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Mini-workshop on "Numerical challenges in relativistic quantum mechanics"
Organizers: Werner Kutzelnigg (Bochum), Eric Séré (Paris-Dauphine)


Bogumil Jeziorski (Warsaw, Poland): "Relativistic and QED effects in the weak interaction of helium atoms"
Friday 19 April 2013, 16:30 - 17:15
Amphi Hermite


Bogumil Jeziorski
Faculty of Chemistry, University of Warsaw, ul. Pasteura 1, 02-093 Warsaw, Poland

Relativistic and QED effects in the weak interaction of helium atoms

The relativistic and QED contributions to the pair potential of helium were computed using orbital as well as explicitly correlated four-electron basis sets [1,2]. As the explicitly correlated calculations are not size-consistent special techniques had to be used to achieve satisfactory accuracy in the weak interaction region. Accurate asymptotic constants were obtained and used to represent the long-range part of the relativistic and QED contributions to the potential.
The computed potential was used to determine properties of the very weakly bound 4He2 dimer and thermophysical properties of gaseous helium. It was shown that the Casimir-Polder (CP) retardation damping of the nonrelativistic interaction, increasing the dimer size by about 2 Å relative to the nonrelativistic value, is almost completely accounted for by the inclusion of the Breit interaction and the Araki-Sucher contributions to the potential. The remaining retardation effect, of the fourth- and higher order in the fine-structure constant, is practically negligible for the bound state, but is important for the thermophysical properties of helium. These properties have theoretical uncertainties that are significantly smaller than those of the most accurate measurements and can be used to establish new metrology standards based on properties of low-density helium. As two 4He atoms form a dimer with significant wave function amplitudes at distances R > 100 Å where the retardation switches the London R−6 decay of the potential to the CP R−7 form it has been assumed in the literature that this switching is responsible for the observed 2 Å (4%) increase of the bond length . We show that is, in fact, insensitive to the potential at R > 20 Å and its increase is due to the Breit and Araki-Sucher corrections computed by us from expressions valid at short R, i.e., beyond the validity range of the CP theory [3] . Computation of these corrections seamlessly extends the CP theory to distances relevant for properties of long molecules.

[1] W. Cencek, M. Przybytek, J. Komasa, J. Mehl, BJ, K. Szalewicz, J. Chem. Phys., 136, 224303 (2012).
[2] M. Przybytek, W. Cencek, J. Komasa, G.Lach, BJ, K. Szalewicz, Phys. Rev. Lett., 104, 183003 (2010).
[3] M. Przybytek, BJ, W. Cencek, J. Komasa, J. Mehl, K. Szalewicz, Phys. Rev. Lett., 108, 183201 (2012).