Detailed calculations on low-energy positron-hydrogen-molecule and helium-antihydrogen scattering

Armour, E. A. G.; Cooper, James N.; Gregory, Margaret; Jonsell, Svante; Plummer, Martyn; Todd, A.C.

doi:10.1088/1742-6596/199/1/012007

Cited by 10 publications

(24 citation statements)

References 23 publications

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“…Some UN method of models calculations published while the present letter was under review gave Z eff = 13.5 [12]. The same article also gave a Z eff ≈ 10 with an explicit H 2 wave function and the UN group did not make a clear statement about which result should be preferred [12]. Table I.…”

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confidence: 85%

“…At present, all previous calculations significantly underestimate the low energy annihilation cross section. The most sophisticated calculations are the Kohn variational calculations performed by Armour and colleagues at the University of Nottingham (UN) [9,11,12]. Their most recent calculations significantly underestimate the annihilation cross section at thermal energies.…”

mentioning

confidence: 99%

“…The result given in Table I used a H 2 wave function which gave 99.7% of the correlation energy and were taken from the Ψ (2,B) t curves in Figures 7 and 8 of [11]. Some UN method of models calculations published while the present letter was under review gave Z eff = 13.5 [12]. The same article also gave a Z eff ≈ 10 with an explicit H 2 wave function and the UN group did not make a clear statement about which result should be preferred [12].…”

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confidence: 99%

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Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

2009

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The confined variational method is used to generate a basis of correlated gaussians to describe the interaction region wave function for positron scattering from the H2 molecule. The scattering length was ≈ −2.7 a0 while the zero energy Z eff of 15.7 is compatible with experimental values. The variation of the scattering length and Z eff with inter-nuclear distance was surprisingly rapid due to virtual state formation at R ≈ 3.4 a0.PACS numbers: 34.10.+x, 34.80.Bm, 34.80.Uv, 03.65.Nk The lack of spherical symmetry makes the calculation of electron or positron scattering from molecules an especially intractable computational problem. The nonspherical potential couples different partial waves resulting in an enormous escalation in the size of the calculation when compared with atomic targets. One consequence of this is that it is difficult to identify a definitive calculation of low energy electron/positron scattering from the simplest of molecules, i.e. H 2 , even under the simplifications of the fixed nucleus approximation.A new approach to compute the wave function for electron/positron scattering from small molecules is developed. It utilizes existing computational technologies from few-body physics that had been used to describe the low energy scattering of simple and composite projectiles from atoms [1,2,3]. The method is applied to the calculation of positron scattering from the H 2 molecule. The cross section for positron annihilation at thermal energies was found to be compatible with experimental values [4,5,6]. This is a significant achievement since the annihilation cross section presents a stringent test to the accuracy of the scattering wave function [7] and its successful prediction solves a previously intractable problem. Our calculations also show the existence of an unexpected virtual state at a H 2 inter-nuclear distance of R ≈ 3.4 a 0 .There have been a number of calculations of low energy e + -H 2 scattering and annihilation [7,8,9,10,11]. At present, all previous calculations significantly underestimate the low energy annihilation cross section. The most sophisticated calculations are the Kohn variational calculations performed by Armour and colleagues at the University of Nottingham (UN) [9,11,12]. Their most recent calculations significantly underestimate the annihilation cross section at thermal energies.We apply a variant of the confined variational method (CVM) [1, 2] to describe low energy positron-H 2 scattering. In the CVM, an artificial confining potential is added to the scattering Hamiltonian thus converting the system into a bound system. This provides a framework that permits the wave function in the interaction region to be obtained with bound state techniques. Of crucial importance to this exercise is the use of the stochastic variational method (SVM) [13,14,15] to describe the interaction region wave function. The SVM and variants [16] constitute a powerful tool for studying few body systems. The SVM uses a wave function that is a linear combination of explicitly correlated...

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Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

2009

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“…It can be seen that the results obtained using the method of modules are larger than those obtained without using this method. The vibrationally averaged value of Z eff (k), obtained using a Morse function, is 13.5 when obtained using the method of models and 9.7 without using this method [24,25]. Thus the value obtained with the method of models is closer to the experimental value of 14.6 [26] than that obtained without using it.…”

Section: Low-energy Positron-hydrogen-molecule Scatteringmentioning

confidence: 53%

“…However, this is not the case for HeH scattering. Cross sections forH loss through the three rearrangement reactions with products He +p + P s, Hep + e + and αp + P s − , respectively, are much smaller than forH loss by antiproton annihilation [37,25].…”

Section: Antihydrogenmentioning

confidence: 99%

Muon, positron and antiproton interactions with atoms and molecules

Armour

2010

J. Phys.: Conf. Ser.

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Effect of positron–atom interactions on the annihilation gamma spectra of molecules

et al. 2012

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Calculations of γ -spectra for positron annihilation on a selection of molecules, including methane and its fluoro-substitutes, ethane, propane, butane and benzene are presented. The annihilation γ -spectra characterise the momentum distribution of the electron-positron pair at the instant of annihilation. The contribution to the γ -spectra from individual molecular orbitals is obtained from electron momentum densities calculated using modern computational quantum chemistry density functional theory tools. The calculation, in its simplest form, effectively treats the low-energy (thermalised, room-temperature) positron as a plane wave and gives annihilation γ -spectra that are about 40% broader than experiment, although the main chemical trends are reproduced. We show that this effective 'narrowing' of the experimental spectra is due to the action of the molecular potential on the positron, chiefly, due to the positron repulsion from the nuclei. It leads to a suppression of the contribution of small positron-nuclear separations where the electron momentum is large. To investigate the effect of the nuclear repulsion, as well as that of short-range electron-positron and positron-molecule correlations, a linear combination of atomic orbital description of the molecular orbitals is employed. It facilitates the incorporation of correction factors which can be calculated from atomic manybody theory and account for the repulsion and correlations. Their inclusion in the 4 2 calculation gives γ -spectrum linewidths that are in much better agreement with experiment. Furthermore, it is shown that the effective distortion of the electron momentum density, when it is observed through positron annihilation γ -spectra, can be approximated by a relatively simple scaling factor. annihilation on a range of molecules including hydrogen, methane and its fluoro-substitutes, ethane, propane, butane and benzene.The first measurement of the Doppler-broadened γ -spectrum for positron annihilation on molecules was made in 1986 by Brown and Leventhal in low-density hydrogen gas [27]. In the early 1990s the confinement of thermalized positrons in a Penning trap allowed Tang et al [28] to measure γ -spectra for a range of molecules, including hydrocarbons and perfluorocarbons. This work was built upon by Iwata et al [3] who measured γ -spectra for positron annihilation on a large range of atoms and molecules in the gas phase. Despite this extensive set of experimental results, there is a paucity of theoretical calculations of the annihilation γ -spectra in molecules. Theoretical predictions of the γ -spectra do exist for the molecular ion H + 2 , for which (numerical) Coulomb-Born and configuration-interaction Kohn variational calculations have been performed [29], and for the small molecules H 2 and N 2 [30,31]. However, the application of these sophisticated methods to larger molecules is considerably more difficult. More than thirty years ago Chuang and Hogg [32] analysed the annihilation γ -spectra for hexane and decane. However, their ca...

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Detailed calculations on low-energy positron-hydrogen-molecule and helium-antihydrogen scattering

Cited by 10 publications

References 23 publications

Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

Muon, positron and antiproton interactions with atoms and molecules

Effect of positron–atom interactions on the annihilation gamma spectra of molecules

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