EGAS41 - Swansea University

41 st EGAS CP 82 Gdańsk 2009
Nonrelativistic energies for lithium-like systems with
exponentially correlated functions
M. Puchalski, K. Pachucki ∗
Institute of Theoretical Physics, University of Warsaw, ul. Hoza 69, 00-681 Warsaw, Poland
∗ Corresponding author: Krzysztof.Pachucki@fuw.edu.pl
The analytical evaluation of four-particle integrals, performed in 1987 by Fromm and
Hill [1], opened up possibilities for high-precision variational calculations of four-particle
systems in a basis of exponential functions of all interparticle distances. These ideas were
explored later by several authors [2, 3] with a moderate success.
We are going to present effective algorithm for the four-body system, based on the
combination of the integration by parts technique [4] and numerical integration methods
[5]. We determined accurate non-relativistic wave functions and energies for the Li atom
and the Be + ion with an uncertainty of 10 8 using only 96 basis functions.
Apart from the nonrelativistivc energy, these functions can be used in matrix element
calculations. They are very useful especially for operators at higher orders of the perturbative
NRQED theory. Together with our high-precision methods in Hylleraas basis [6],
we are aiming to determine mα 6 and mα 7 effects in the hyperfine structure of lithium-like
systems.
Acknowledgment
This work is supported by NIST PMG 60NANB7D6153.
References
[1] D.M. Fromm, R.N. Hill, Phys. Rev. A 36, 1013 (1987)
[2] V.S. Zotev, T.K. Rebane V.S., Phys. Rev. A 65, 062501 (2001)
[3] F. Harris, arXiv:0901.3942
[4] F.V. Tkachov, Phys. Lett. B 100, 65 (1981); K.G. Chetyrkin, F.V. Tkachov, Nucl.
Phys. B 19281159
[5] J. Ma, V. Rokhlin, S. Wandzura, SIAM J. Numer. Anal. 33, 971 (1996)
[6] M. Puchalski, K. Pachucki, Phys. Rev. A 73, 022503 (2006), Phys. Rev. A 78, 052511
(2008), Phys. Rev. A 79, 032510 (2009)
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