Engineering topics

Temkin, A.

Publications and source records attributed to Temkin, A..

At least 19 records

NASA NTRS2007

Photo-Double Ionization: Threshold Law and Low-Energy Behavior

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.

Bhatia, A. K.↗

NASA NTRS2004

Autoionization

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.

Bhatia, A.↗

NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Shertzer, Janine↗

NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Shertzer, J.↗

NASA NTRS2002

CCKT Calculation of e-H Total Cross Sections

We are in the process of carrying out calculations of e-H total cross sections using the 'complex-correlation Kohn-T' (CCKT) method. In a later paper, we described the methodology more completely, but confined calculations to the elastic scattering region, with definitive, precision results for S-wave phase shifts. Here we extend the calculations to the (low) continuum (1 much less than k(exp 2) much less than 3) using a Green's function formulation. This avoids having to solve integro-differential equations; rather we evaluate indefinite integrals involving appropriate Green's functions and the (complex) optical potential to find the scattering function u(r). From the asymptotic form of u(r) we extract a T(sub L) which is a complex number. From T(sub L), elastic sigma(sub L)(elastic) = 4pi(2L+1)((absolute value of T(sub L))(exp 2)), and total sigma (sub L)(total) = 4pi/k(2L+1)Im(T(sub L)) cross sections follow.

Bhatia, Aaron K.↗

NASA NTRS2001

Complex Correlation Calculation of e-H Total Cross Sections

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.

Bhatia, A. K.↗

NASA NTRS2001

Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis

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.

Shertzer, J.↗

NASA NTRS2001

Complex Correlation Calculation of e(-) - H Total Cross Sections

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.

Bhatia, A. K.↗

NASA NTRS2001

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections: Electron-Hydrogen Elastic Scattering - Part 1

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,

Bhatia, A. K.↗

NASA NTRS2000

Exchange Forces in Dispersion Relations Investigated Using Circuit Relations

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.

Vrinceanu, D.↗

NASA NTRS1999

S-Wave Dispersion Relations: Exact Left Hand E-Plane Discontinuity from the Born Series

We show, for a superposition of Yukawa potentials, that the left hand cut discontinuity in the complex E plane of the (S-wave) scattering amplitude is given exactly, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This also establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. We can thus construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The high numerical precision achievable by the DR is demonstrated for the exponential potential at zero scattering energy. We also briefly discuss the extension of our results to Field Theory.

Bessis, D.↗

NASA NTRS1999

Partial Wave Dispersion Relations: Application to Electron-Atom Scattering

In this Letter we propose the use of partial wave dispersion relations (DR's) as the way of solving the long-standing problem of correctly incorporating exchange in a valid DR for electron-atom scattering. In particular a method is given for effectively calculating the contribution of the discontinuity and/or poles of the partial wave amplitude which occur in the negative E plane. The method is successfully tested in three cases: (i) the analytically solvable exponential potential, (ii) the Hartree potential, and (iii) the S-wave exchange approximation for electron-hydrogen scattering.

Temkin, A.↗

NASA NTRS1993

Ab initio method for calculating total cross sections

A method for calculating total cross sections without formally including nonelastic channels is presented. The idea is to use a one channel T-matrix variational principle with a complex correlation function. The derived T matrix is therefore not unitary. Elastic scattering is calculated from T-parallel-squared, but total scattering is derived from the imaginary part of T using the optical theorem. The method is applied to the spherically symmetric model of electron-hydrogen scattering. No spurious structure arises; results for sigma(el) and sigma(total) are in excellent agreement with calculations of Callaway and Oza (1984). The method has wide potential applicability.

Bhatia, A. K.↗

NASA NTRS1991

Inclusion of Theta(12) dependence in the Coulomb-dipole theory of the ionization threshold

The Coulomb-dipole (CD) theory of the electron-atom impact-ionization threshold law is extended to include the full electronic repulsion. It is found that the threshold law is altered to a form in contrast to the previous angular-independent model. A second energy regime, is also identified wherein the 'threshold' law reverts to its angle-independent form. In the final part of the paper the dipole parameter is estimated to be about 28. This yields numerical estimates of E(a) = about 0.0003 and E(b) = about 0.25 eV.

Srivastava, M. K.↗

NASA NTRS1988

Polarization asymmetry in two-electron photodetachment - A cogent test of the ionization threshold law

A very sensitive test of the electron-atom ionization threshold law is suggested: for spin-aligned heavy negative ions it consists of measuring the polarization asymmetry A(PA) coming from double detachment by left- versus right-circularly polarized light. The respective yields are worked out for the Te(-) (5p)5 2P(3/2) ion. The Coulomb-dipole theory predicts A(PA) to be the ratio of two oscillating functions in sharp contrast to any power law (specifically that of Wannier, 1953) for which the ratio is expected to be a smooth function of energy.

Temkin, A.↗

NASA NTRS1988

Further study of a new dispersion relation for electron-atom scattering

A recently proposed dispersion relation (DR) is tested for e-He scattering; the results show that the new DR is not satisfied. Therefore, the analytic structure of the difference amplitude, previously assumed to be nonsingular, is investigated on the negative scattering energy axis. Even under severe approximations, the difference amplitude contains both poles and branch points. This suggests, however, a useful approximation of these contributions to the DR which gives very satisfactory agreement in both e-H and e-He scattering.

Bhatia, A. K.↗

NASA NTRS1987

Inclusion of electron correlation for the target wave function in low- to intermediate-energy e-N2 scattering

In a recent calculation, an exact exchange method was developed for use in the partial-differential-equation approach to electron-molecule scattering and was applied to e-N2 scattering in the fixed-nuclei approximation with an adiabatic polarization potential at low energies (0-10 eV). Integrated elastic cross sections were calculated and found to be lower than experiment at energies both below and above the Pi(g) resonance. It was speculated at that time that improved experimental agreement could be obtained if a correlated target representation were used in place of the uncorrelated one. The present paper implements this suggestion and demonstrates the improved agreement. These calculations are also extended to higher energies (0-30 eV) so asd to include the Sigma(u) resonance. Some discrepancies among the experiments and between experiment and the various calculations at very low energy are noted.

Weatherford, C. A.↗

NASA NTRS1986

Projection-operator calculations of the lowest e(-)-He resonance

The 1s (2s)2:2S Schulz resonance of He(-) is investigated theoretically, applying the full projection-operator formalism developed by Temkin and Bhatia (1985) in a Rayleigh-Ritz variational calculation. The technique is described in detail, and results for five different approximations of the He target state are presented in a table. Good convergence is obtained, but it is found that even the best calculated value of the resonance is about 130 meV higher than the experimentally measured value of 19.367 + or - 0.007 eV (Brunt et al., 1977), a discrepancy attributed to the contribution of the shift in the Feshbach formalism.

Berk, A.↗