Methods and programs in collisions of positrons with atoms and molecules

Armour, E. A. G.; Humberston, J W

doi:10.1016/0370-1573(91)90110-8

Cited by 71 publications

(76 citation statements)

References 64 publications

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“…I have neglected the reduced mass and mass polarization corrections to the kinetic energy of the leptons as this is the usual practice in calculations of both atomic and molecular scattering (see, for example, [9]). The reduced mass corrections would be easy to include but including the mass polarization corrections would be more complicated.…”

Section: Investigation Of Resonances Using the Kohn Methodsmentioning

confidence: 99%

Treatment of resonances in the scattering of a heavy positron byH2that are due to interaction with vibrationally excited quasibound states

Armour

2010

Phys. Rev. A

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For a positron with wave number k, the rate of annihilation when scattered by an atom or molecule is proportional to Z eff (k), the effective number of electrons in the target that are available to the positron for annihilation. There is currently great interest in the very large positron annihilation rates, and hence values of Z eff (k), that have been observed in low-energy positron scattering by some molecules. These are observed experimentally to occur at energies just below the energies of excited vibrational states of the molecule concerned. This has been explained by Gribakin [Phys. Rev. A 61, 022720 (2000)] and Gribakin and Lee [Phys. Rev. Lett. 97, 193201 (2006)] as being due to Feshbach resonances involving excited quasibound vibrational states. These treatments make skilful use of approximate methods. It is of interest to determine how the expression obtained for the resonant contribution to Z eff (k) from a quasibound state using a very accurate method is related to the expressions obtained in the previously mentioned articles. In view of this, in this article I carry out a detailed ab initio theoretical treatment of positron scattering by H 2 using the Kohn variational method. H 2 is the simplest molecule, which makes it easier to take into account all the interactions involved. However, a positron does not form a bound state with H 2 . To investigate resonant behavior in Z eff (k), I increase the mass m p of the positron so that it forms a weakly bound state with H 2 . This gives rise to excited quasibound vibrational states. The expression I obtain for the resonant contribution to Z eff (k) has some similarity with the expressions obtained by Gribakin and Lee. This gives some support to their explanation of the very large values of Z eff (k). However, they make no explicit mention of corrections to the Born-Oppenheimer (BO) approximation. These play a key role in my treatment as they couple the quasibound states to the continuum. I am able to show how the BO corrections are taken into account implicitly in calculating the expressions obtained by Gribakin and Lee. The most important difference between my treatment and their treatments is that in my treatment Z eff (k) may be infinite at the resonant energy, whereas in the other treatments it is likely to be large, but can never be infinite. Further investigation is necessary to determine the origin of this infinity in my treatment. My treatment could be applied to positron scattering by molecules such as methyl halides in which very high Z eff (k) values are observed, though using the Kohn variational method would be considerably more complicated than in the case of H 2 .

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Section: Investigation Of Resonances Using the Kohn Methodsmentioning

confidence: 99%

Treatment of resonances in the scattering of a heavy positron byH2that are due to interaction with vibrationally excited quasibound states

Armour

2010

Phys. Rev. A

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“…Unlike some other applications of the Kohn method to simple systems [5,7,8], the present approach does not include basis functions with interelectronic coordinates and instead uses a basis of functions all centered on the nucleus. The use of such a configuration-interaction (CI) -type basis does entail some large-scale calculations, but the issues involved in doing these calculations at low energies have been effectively solved [9].…”

Section: Introductionmentioning

confidence: 99%

Positron scattering and annihilation from hydrogenlike ions

2004

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The Kohn variational method is used with a configuration-interaction-type wave function to determine the J = 0 and J = 1 phase shifts and annihilation parameter Z eff for positron-hydrogenic ion scattering. The phase shifts are within 1 -2% of the best previous calculations. The values of Z eff are small and do not exceed unity for any of the momenta considered. At thermal energies Z eff is minute with a value of order 10 −50 occurring for He + at k = 0.05a 0 −1 . In addition to the variational calculations, analytic expressions for the phase shift and annihilation parameters within the Coulomb wave Born approximation are derived and used to help elucidate the dynamics of positron collisions with positive ions.

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“…Kohn calculations using exact target states have been carried out by Humberston and are described, for example, in [26]. He found that, at low energies, the variational approximation to the phase shift tended to increase monotonically as the flexibility of the trial wave function was improved by the inclusion of a greater number of short-range correlation functions.…”

Section: Optimizationmentioning

confidence: 99%

“…Earlier changes to this framework had already been made during our previous calculations [1], where code designed originally for investigations of helium-antihydrogen scattering [25] was adapted so that it could be applied to (e + − H 2 ) scattering. Those initial modifications allowed for the evaluation of integrals containing terms in ρ 13 ρ 23 /ρ 12 by using a triple Neumann expansion [26,27]. To carry out the calculations described here involving ψ (B) G , it was necessary to extend these modifications to allow for the evaluation of integrals containing factors of the form…”

Section: The Hydrogen Moleculementioning

confidence: 99%

The importance of an accurate target wavefunction in variational calculations for (e⁺–H₂) scattering

Cooper

Armour

Plummer

2008

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

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Abstract. Using the complex Kohn method, we have calculated variational values of phase shifts and the annihilation parameter, Z eff , for the elastic scattering of positrons by molecular hydrogen. Our results are sensitive to small changes in the accuracy of the wave function representing the target hydrogen molecule. We have developed a systematic approach to demonstrate that, at low positron energies, there are particular forms of the Kohn trial wave function for which the results of variational calculations are not reliable, even when the target wave function accounts for as much as 96.8% of the correlation energy of H 2 . We find that reliable results can be recovered if our calculations are extended to admit more sophisticated target wave functions accounting for 99.7% of the correlation energy. Remaining discrepancies between theory and experiment are briefly discussed.

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Methods and programs in collisions of positrons with atoms and molecules

Cited by 71 publications

References 64 publications

Treatment of resonances in the scattering of a heavy positron byH2that are due to interaction with vibrationally excited quasibound states

Treatment of resonances in the scattering of a heavy positron byH2that are due to interaction with vibrationally excited quasibound states

Positron scattering and annihilation from hydrogenlike ions

The importance of an accurate target wavefunction in variational calculations for (e⁺–H₂) scattering

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Methods and programs in collisions of positrons with atoms and molecules

Cited by 71 publications

References 64 publications

Treatment of resonances in the scattering of a heavy positron byH2that are due to interaction with vibrationally excited quasibound states

Treatment of resonances in the scattering of a heavy positron byH2that are due to interaction with vibrationally excited quasibound states

Positron scattering and annihilation from hydrogenlike ions

The importance of an accurate target wavefunction in variational calculations for (e+–H2) scattering

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The importance of an accurate target wavefunction in variational calculations for (e⁺–H₂) scattering