Eur. Phys. J. D (2012) 66: 290
https://doi.org/10.1140/epjd/e2012-30328-5

Regular Article

On the breakdown of the Dirac kinetic energy operator for estimating normal mass shifts

¹ Service de Chimie quantique et Photophysique, Université Libre de Bruxelles, 1050 Brussels, Belgium
² Institute of Theoretical Physics and Astronomy, Vilnius University, 01108 Vilnius, Lithuania
³ School of Technology, Malmö University, 20506 Malmö, Sweden

^a e-mail: mrgodef@ulb.ac.be

Received: 23 May 2012
Received in final form: 2 August 2012
Published online: 27 November 2012

Abstract

The Dirac kinetic energy (DKE) form of the normal mass shift operator (m_e/M ∑_i=1^N T_i), which is an approximation of the (1/2M ∑_i=1^N p_i²) operator built on the relativistic electron momenta, is widely used in relativistic atomic structure calculations. In the present paper, we illustrate the progressive breakdown of the Dirac kinetic energy form relatively to the momentum form when increasing the nuclear charge along the lithium isoelectronic sequence. Both forms are incorrect in the relativistic case but the DKE operator provides expectation values that are closer to the results obtained with the more complete relativistic recoil operator.