A new dispersion relation for electron-atom scattering

Temkin, A.; Bhatia, A. K.; Kim, Y S

doi:10.1088/0022-3700/19/19/011

Cited by 4 publications

(7 citation statements)

References 23 publications

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“…We shall try to understand these results quantum mechanically, and again we find it preferable to think of the process as two-electron photodetachment (i.e., photo-double detachment) of H − . To photo-double detach both electrons from H − requires a photon energy of ∼14.0 eV (in the TP model, the second electron is bound by ∼0.37 eV = 0.027 Ry [11].) This corresponds to a photon of wavelength λ ∼ 1500a 0 .…”

Section: Discussionmentioning

confidence: 99%

“…(We know, in fact, that in the TP model [11] there is only one eigenvalue, ε N ν below the N = 1 state of hydrogen.) The significance of this is that the term in the optical potential associated with that eigenvalue is repulsive (i.e., since E is positive, the denominator of that term is positive, and the numerator is positive definite), whereas all the remaining terms are essentially attractive (of which there are in principle a continuous infinity of terms, but each of, presumably, increasingly smaller width as ν increases), because their denominators are negative (when E is close to threshold).…”

Section: Discussionmentioning

confidence: 99%

“…Equating the logarithmic derivative, the absolute phase shift [7] (in the limit of large N ) is given by 11) and the amplitude is…”

Section: A Analytical Solutionmentioning

confidence: 99%

“…The advantage of the PDD matrix element is that there is no question that the exact initial bound state of H − ion, i (r 1 ,r 2 ), is independent of the final state energy E, and that the integral is convergent. (In the TP model H − continues to be bound with about half its full electron affinity [11].) On the other hand, the final state does depend on E; it can be written (after the analytic continuation has been made) as…”

Section: The Threshold Lawmentioning

confidence: 99%

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Electron scattering from excited states of hydrogen: Implications for the ionization threshold law

Temkin

Shertzer

2013

Phys. Rev. A

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The elastic scattering wave function for electrons scattered from the N th excited state of hydrogen is the final state of the matrix element for excitation of that state. This paper deals with the solution of that problem primarily in the context of the Temkin-Poet (TP) model [A. Temkin, Phys. Rev. 126, 130 (1962); R. Poet, J. Phys. B 11, 3081 (1978)], wherein only the radial parts of the interaction are included. The relevant potential for the outer electron is dominated by the Hartree potential, V H N (r). In the first part of the paper, V H N (r) is approximated by a potential W N (r), for which the scattering equation can be analytically solved. The results allow formal analytical continuation of N into the continuum, so that the ionization threshold law can be deduced. Because the analytic continuation involves going from N to an imaginary function of the momentum of the inner electron, the threshold law turns out to be an exponentially damped function of the available energy E, in qualitative accord with the result of Macek and Ihra [J. H. Macek and W. Ihra, Phys. Rev. A 55, 2024 (1997)] for the TP model. Thereafter, the scattering equation for the Hartree potential V H N (r) is solved numerically. The numerical aspects of these calculations have proven to be challenging and required several developments for the difficulties to be overcome. The results for V H N (r) show only a simple energy-dependent shift from the approximate potential W N (r), which therefore does not change the analytic continuation and the form of the threshold law. It is concluded that the relevant optical potential must be included in order to compare directly with the analytic result of Macek and Ihra. The paper concludes with discussions of (a) a quantum mechanical interpretation of the result, and (b) the outlook of this approach for the complete problem.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Equating the logarithmic derivative, the absolute phase shift [7] (in the limit of large N ) is given by 11) and the amplitude is…”

Section: A Analytical Solutionmentioning

confidence: 99%

Section: The Threshold Lawmentioning

confidence: 99%

See 2 more Smart Citations

Electron scattering from excited states of hydrogen: Implications for the ionization threshold law

Temkin

Shertzer

2013

Phys. Rev. A

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“…The dispersion relation for electron (and positron) scattering has been formulated by Gerjuoy and Krall [63]. It relates the real part of the scattering amplitude f (E,0) at a given energy E and zero scattering angle with the Born amplitude for direct (f B ) and exchange (g B ) scattering [64].…”

Section: Dispersion Relationmentioning

confidence: 99%

Total Cross Sections for Electron and Positron Scattering on Molecules: In Search of the Dispersion Relation

Carelli

Fedus

Karwasz

2021

Atoms

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More than one hundred years of experimental and theoretical investigations of electron scattering in gases delivered cross-sections in a wide energy range, from few meV to keV. An analogy in optics, characterizing different materials, comes under the name of the dispersion relation, i.e., of the dependence of the refraction index on the light wavelength. The dispersion relation for electron (and positron) scattering was hypothesized in the 1970s, but without clear results. Here, we review experimental, theoretical, and semi-empirical cross-sections for N2, CO2, CH4, and CF4 in search of any hint for such a relation—unfortunately, without satisfactory conclusions.

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Angular dependence of autoionisation linewidths due to post-collision interaction in e-He collisions

Brink

Eck

Heideman

1989

J. Phys. B: At. Mol. Opt. Phys.

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In this paper the authors present measurements of energy positions and widths of ejected- and scattered-electron profiles in electron-helium collisions. The energy of the incoming electrons is chosen such that following the excitation and the subsequent autoionisation of a doubly excited helium atom the ejected and the scattered electrons have roughly the same energy. An angle-dependent broadening of the ejected-electron profiles is observed; this may be caused by post-collision interaction (PCI) between the two electrons. The experimental results are in qualitative agreement with a semiclassical description of PCI in this energy region.

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A new dispersion relation for electron-atom scattering

Cited by 4 publications

References 23 publications

Electron scattering from excited states of hydrogen: Implications for the ionization threshold law

Electron scattering from excited states of hydrogen: Implications for the ionization threshold law

Total Cross Sections for Electron and Positron Scattering on Molecules: In Search of the Dispersion Relation

Angular dependence of autoionisation linewidths due to post-collision interaction in e-He collisions

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