Effect in Heavy Atoms

An extremely important enhancement occurs in heavy atoms as first pointed out by Bouchiat and Bouchiat. The essential points can be 

One would expect the momentum to increase as Z near the nucleus because of the increased nuclear charge attracting the electron. Another factor of Z enhancement can be seen by using the expression Fermi and Segre derived for s(0) in order to calculate the isotope shift in alkali-like atoms  

We have added K the relativistic correction factor which may be as large as 10 for heavy atoms. Equation (17) was first derived by Bouchiat and Bouchiat and is useful for estimating the order of magnitude of PNC effects in atoms. 

An accurate calculation in heavy atoms requires a thoroughgoing relativistic treatment. The central field-independent particle approximation gives a first-order answer, but corrections involving electron exchange, noncentral effects, and other electron-electron correlations are needed in many cases. Details of the calculations have been reviewed elsewhere  

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Abstract. Investigation of P,T-parity nonconservation (PNC) phenomena is of fundamental importance for physics. Experiments to search for PNC effects have been performed on TIE and YbF molecules and are in progress for PbO and PbF molecules. For interpretation of molecular PNC experiments it is necessary to calculate those needed molecular properties which cannot be measured. In particular, electronic densities in heavy-atom cores are required for interpretation of the measured data in terms of the P,T-odd properties of elementary particles or P,T-odd interactions between them. Reliable calculations of the core properties (PNC effect, hyperfine structure etc., which are described by the operators heavily concentrated in atomic cores or on nuclei) usually require accurate accounting for both relativistic and correlation effects in heavy-atom systems. In this paper, some basic aspects of the experimental search for PNC effects in heavy-atom molecules and the computational methods used in their electronic structure calculations are discussed. The latter include the generalized relativistic effective core potential (GRECP) approach and the methods of nonvariational and variational one-center restoration of correct shapes of four-component spinors in atomic cores after a two-component GRECP calculation of a molecule. Their efficiency is illustrated with calculations of parameters of the effective P,T-odd spin-rotational Hamiltonians in the molecules PbF, HgF, YbF, BaF, TIF, and PbO. 

Study of P- and T-parity nonconservation effects in heavy-atom molecules Historical background... 

Relativistic effects in heavy atoms are most important for inner-shell electrons. In ab initio and DFT calculations these electrons are often treated through relativistic effective core potentials (RECP), also known as pseudopotentials. This approach is sometimes called quasirelativistic, because it accounts for relativity effects in a rather simplified scalar way. The use of pseudopotentials not only takes into account a significant part of the relativistic corrections, but also diminishes the computational cost. 

Also in the molecular case perturbation theory helps to clarify individual contributions to the property ax cording to their order [120] but more crucial is the fact that perturbation theory becomes an inadequate means for the proper description of relativistic effects in heavy atoms. Furthermore spin-orbit effects can substantially influence the result and methods using multi-component wave functions incorporating spin-orbit coupling from the beginning are favorable. 

Dietz, K., 1985, On the Relativistic Theory of Inhomogeneous Many-Electron Systems, in Atomic Theory Workshop on Relativistic and Q.E.D. Effects in Heavy Atoms, AIP Conf Proc. No. 136, eds H.P. Kelly and Y.-K. Kim (American Institute of Physics, New York) p. 36. 

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