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

Abstract

The Dirac kinetic energy (DKE) form of the normal mass shift operator $$\left( {\tfrac{{m_e }} {M}\sum\nolimits_{i = 1}^N {T_i } } \right)$$ , which is an approximation of the $$\left( {\tfrac{1} {{2M}}\sum\nolimits_{i = 1}^N {P_i^2 } } \right)$$ 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.