Screening, nuclear

When multi-electron atoms are combined to form a chemical bond they do not utilize all of their electrons. In general, one can separate the electrons of a given atom into inner-shell core electrons and the valence electrons which are available for chemical bonding. For example, the carbon atom has six electrons, two occupy the inner Is orbital, while the remaining four occupy the 2s and three 2p orbitals. These four can participate in the formation of chemical bonds. It is common practice in semi-empirical quantum mechanics to consider only the outer valence electrons and orbitals in the calculations and to replace the inner electrons + nuclear core with a screened nuclear charge. Thus, for carbon, we would only consider the 2s and 2p orbitals and the four electrons that occupy them and the +6 nuclear charge would be replaced with a +4 screened nuclear charge. 

In the scale of Allred and Rochow, electronegativity is measured as the electrostatic force exerted at the covalent radius (rcov) of the atom [14,15]. This electronegativity can be written as a function of the screened nuclear charge (Z ) and the atomic size as ... 

The nuclear-only DKH (nDKH) approximation described above may be trivially extended to include spin-orbit coupling (SOC) effects. Unfortunately, the nDKH approximation systematically overestimates the spin-orbit splittings of the one-electron energies (in some cases by as much as 100%) due to the neglect of compensating two-electron SOC terms.[78] This error can be corrected through the use of the screened-nuclear-spin-oibit (SNSO) approximation, developed by Boettger [78] see discussion below. 

SNSO screened nuclear (potential) spin-orbit (method)... 

A1 Representative GenSim main busbar screen (nuclear)... 

Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) is also used to study nuclear materials. Commonly, samples are introduced into an ICP-MS via an aerosol. However, LA has become the sample introduction technique of choice for solid samples and those samples that cannot be easily aero-solubilized [100]. Nanosecond LA coupled to an ICP-TOF-MS can rapidly screen nuclear and nonnuclear solid samples for a wide array of nuclides and isotopes (nuclides of the same element) [101]. LA-ICP-MS is also used to analyze uranium oxide [102-103] these studies determine the ratios of U-235, U-236, and U-238 isotopes in the sample from microgram sample quantities. Isotopic ratio calculations are essential to determine if the sample is natural or of human origin. 

Of course, the inclusion of the spin-orbit terms increases the computational demand for DKH calculations because the number of terms is enlarged, and, when included in a variational procedure, the one-electron orbitals must be two-component functions that would require significant extensions to a nonrelativistic one-component computer program. For the efficient calculation of two-electron spin-orbit terms, Boettger proposed an efficient screened-nuclear spin-orbit approximation [659]. Shortly after its proposal, this model has been extended and investigated further [660,661]. 

S. Majumder, A. V. Matveev, N. Rosch. Spin-orbit interaction in the Douglas-BCroU approach to relativistic density functional theory the screened nuclear potential approximation for molecules. Chem. Phys. Lett., 382 (2003) 186-193. 

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