Electro- and Magnetostatic Interactions
This chapter will include all of those static interactions that can in some way effect the total energy of any given level of an atom or ion of interest. That’s a tall order. Consider that the total energy of an atom is known, having solved the problem pr
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Electro- and Magnetostatic Interactions
This chapter will include all of those static interactions that can in some way effect the total energy of any given level of an atom or ion of interest. That’s a tall order. Consider that the total energy of an atom is known, having solved the problem presented in the previous chapter; that is, all of the electrons are in stationary states about some nucleus, with the only interactions being electrostatic attraction to the nucleus and repulsion to other electrons. The solution to such a problem would have ignored additional interactions. The largest, and one alluded to in previous chapters, is the fine-structure interaction. This is the coupling of the angular momenta of the outer electrons, the ones in open subshells. All filled shells and subshells have zero total angular momentum, so those electrons cannot take part. Whichever way one chooses to couple the angular momenta, and there are many different possible ways (Russell–Saunders coupling being just one), the total angular momentum, J, is a good quantum number. At this stage the question you might want to ask is why aren’t all of the different levels with differing J values degenerate? The answer is that if the Hamiltonian were composed only of the terms considered in the previous chapter, they all would be degenerate. But measurement shows that they are not, so something must have been left out of the Hamiltonian. Actually quite a few terms have been left out of the Hamiltonian which is known by solving the one-electron hydrogen atom relativistically. In recent years, the two-electron atom has been solved relativistically (not in closed form but to extraordinary precision), so it really is known that there are lots of interactions among the orbital and spin angular momenta of the electrons that produce additional terms in the Hamiltonian. The good news is that they can be handled quite successfully by perturbation techniques. The plot thickens when one considers the fact that the nucleus also can have a net angular momentum with an associated magnetic dipole moment, and an electric quadrupole moment and these too can interact with the electron cloud to alter the total energy and produce a new total angular momentum. What is interesting is that these nuclear effects are typically orders of magnitude smaller than the finestructure effects mentioned above, and if one is performing an experiment to a R.L. Brooks, The Fundamentals of Atomic and Molecular Physics, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-1-4614-6678-9 3, © Springer Science+Business Media New York 2013
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3 Electro- and Magnetostatic Interactions
level of precision that is not sensitive to such small interactions, then ignoring those interactions is OK. We do, however, live in a world of high-precision measurements, so it is commonly the case that one has to consider the specific atom and levels of interest before deciding on which interactions to include.1 The above comments still ignore external electric and magnetic fields. Interac
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