Engineering topics

Temkin, A.

Publications and source records attributed to Temkin, A..

At least 37 records · Page 2

NASA NTRS1986

A new dispersion relation for electron-atom scattering

A new forward-angle dispersion relation (DR) for electron-atom scattering is proposed. It is based on a subtraction of the static-exchange amplitude from the exact elastic scattering amplitude. Arguments are advanced to explain why this should obviate the difficulties associated with the Gerjuoy-Krall DR, specifically with the exchange Born amplitude. The new DR is tested in the elastic energy range for e-H scattering and compared with the GKDR.

Temkin, A.↗

NASA NTRS1985

Sum rules and other properties involving resonance projection operators

A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.

Berk, A.↗

NASA NTRS1985

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

Weatherford, C. A.↗

NASA NTRS1985

Autoionization: Recent developments and applications

Among the topics discussed are: theory of resonance and autoionization of two-electron atoms and ions; projection and quasi-projection operators for electron impact resonances on many-electron atomic targets; and hole projection methods for calculating Feshbach resonances and inner-shell vacancies. Consideration is also given to: complex stabilization methods; complex coordinate and complex basis function calculations; and the variational principle. The application of autoionization calculations to solar and astrophysical plasma diagnostics is also discussed in detail.

Temkin, A.↗

NASA NTRS1985

Theory and calculation of resonances and autoionization of two-electron atoms and ions

Techniques for calculating the electron scattering from one-electron hydrogen-like targets on the basis of the Feshback formalism, are discussed. The principal similarities between resonance parameters in the Feshbach formalism and the corresponding Breit-Wigner quantities, are described in detail. Special attention is devoted to a description of the Fano line shape parameter q, and a technique for formulating it in terms of a projector operator is proposed. The theoretical methods are illustrated by numerical calculations for 1S, 3P, and 1D states of H(-) below the first excited threshold of the target atom. Calculations of 1,3S 1,3P, 1,3D states for He are also presented.

Temkin, A.↗

NASA NTRS1985

Projection and quasi-projection operators for electron impact resonances on many-electron atomic targets

A framework is established for deriving true projection operators in electron resonance calculations involving many electron targets (ions and atoms). The analytical approach is based on Feshbach's formalism the true and quasi-projection operators (QPO) one-electron systems. In the case of QPOs, the formalism is explicitly generalized to treat autoionization states lying in the region of inelastic scattering. In order to illustrate the analytical method, a recent calculation of the lowest 2P0 resonance in He is described. The application of the modified Feshbach formalism to calculation of nonresonant phase shifts in many electron systems is also discussed.

Temkin, A.↗

NASA NTRS1984

Electron-atom spin asymmetry and two-electron photodetachment - Addenda to the Coulomb-dipole threshold law

Temkin (1982) has derived the ionization threshold law based on a Coulomb-dipole theory of the ionization process. The present investigation is concerned with a reexamination of several aspects of the Coulomb-dipole threshold law. Attention is given to the energy scale of the logarithmic denominator, the spin-asymmetry parameter, and an estimate of alpha and the energy range of validity of the threshold law, taking into account the result of the two-electron photodetachment experiment conducted by Donahue et al. (1984).

Temkin, A.↗

NASA NTRS1983

Calculation of the polarization potential for e-N2 collisions

A polarization potential V(pol) for e-N2 collisions is calculated by the generalization of the static part of the method of polarized orbitals to molecular targets. Partial differential equations (PDE) are derived for polarized orbitals, which are functions of the distance (r) from the molecular center and angle (theta) from the molecular axis. The equations are solved with the use of the noniterative PDE technique. From the polarized orbitals a polarization potential can be constructed whose r and theta dependence is found to be significantly different from the well-known phenomenological one. The two potentials are further compared by carrying out limited hybrid-theory scattering calculations. Only those scattering results based on the calculated V(pol) are in satisfactory accord with experiment.

Onda, K.↗

NASA NTRS1983

The threshold laws for electron-atom and positron-atom impact ionization

The Coulomb-dipole theory is employed to derive a threshold law for the lowest energy needed for the separation of three particles from one another. The study focuses on an electron impinging on a neutral atom, and the dipole is formed between an inner electron and the nucleus. The analytical dependence of the transition matrix element on energy is reduced to lowest order to obtain the threshold law, with the inner electron providing a shield for the nucleus. Experimental results using the LAMPF accelerator to produce a high energy beam of H- ions, which are then exposed to an optical laser beam to detach the negative H- ion, are discussed. The threshold level is found to be confined to the region defined by the upper bound of the inverse square of the Coulomb-dipole region. Difficulties in exact experimental confirmation of the threshold are considered.

Temkin, A.↗

NASA NTRS1982

Threshold law for electron-atom impact ionization

A derivation of the explicit form of the threshold law for electron impact ionization of atoms is presented, based on the Coulomb-dipole theory. The important generalization is made of using a dipole function whose moment is the dipole moment formed by an inner electron and the nucleus. The result is a modulated quasi-linear law for the yield of positive ions which applies to positron-atom impact ionization.

Temkin, A.↗

NASA NTRS1982

Threshold law for positron-atom impact ionisation

The threshold law for ionisation of atoms by positron impact is adduced in analogy with our approach to the electron-atom ionization. It is concluded the Coulomb-dipole region of the potential gives the essential part of the interaction in both cases and leads to the same kind of result: a modulated linear law. An additional process which enters positron ionization is positronium formation in the continuum, but that will not dominate the threshold yield. The result is in sharp contrast to the positron threshold law as recently derived by Klar on the basis of a Wannier-type analysis.

Temkin, A.↗

NASA NTRS1980

Quasi-projection-operator calculation of autoionization states of O5/+/ /O VI/ and Si11/+/ /Si XII/

A practical approach to calculating diagnostic parameters includes both scattering and statelike (autoionization) elements. The paper presents inelastic quasi-projection-operator calculations of autoionization states of the three-electron ions of oxygen and silicon for states below the n = 3 manifod of the respective two-electron parent (O VI and Si XII). Wave functions containing up to 40 configurations are calculated. The O VI calculated results agree with experimental results within the experimental error (about + or - 2 eV) while for the Si XII case, it was necessary to include relativistic effects. Where formulas are available (states for which p + q = 2), the Si XII results are also in good agreement with experimental results for 2Se, 2Po, and 2De states. Since the calculated results for some of the higher states did not agree with identifications proposed by Trabert et al. (1979), alternative identifications are suggested.

Wakid, S.↗

NASA NTRS1980

Electron-impact excitation of Li II in the distorted-wave approximation

The 1(1)S yields 2(3)P electron-impact-excitation cross section for Li II is calculated in the distorted-wave approximation. Two forms of the distorted-wave method are examined; in the first form both the initial and final wave functions are distorted, while in the second form only the initial wave function is distorted. In both forms a partial-wave expansion of the scattered amplitude is made, and exchange is incorporated in a consistent manner. The effects of including more than one configuration in the target-state wave function are also examined. For incident energies greater than 90 eV, distorted-wave calculations agree moderately well with recent experimental and theoretical results.

Pindzola, M. S.↗

NASA NTRS1980

Effect of blackbody radiation on the threshold for two-electron photodetachment of H/-/

The threshold law of the titled process, which is of the same form as that for electron-impact ionization of H, can experimentally be contaminated by simultaneous single photodetachment and Rydberg excitation of the residual atom, followed by ionization of the Rydberg atom by (room-temperature) blackbody photons. This gives a signal indistinguishable from direct double photodetachment. The correction is here calculated and shown to be finite at the double photodetachment threshold, and to have, possibly, an implication about the form of the threshold law itself. However, at room temperature its contribution is found to be small as it pertains to a recently initiated experiment at the Los Alamos Meson Physics Facility for available energies greater than a millivolt above threshold. The temperature dependence of the correction is shown to be large (k/B/T) to the 7/2; thus at higher temperatures the effect may be observable.

Temkin, A.↗

NASA NTRS1980

Quasi-projection-operator calculation of inelastic resonances in He/-/ and Li

Feshbach resonances of electrons incident of He and Li(+) are calculated below the 3(S-3) target threshold by means of the inelastic quasi-projection-operator technique of Temkin and Bhatia (1972). A configuration-interaction-type wave function is employed with up to 46 configurations. The calculations reveal, with reasonable accuracy, all presently observed Feshbach resonances. The method does not reveal shape resonances, but, for isoelectronic systems with greater nuclear charge, it is argued that shape resonance should become less important. This is already apparent in the case of Li, for which the known resonances are calculated and higher resonances, for which there are as yet no experimental data, are predicted.

Wakid, S.↗

NASA NTRS1979

Calculation of resonant effects in electron-impact excitation of positive ions Application to oxygen VII

The general reaction theory of Feshbach is applied to the calculation of resonant effects in near-threshold electron-positive-ion excitation. The theory divides configuration space into open- and closed-channel parts, resonance effects being described by the closed-channel part. The open-channel part is handled in a distorted-wave approximation to the set of open-channel coupled equations. Various methods are suggested for handling the closed-channel part. However, an 'attached-excited-target approximation' is used explicitly, which is further approximated by a set of uncoupled closed-channel equations. As an example, the 1 1S-2 1P excitation cross section of O VII below the 3 3S threshold is calculated. Various distorted-wave approximations are investigated and results from most of them are quite similar. Resonant effects arising from the attachment of the colliding electron with the 3 3S state are found to be small, but other close-lying n = 3 states have not yet been included.

Pindzola, M. S.↗

NASA NTRS1978

Internuclear dependence of the polarizability of N2

A study is made of the internuclear dependence of the polarizability of N2. Specifically, the dependencies of parallel and perpendicular polarizabilities on internuclear separation is found for the N2 molecule in its ground state. Results are presented for vibrationally elastic cross sections as functions of incident electron energy in an eight-state calculation and for the excitation of the first vibrational state.

Temkin, A.↗

NASA NTRS1977

A distorted-wave methodology for electron-ion impact excitation - Calculation for two-electron ions

A distorted-wave program is being developed for calculating the excitation of few-electron ions by electron impact. It uses the exchange approximation to represent the exact initial-state wavefunction in the T-matrix expression for the excitation amplitude. The program has been implemented for excitation of the 2/1,3/(S,P) states of two-electron ions. Some of the astrophysical applications of these cross sections as well as the motivation and requirements of the calculational methodology are discussed.

Bhatia, A. K.↗