Atomic Multiplets

Abstract

In this chapter, we extend the study of atomic structure from atoms with one valence electron to those with two or more valence electrons. As illustrated in the two previous chapters, excited states of one valence electron atoms having a given angular momentum and parity can be described in the independent-particle model using a single Slater determinant. For atoms with two or more electrons, a linear combination of two or more Slater determinants are typically needed to describe a particular state. In addition to the state of interest, this linear combination describes one or more closely related states; the collection of states given by the linear combination of Slater determinants is referred to as a multiplet. To study multiplets, it is convenient to replace the description of states using Slater determinants by the equivalent second-quantization descrip-tion of the following section. The rules of second-quantization rules are familiar from studies of the harmonic oscillator in quantum mechanics. A more complete discussion may be found in Lindgren and Morrison (1985). 4.1 Second-Quantization We start our discussion of second quantization by examining the description of one-and two-electron states. As in the previous chapters, we let a single index k designate the set of one-particle quantum numbers (n k l k m k µ k). The one-electron state |k, describe by its wave function ψ k (r) previously, is represented in second quantization by an operator a