260
D. G. Green and G. F. Gribakin
increasing electron binding energy. We find that the type of the positron wavefunction used, i.e., Dyson orbital which accounts for the positron-atom correlation attraction vs repulsive static-field (HF) wavefunction, has relatively little effect on the EF,
except for the valence orbitals in most polarisable targets. We also find a relatively
weak dependence of the EF for the core and inner-valence electrons on the positron’s
orbital angular momentum.
The weak momentum-dependence of the EF obtained in positron-atom calculations suggests that they can be used to improve the calculations of positron annihilation in more complex environments. One such system is positronium colliding
with noble-gas atoms, where calculations of Ps-atom pick-off annihilation rates that
neglect the short-range vertex enhancement strongly underestimate the measured
rates [70]. Another context where similar EF can be used is positron annihilation in
molecules. Here there is a sharp contrast between the large amount of experimental information, including í µí»¾-spectra, for a wide range of molecule [69] and paucity
of credible theoretical data [23, 71]. The positron-molecule problem is particularly
interesting because the Z eff values for most polyatomic molecules show orders-ofmagnitude increases due to resonant positron annihilation [71]. In such molecules
the positron annihilates from a temporarily formed weakly-bound state. Attempts to
calculate such states using standard quantum-chemistry methods have been numerous but not very successful [71] (i.e., there is only a small number of systems where
theory and experiment can be compared, and the agreement is mostly qualitative
[72]).
The calculations presented in this paper could be extended to other atoms, including those with open shells. Partial filling of electron shells can be taken into account
in the many-body-theory sums using fractional occupation numbers (cf. Ref. [73]),
and the positron wavefunction is insensitive to such details of the electronic
structure at the static (HF) level. (At the level of Dyson orbitals, one will need
to calculate the positron self-energy using fractional electron-shell occupancies.)
Calculations are particularly straightforward for annihilation with core electrons, as
their enhancement factor is described well by the first-order correction to the annihilation vertex.
Acknowledgements DGG is supported by a United Kingdom Engineering and Physical Sciences
Research Council Fellowship, grant number EP/N007948/1.
References
1. Asoka-Kumar P, Alatalo M, Ghosh V, Kruseman A, Nielsen B, Lynn K (1996) Phys Rev Lett
77:2097. https://doi.org/10.1103/PhysRevLett.77.2097
2. Lynn KG, MacDonald JR, Boie RA, Feldman LC, Gabbe JD, Robbins MF, Bonderup E,
Golovchenko J (1977) Phys Rev Lett 38:241. https://doi.org/10.1103/PhysRevLett.38.241
3. Iwata K, Gribakin GF, Greaves RG, Surko CM (1997) Phys Rev Lett 79:39. https://doi.org/10.
1103/PhysRevLett.79.39
D. G. Green and G. F. Gribakin
increasing electron binding energy. We find that the type of the positron wavefunction used, i.e., Dyson orbital which accounts for the positron-atom correlation attraction vs repulsive static-field (HF) wavefunction, has relatively little effect on the EF,
except for the valence orbitals in most polarisable targets. We also find a relatively
weak dependence of the EF for the core and inner-valence electrons on the positron’s
orbital angular momentum.
The weak momentum-dependence of the EF obtained in positron-atom calculations suggests that they can be used to improve the calculations of positron annihilation in more complex environments. One such system is positronium colliding
with noble-gas atoms, where calculations of Ps-atom pick-off annihilation rates that
neglect the short-range vertex enhancement strongly underestimate the measured
rates [70]. Another context where similar EF can be used is positron annihilation in
molecules. Here there is a sharp contrast between the large amount of experimental information, including í µí»¾-spectra, for a wide range of molecule [69] and paucity
of credible theoretical data [23, 71]. The positron-molecule problem is particularly
interesting because the Z eff values for most polyatomic molecules show orders-ofmagnitude increases due to resonant positron annihilation [71]. In such molecules
the positron annihilates from a temporarily formed weakly-bound state. Attempts to
calculate such states using standard quantum-chemistry methods have been numerous but not very successful [71] (i.e., there is only a small number of systems where
theory and experiment can be compared, and the agreement is mostly qualitative
[72]).
The calculations presented in this paper could be extended to other atoms, including those with open shells. Partial filling of electron shells can be taken into account
in the many-body-theory sums using fractional occupation numbers (cf. Ref. [73]),
and the positron wavefunction is insensitive to such details of the electronic
structure at the static (HF) level. (At the level of Dyson orbitals, one will need
to calculate the positron self-energy using fractional electron-shell occupancies.)
Calculations are particularly straightforward for annihilation with core electrons, as
their enhancement factor is described well by the first-order correction to the annihilation vertex.
Acknowledgements DGG is supported by a United Kingdom Engineering and Physical Sciences
Research Council Fellowship, grant number EP/N007948/1.
References
1. Asoka-Kumar P, Alatalo M, Ghosh V, Kruseman A, Nielsen B, Lynn K (1996) Phys Rev Lett
77:2097. https://doi.org/10.1103/PhysRevLett.77.2097
2. Lynn KG, MacDonald JR, Boie RA, Feldman LC, Gabbe JD, Robbins MF, Bonderup E,
Golovchenko J (1977) Phys Rev Lett 38:241. https://doi.org/10.1103/PhysRevLett.38.241
3. Iwata K, Gribakin GF, Greaves RG, Surko CM (1997) Phys Rev Lett 79:39. https://doi.org/10.
1103/PhysRevLett.79.39