonance and consequently a lowering of the molecular symmetry. A 2 Sigma +g resonance was located at 6 eV and is the analogue of that observed in isoelectronic N2 at 8 eV. Further information has been obtained on the Feshbach resonance series and assignments have been proposed based on the grandparent model.

Vibrational excitation of N2O by electron impact via resonant processes in the 2 eV region: an angular study

The angular behaviour of the differential cross sections for vibrational excitation of N2O by electron impact has been measured in the 1.4-3.1 eV energy range. These observations have been interpreted using angular correlation theory and lead one to propose that both Sigma and Pi resonances are present, each with only one contributing partial wave. Above 2.4 eV the Pi contribution would be twice that of Sigma and below 1.8 eV only the Sigma state would be present. These conclusions have been shown to be consistent with the angular distributions for O- formation measured previously where a reinterpretation of these results would also indicate the presence of both resonances. Finally, an angular study of vibrational excitation through the 8 eV resonance indicates Sigma symmetry with a single p sigma wave.

Quadrupole interaction studies of graphite indium chloride using time-differential perturbed angular correlations

The technique of time-differential perturbed angular correlations has been applied to the study of quadrupole interactions in graphite intercalated with indium chloride. Indeed, these experiments represent the first application of this particular spectroscopic technique to graphite intercalation systems. With 111In incorporated as a probe, γ-γ angular correlation measurements were performed on the 173–247 keV cascade in the daughter product 111Cd. Information on quadrupole interactions was obtained from Fourier analysis of the data and by comparison with theoretical fits based on standard angular correlation theory. Three sites are found for intercalated InCl 3: two of these correspond to static electric field gradient interactions, which for a Grafoil sample yielded mean values of v q (1) = 57.8 ± 0.8 MHz and v q (2) = 267 ± 5 MHz; it is suggested that the third, time-dependent component represents a site to which electron transfer is inhibited. The possibility that signals may have been observed from adsorbed as opposed to intercalated InCl 3 was eliminated by comparison with measurements on Spheron 6 carbon black.

Vibrational excitation of CH4by electron impact: 3-20 eV

Differential cross sections (DCS) for the vibrational excitations ( nu 2,4, 170 meV; nu 1,3, 360 meV) of CH4 by electron impact have been investigated for incident energies of 3 to 20 eV in the range of 30 to 140 degrees using a crossed-beam apparatus. Integral and momentum transfer cross sections are calculated from the DCS. At about 7.5 eV, the angular distribution shows d-wave behaviour, and the integral cross sections are enhanced to about 10-16 cm2. The parameters of angular correlation theory with the irreducible tensor method for the T2 molecular symmetry of CH4 were obtained by fitting. It was found that the d wave alone suffices to explain the angular distributions due to the presence of a broad resonant excitation process in the nu 2,4 and nu 1,3 channels. At incident energies of 10 to 20 eV, the angular distributions are isotropic within the experimental error. At lower energies of 3 to 5 eV, the distributions are practically constant within the angular range of 40 to 140 degrees , but the cross sections continuously increase towards smaller angles.

Intermediate state perturbation in low temperature nuclear orientation

This paper deals with the perturbation of low temperature nuclear orientation in an intermediate state by an interaction not axially symmetric around the orientation axis. The directional distribution of the emitted radiation is factorized into initial orientation tensors and perturbation factors known from perturbed angular correlation theory. Low temperature nuclear orientation coefficients have been calculated numerically for111Cd in a polycrystalline sample with axially symmetric electric field gradient. Nuclear orientation experiment on111In in indium host confirms theoretical perturbation predictions and demonstrates the sensitivity of the method on different parameters. Moreover this orientation allows the determination, in magnitude and sign of111In (ground state) nuclear magnetic moment: μ = +5.48(10)μn.

Statistical theory of angular momentum polarization in chemical reactions

A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directi...

Studies of low-lying levels of 33S by the [formula omitted] reaction

The 30 Si(α, nγ) 33 S reaction was used to investigate 33S levels up to 4.3 MeV excitation energy. Each individual state was populated in turn with bombarding energies chosen to be sufficiently near threshold that neutrons of low-order angular momentum were emitted. Accurate excitation energies were determined. The angular distributions of γ-rays de-exciting these levels were analyzed according to standard angular-correlation theory. Experimental results include the spin limitations: J π(2969) = 7 2 + , J(4048) = 5 2 or 9 2 , J(4094) ≧ 3 2 , J(4142) = 3 2 or 5 2 . It is concluded that there exist two levels in 33S near 4.05 MeV excitation energy with a separation of 5±4 keV. The mixing-ratio determinations permit a critical comparison of recent shell-model calculations with the experimental data. The calculations are in reasonably good agreement with the experimental data.

Calculation of Differential Angular Correlation Factors for Non-coaxial Electric and Magnetic Fields

The influence of non-coaxial magnetic and electric fields on radioactive nuclei embedded as impurities in ferromagnetic materials is considered. The attenuation factor G22(t), as defined in perturbed angular correlation theory [1], is calculated for different angles β0 between the directions of the magnetic field and the electric field gradient and for different ratios of the magnetic and electric frequencies. The method has been tested for Cd in ferromagnetic gadolinium.

Investigation of photon-photon angular correlations in atomic mercury

By application of the time differential coincidence technique developed in nuclear spectroscopy, for the first time the angular correlation of light quanta of atomic decays was observed. The experiments were carried out with the 73S1-63P1-61So-cascade of mercury excited by electron impact at energies of 50 eV. The two transitions of 4358 and 2536 A were selected by interference filters and detected by photomultipliers. Time differential coincidence spectra were measured at the two angular positions 0=90 ° and 0=180 °. It was found that the excitation of the 73S1-state by the electron beam leads to no alignment. Therefore the usual γ-γ angular correlation theory is applicable. Perturbations occur by static interaction with external magnetic fields and by free hyperfine interaction in the odd isotopes of mercury. The interaction frequencies of the free hyperfine interaction are in all cases too high to be resolved. Measurements were performed using mercury of natural abundances, with and without external magnetic fields. First of all the spin rotation in the magnetic field of the earth (690 mG) was observed, giving for theg-factor of the 63P1-state $$g(Hg, 6^3 P_1 ) = 1.35 \pm 0.10.$$ This value is in agreement with the more precise values determined by other techniques. Shielding of the earth's field gave a nearly unattenuated angular correlation, with an integral attenuation factor of $$G_2 = 0.98 \pm 0.06.$$ The value of the angular correlation coefficientA2. $$A_2 = - 0.188 \pm 0.009,$$ is in good agreement with the expected average value for the natural isotope mixture $$\overline {A_2^{theor} } = - 0.196.$$ A third measurement in an external magnetic field of 5.6 G showed several complete spin rotations. A nice fit was possible by using the superposition of all six participating cascades in the hyperfine level schemes of the different isotopes. The theoretical anisotropies,g F -values, and intensities were inserted according to natural isotope abundances.

Theory of Angular Correlations for Two Nucleons Emitted in the Nuclear Absorption of Slow Pions

A theory is developed for the angular correlation for two fast nucleons emitted when a nucleus absorbs a slow pion, based on the assumption that the reaction is direct. It is shown that for a quite general class of models for the two-nucleon absorption mechanism, there are selection rules which relate the final angular momenta of the two nucleons to the angular momenta carried initially by the two nucleons in the target nucleus. The selection rules involve the relative and center-of-mass motions, separately, of the nucleon pair. The angular correlation of interest is therefore defined with respect to the angle between the relative and c.m. momenta of the emitted nucleons. The selection rules provide a direct connection between the observed angular correlation and the two-nucleon angular momentum structure of the target nucleus. Some examples are given for the application of this theory to the study of nuclear structure.