Many-Electron Atoms Selection Rules and Spectra

5 MANY-ELECTRON ATOMS SELECTION RULES AND SPECTRA 

An interesting example of a many-electron spectrum is that of He, in which the shown low-energy transitions involve orbital jumps of one of the two electrons. For this case our one-electron atomic selection rules (A/ = 1, Ay = 0, 1) hold for the electron involved in the transition. The He electronic spectrum resembles 

Strong El transitions in many-electron atoms are observed only when one electron changes its orbital quantum numbers for this electron, the selection rule A/= +1 must be obeyed (cf. our discussion following Eq. 2.12). To appreciate this, we recall that spatial wavefunctions in many-electron atoms may be expressed (Section 2.3) in terms of products (1, 2. p) = i(i)(j 2 2) 4 pip) of one-electron orbitals 0i(l), / 2(2),. .., (j p p Since the pertinent electric dipole operator is p= — eSr, the El transition moment from electronic state 2,. .., p) to state 2,. .., p) = i(l)( 2(2). .. 0p(p) 

Each of these terms contains a factor i(OI il0j(O) analogous to the hydrogenlike transition moment (2.10), multiplied by orthogonality integrals 0jU) l jiJ)y for all other electrons j i. Hence, if electron i jumps to a new orbital, i.e., -(i) orthogonality requires that all other electrons remain in 

The El selection rules may also be formulated in terms of the quantum numbers L, S, and J for the many-electron orbital, spin, and total angular momentum. These prove to be 

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