Calculation of Zeff for low-energy positron scattering by the hydrogen molecular ion

1996 ◽  
Vol 74 (7-8) ◽  
pp. 501-504 ◽  
Author(s):  
E. A. G. Armour ◽  
J. M. Carr
Keyword(s):  
Wave Function ◽  
Phase Shift ◽  
Variational Method ◽  
Partial Wave ◽  
Born Approximation ◽  
Low Energy ◽  
Positron Scattering ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion ◽  
Coulomb Phase

The Kohn variational method has recently been applied to the calculation of the addition to the Coulomb phase shift, in positron scattering, by the hydrogen molecular ion below the positronium-formation threshold at 9.45 eV. In this paper the wave function obtained for the lowest spheroidal partial wave of [Formula: see text] symmetry is used to calculate the contribution to Zeff from this symmetry. The results are significantly larger than those obtained using the Coulomb–Born approximation.

Momentum distribution in molecular systems

1941 ◽  
Vol 37 (4) ◽  
pp. 397-405 ◽  
Author(s):  
W. E. Duncanson
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Momentum Distribution ◽  
Wave Functions ◽  
Appreciable Change ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion ◽  
Molecular Systems ◽  
Similar Work ◽  
The One

The momentum distribution for the electron in the hydrogen molecular ion has been calculated for various wave functions, including the one used by James with which he obtained such a good value for the binding energy. The method adopted for this particular wave function is outlined and the results show appreciable change with improvement in the wave function. In conclusion there are discussed the implications of the present calculations on similar work on the H2 molecule.

The application of variational methods to atomic scattering problems III. The elastic scattering of electrons by helium atoms

1953 ◽  
Vol 219 (1136) ◽  
pp. 102-109 ◽  
Keyword(s):  
Differential Equation ◽  
Wave Function ◽  
Elastic Scattering ◽  
Phase Shift ◽  
Variational Method ◽  
Zero Order ◽  
Scattering Problems ◽  
Helium Atoms ◽  
Atomic Scattering ◽  
Slow Electrons

The variational method of Hulthèn has been applied to the elastic scattering of slow electrons by helium atoms, the effect of exchange being taken into account in calculating the zero-order phase shift. Satisfactory agreement has been obtained with the results given by numerical integration of the integro-differential equation determining the scattering when the total wave function is taken to be completely antisymmetric. Even at very low electron energies (0·04 eV) the agreement with experiment is good.

Investigation of Resonances in the Scattering of a Heavy ‘Positron’ by H2 that Involve Vibrationally Excited Quasi-Bound States

2010 ◽  
Vol 666 ◽  
pp. 25-30
Author(s):  
Edward A.G. Armour
Keyword(s):  
Variational Method ◽  
Bound States ◽  
Low Energy ◽  
Annihilation Rate ◽  
Effective Number ◽  
Feshbach Resonances ◽  
Vibrational States ◽  
Vibrationally Excited ◽  
Positron Scattering ◽  
Very High

There is currently great interest in the very large values of the positron annihilation rate that have been observed in low-energy positron scattering by some molecules. The annihilation rate is proportional to , the effective number of electrons in the target available to the positron for annihilation. These very high rates and associated values of have been 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 Vol. 61 (2000), p. 022720] and Gribakin and Lee [Phys. Rev. Lett. Vol. 97 (2006), p. 193201] as being due to Feshbach resonances involving excited quasi-bound vibrational states. Their explanation is partly phenomenological. In this paper, I describe the results of an ab initio treatment of this resonant behaviour in the case of the scattering of a heavy ‘positron’ by , using the Kohn variational method.

wave functions

1965 ◽  
Vol 61 (1) ◽  
pp. 207-209 ◽  
Author(s):  
A. R. Holt
Keyword(s):  
Wave Function ◽  
Spherical Harmonics ◽  
Energy Levels ◽  
Wave Functions ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion ◽  
Polar Representation ◽  
Image Position

Cohen and Coulson (4) and Cohen (5) have obtained wave-functions and energy levels for the hydrogen molecular ion in a spherical polar representation. They expanded the wave-function in terms of spherical harmonics, and their expansion may be written aswhere S = 2k for even states, and S = 2k + 1 for odd states.

Calculations of positron scattering on the hydrogen molecular ion

2019 ◽  
Vol 53 (1) ◽  
pp. 015203
Author(s):  
N A Mori ◽  
R Utamuratov ◽  
L H Scarlett ◽  
D V Fursa ◽  
A S Kadyrov ◽  
...  
Keyword(s):  
Positron Scattering ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion
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