Angular Correlation Parameters Research Articles

Coupled-channels optical theory for e-H scattering

Cross sections and angular correlation parameters for scattering within the 1s, 2s, 2p channel space in the electron-hydrogen problem are calculated at 50, 54.4, 100 and 200 eV. The integral equations for the momentum-space formulation of the problem are solved with a numerical accuracy of approximately 1%. Discrete and continuum channels outside the reaction space are explicitly taken into account by computing the corresponding optical potentials and adding them to the coupling potential. Exchange terms are calculated at all stages. Relative elastic cross sections, absolute inelastic cross sections, total reaction cross sections, and angular correlation parameters up to 60 degrees agree with experiment.

Excitation of atomic hydrogen by electron impact in an on-shell Faddeev-Watson approximation

The second-order Faddeev-Watson approximation is applied to the excitation of atomic hydrogen by electron impact. By restricting the total kinetic energy of the electrons in the intermediate state to the three-body energy shell a simplification is effected when approximates the dynamics to a double Coulomb binary encounter. The resulting transition matrix elements involve multi-dimensional integrals which are evaluated numerically. Although the model fails for low momentum transfers it predicts differential cross sections and angular correlation parameters for electron-hydrogen excitation which are in reasonable agreement with experiment at high momentum transfers.

Third-order effects of electron-hydrogen scattering

Recent comparisons of experimental and theoretical angular correlation parameters have revealed that no theoretical calculations are in good agreement with the experimental data. If the scattering is viewed from the perspective of the conventional Born series, it is now clear that second- and perhaps higher-order terms will have to be evaluated before agreement with experiment can be achieved. The authors investigate the size of some third- and higher-order contributions to the Born series. It is shown that these third- and higher-order effects are small.

Elastic and inelastic scattering of electrons by atomic hydrogen at intermediate energies in a coupled-channel second-order potential model

A second-order model employing a pseudostate expansion in intermediate states is applied in a 1s-2s-2p coupled-channel formalism to electron scattering by atomic hydrogen in the energy range 54 to 200 eV. Although the model predicts cross sections for elastic scattering, and excitation of the n=2 levels, which are in reasonable accord with the experimental data, the predicted results for the angular correlation parameters show little improvement over the 1s-2s-2p close-coupling model.

Influence of the Angular Linkage on the Mesomorphic Properties of Cholesteryl Arylbenzoates

Abstract Some cholesteryl esters of arylbenzoic acids incorporating angular linkage such as –CO–, –O–, –S–, and –CH2–, have been prepared, and the transition temperatures and heats have been determined. The cholesteric-isotropic transition temperatures are likely to correlate with the angular correlation parameters of these carboxylic acid moieties. The mesomorphic phenomena are discussed in terms of the molecular structure and electronic effect of these linkages.

Inclusion of fine and hyperfine effects in electron-sodium excitation

Electron-photon angular-correlation parameters are given for the $^{2}P$ states of sodium which include both fine and hyperfine effects. These expressions contain interference terms between scattering amplitudes which are only observable in angular-correlation experiments and give rise to zero-field quantum beats in the excitation of the $^{2}P_{\frac{3}{2}}$ state. By neglecting fine structure, partial cross sections for the $^{2}P_{J}(F,{M}_{F})\ensuremath{\leftarrow}^{2}S_{\frac{1}{2}}(F=2,{M}_{F}=2)$ excitations are given in terms of direct and exchange-scattering amplitudes.

Evaluation of angular correlation parameters and the dielectric constant in the RISM approximation

We prove, using a projection operator method, a number of results obtained when site-site correlation functions are evaluated in the RISM approximation. In non-polar fluids, the angular correlation parameter G 2 is identically zero for any symmetric linear molecule, while G 1 is identically zero for an arbitrary linear molecule. In rigid polar fluids, the dielectric constant є is found to be given by the ideal-gas type expression є = 1 + 3y, where y = 4πβρμ2/9.

Effect of polarization and absorption on differential cross sections and angular correlation parameters for electron excitation of helium

The effects of local polarization and absorption potentials on differential cross sections and angular correlation parameters are studied within the distorted-wave approximation for electron excitation of the $2^{1}P$ state of helium. For examining the effect of local polarization, we have compared a recent numerical self-consistent adiabatic polarization potential for helium with the commonly used hydrogenic adiabatic polarization potential. Different radial regions for the polarization potential were studied to determine their contribution to the overall effect of polarization. Calculations are also presented which show the effects of different strengths for a local absorption potential.

Mesogenic and Non Mesogenic Central Rigid Cores

Abstract The mesogenic power of several central rigid cores is measured by means of depolarized Rayleigh scattering. It is shown that there is a close relation between the angular correlation parameter J and the mesogenic power that lead us to define mesogenic and non mesogenic rigid cores. An attempt is made to explain these facts by consideration of certain different structural aspects.

The form of electron-atom excitation amplitudes at high momentum transfers in the Faddeev-Watson approximation

A form of the off-shell Coulomb T matrix, which has a well defined on-shell limit, is used in the Fadeev-Watson multiple-scattering expansion for a direct three-body collision process. Using the excitation of atomic hydrogen by electron impact as an example, approximations to the second-order terms, which are valid for high momentum transfers of the incident electron, are derived. It is shown how the resulting asymptotic behaviour of the second-order Faddeev-Watson approximation is related to the high momentum transfer limit of the second Born approximation. The results are generalised to the excitation of more complex atoms. The asymptotic forms of the Faddeev-Watson and Born approximations are compared with other theories and with measurements of differential cross sections and angular correlation parameters for the excitation of H(2p) and He(21P). The results indicate that the Faddeev-Watson approximation converges more rapidly at high momentum transfers than does the Born approximation.

Sensitivity of differential cross sections and angular correlation parameters to scattering parameters

Over the last few years there have been several methods proposed by different investigators for calculating distorted-wave amplitudes. It is difficult to compare the relative merits of these calculations since widely different atomic potentials and wavefunc- tions have been used in the various calculations. We have examined these different approximations by calculating different distorted-wave amplitudes using a common Hartree-Fock basis for atomic potentials and wavefunctions. This procedure allows us to examine the relative effects of different types of approximations. For purposes of comparison, we have calculated differential cross sections and angular correlation parameters for electron impact excitation of the 2'P and 3lP allowed transitions of helium for incident electron energies in the range 40-200 eV. All of the calculations include both the direct and exchange amplitudes, and calculations were performed using both a static atomic distorting potential and a complex optical potential which included polarisation, exchange and absorption distortion in addition to the distortion of the static potential.

The electron impact excitation of the 21P state of helium in the eikonal-Born series approximation

The eikonal-Born series approximation is used to study the excitation of the 21P state of helium by 200-500 eV electron impact. The differential cross sections are in excellent agreement with recent absolute measurements, particularly at the higher energies. In contrast to this, further work is required to obtain satisfactory values of the angular correlation parameters.

Angular correlation parameters for 1s-2p excitation of hydrogen calculated in the distorted-wave approximation

An uncoupled distorted-wave formalism is presented. Source parameters necessary for obtaining the coincidence rate of Ly- alpha photons and scattered electrons for electron excitation of the 2p state of hydrogen at 54, 100, and 200 eV are calculated in this formalism. These results are compared with source parameters obtained in other theoretical models.

Differential cross sections and angular correlation parameters for the excitation of the n = 3 levels of helium by electron impact

Angular distributions and (x, λ) angular correlation parameters are calculated in the generalized distorted wave model of Bransden and Issa for 31P excitation of helium in the energy interval 100 to 500 eV. Comparison is made with the experimental data at 100 eV and with the results of the theoretical models. Angular distributions are also presented for the excitation of the 31S and 31D levels, for which a comparison with data is not yet possible.

Calculation of the dielectric and Kerr constant angular correlation parameters

The angular correlation parameters G L involved in the dielectric and Kerr constants are written as averages over the angular pair correlation function. A perturbation theory for these parameters is developed, based on the expansion of Gubbins and Gray for the angular pair correlation function. Numerical calculations are presented showing the influence of polar and quadrupolar forces on these parameters.

Ten-channel eikonal treatment of electron-metastable-helium collisions: Differential and integral cross sections for2P1,3andn=3excitations from He (2S1,3) and the (λ, χ, Π) parameters

We present a ten-channel eikonal treatment of the $2^{1,3}P$, $3^{1,3}S$, $3^{1,3}P$, and $3^{1,3}D$ excitations of atomic helium, initially in the $2^{1,3}S$ metastable states, by incident electrons with energy $E$ (eV) in the range $5\ensuremath{\le}E\ensuremath{\le}100$. Integral and differential inelastic cross sections are obtained. Also, the angular-correlation parameters $\ensuremath{\lambda}$ and $\ensuremath{\chi}$, which respectively provide the relative population and relative phase of the collisionally excited $P$ magnetic substates, and the circular polarization fraction $\ensuremath{\Pi}$ of radiation emitted from these $P$ states, are determined as functions of scattering angle $\ensuremath{\theta}$ and $E$. No measurements exist to date. The principle of detailed balance is explicitly demonstrated for the $2^{1}S\ensuremath{-}1^{1}S$ superelastic collision.

Angular correlations in linear copolymers from the compositional dependence of their dipole moments. I. Random copolymerization

A theory is developed, without recourse to a detailed model, for evaluating certain linear combinations of the average cosines of the angles between dipole moments of pairs of structural units that are closely spaced along the chain contour. Measurements of the compositional dependence of the effective dipole moment per structural unit together with a knowledge of the compositional dependence of the probabilities for various types of sequences of structural units provide the required information. The theory offers a possibility for testing the validity of certain restrictive assumptions that are implicit in earlier treatments of the problem. Additionally, the theory provides a basis for determining unequivocally from experimental measurements whether angular correlations exist among the structural units that contribute to the orientational part of the polarization and whether the angular correlation parameters, if they exist, depend on the types of structural units involved.

Angular correlation studies for α-particle excitation of the 1.78 MeV 2 + state in 28Si

The α-γ in-plane angular correlations of the reaction 28Si(α, α 1γ) 28Si have been measured at 10, 12, 14 and 18 MeV. Correlations were obtained for c.m. scattering angles from 20° to 170° in 3° steps. Extracted angular-correlation parameters show a strong energy dependence, with a more rapid variation of the correlation pattern as a function of scattering angle with bombarding energy increase. Detailed coupled-channels analyses of the 18 MeV data with coupling of the first three excited states to the ground state of 28Si were performed and a prolate deformation β R = 0.3 was deduced.

A 56-channel goniometer for gamma-gamma directional correlation studies

A multi-channel goniometer (MCG) with eight detectors is described. All fiftysix coincidence combinations of two cascading gamma rays are analyzed in one common time to amplitude converter. Before the time analysis in the TAC is allowed, a logic system selects pulse pairs appearing within a preset time interval. This facilitates a reliable coding of the address register. The data are stored in the memory of a two parameter multi-channel analyzer. The MCG has been tested in a series of control experiments and computer checks with simulated data. The results show that the upper limit of the counting rate that may be allowed is set by single channel performance in the same way as for a two detector instrument. The high efficiency of the MCG can thus be fully utilized in absolute measurements of angular correlation parameters.

Four- and five-pion production in pp collisions at 6.92 GeV/ c

We have studied pp interactions at 6.92 GeV/ c incident lab momentum leading to six and more charged non-strange particles. The values for the six- and eight-prong cross sections were found to be 1.08 ± 0.07 and 0.02 ± 0.01 mb respectively. The behaviour of the normalized average matrix-element squared as a function of incident momentum for the six- and seven-body final states and the predictions of the quark additive model have been investigated. The c.m. angular distributions and the longitudinal and transverse momenta distributions for the outgoing particles are presented and discussed. The production of isobars and mesons has been investigated. Cross sections for the production of Δ ++ (1236), Δ −(1236), N ∗(1525) and ω-meson are presented. The angular correlation parameters for the multi-pion systems are given.