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  • Atomic and Molecular Physics  (13)
  • Cell & Developmental Biology  (6)
  • Life and Medical Sciences  (6)
  • Gyrotron  (2)
  • 1
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    Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections (2001)
    In:  CASI
    Details
    Publication Date: 2013-08-29
    Description: We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,
    Keywords: Atomic and Molecular Physics
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  • 2
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    Autoionization (2004)
    In:  CASI
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    Publication Date: 2018-06-06
    Description: Since the original chapter, we briefly review two calculational methods used for basic applications in autoionization of few body systems: (a) complex rotation and (b) a pseudopotential method. Complex rotation, briefly mentioned above, has been extensively applied with great accuracy. Two additional basic systems to be mentioned here are H(sup -) and Ps(sup -) (Ps=positronium). In complex rotation the particle distances are multiplied by the common phase factor given.
    Keywords: Atomic and Molecular Physics
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  • 3
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    Complex Correlation Calculation of e(-) - H Total Cross Sections (2001)
    In:  Other Sources
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    Publication Date: 2019-07-17
    Description: Calculation of e(-) - H total and elastic partial wave cross sections is being carried out using the complex correlation variational T-matrix method. In this preliminary study, elastic partial wave phase shifts are calculated with the correlation functions which are confined to be real. In that case the method reduces to the conventional optical potential approach with 2 projection operators. The number of terms in the Hylleraas-type wave function for the S-1 phase shifts is 95 while for the S-3 it is 56, except for k = 0.8 where it is 84. Our results, which are rigorous lower bounds, are seen to be in general agreement with those of Schwartz, but they are of greater accuracy and outside of his error limits for k = 0.3 and 0.4 for S-1. The main aim of this approach is the application to higher energy scattering. By virtue of the complex correlation functions, the T-matrix is not unitary so that elastic and total scattering cross sections are independent of each other. Our results will be compared specifically with those of Bray and Stelbovics.
    Keywords: Atomic and Molecular Physics
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  • 4
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    Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis (2001)
    In:  Other Sources
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    Publication Date: 2019-07-17
    Description: Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.
    Keywords: Atomic and Molecular Physics
    Type: Atomic Physics; Apr 01, 2001; CT; United States
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  • 5
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    Exchange Forces in Dispersion Relations Investigated Using Circuit Relations (2000)
    In:  Other Sources
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    Publication Date: 2019-07-17
    Description: We propose a novel method to compute in an exact manner the left-hand cut discontinuity of the electron-Atom partial wave scattering amplitude in the complex energy plane within the static stage approximation. Zero energy dispersion relations for electron-Hydrogen scattering are computed numerically for illustration.
    Keywords: Atomic and Molecular Physics
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  • 6
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    Calculation of the Full Scattering Amplitude without Partial Wave Decomposition (2004)
    In:  Other Sources
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    Publication Date: 2019-07-18
    Description: The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.
    Keywords: Atomic and Molecular Physics
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  • 7
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    Complex Correlation Calculation of e-H Total Cross Sections (2001)
    In:  Other Sources
    Details
    Publication Date: 2019-07-17
    Description: Calculation of e-H total and elastic partial wave cross sections is being carried out using the complex correlation variational T-matrix method. In this preliminary study, elastic partial wave phase shifts are calculated with the correlation functions which are confined to be real. In that case the method reduces to the conventional optical potential approach with projection operators. The number of terms in the Hylleraas-type wave function for the S phase shifts is 95 while for the S it is 56, except for k=0.8 where it is 84. Our results, which are rigorous lower bounds, are given. They are seen to be in general agreement with those of Schwartz, but they are of 0 greater accuracy and outside of his error limits for k=0.3 and 0.4 for S. The main aim of this approach' is the application to higher energy scattering. By virtue of the complex correlation functions, the T matrix is not unitary so that elastic and total scattering cross sections are independent of each other. Our results will be compared specifically with those of Bray and Stelbovics.
    Keywords: Atomic and Molecular Physics
    Type: Jul 18, 2001 - Jul 24, 2001; NM; United States
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  • 8
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    Complex Correlation Calculation of e-H Total Cross Sections (2001)
    In:  Other Sources
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    Publication Date: 2019-07-17
    Description: Calculation of e - H total and elastic partial wave cross sections is being carried out using the complex correlation variational T-matrix method. In this preliminary study, elastic partial wave phase shifts are calculated with the correlation functions which are confined to be real. In that case the method reduces to the conventional optical potential approach with projection operators.
    Keywords: Atomic and Molecular Physics
    Type: XXII ICPEAC; Jul 18, 2001 - Jul 24, 2001; Unknown
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  • 9
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    Calculation of the Scattering Amplitude Without Partial Wave Expansion (2001)
    In:  Other Sources
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    Publication Date: 2019-07-17
    Description: Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.
    Keywords: Atomic and Molecular Physics
    Type: XXII ICPEAC; Jul 18, 2001 - Jul 24, 2001; Unknown
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  • 10
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    Photo-Double Ionization: Threshold Law and Low-Energy Behavior (2007)
    In:  Other Sources
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    Publication Date: 2019-07-19
    Description: The threshold law for photoejection of two electrons from atoms (PDI) is derived from a modification of the Coulomb-dipole (C-D) theory. The C-D theory applies to two-electron ejection from negative ions (photo-double detachment:PDD). The modification consists of correctly accounting for the fact that in PDI that the two escaping electrons see a Coulomb field, asymptotically no matter what their relative distances from the residual ion are. We find in the contralinear spherically symmetric model that the analytic threshold law Q(E), i.e. the yield of residual ions, to be Q Integral of (E) varies as E + (C(sub w) E(sup gamma W)) +CE(sup 5/4) sin [1/2 ln E + phi]/ln(E). The first and third terms are beyond the Wannier law. Our threshold law can only be rigorously justified for residual energies 〈= 10(exp -3) eV. Nevertheless in the present experimental range (0.1 - 4 eV), the form, even without the second term, can be fitted to experimental results of PDI for He, Li, and Be, in contrast to the Wannier law which has a larger deviation from the data for Li and Be.
    Keywords: Atomic and Molecular Physics
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