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If, on the other hand, it suffers another collision with an electron while still in the excited state, it may collisionally de–excite back down to the ground state. The collisional cross–section is a strongly varying function of energy, in general varying approximately inversely as the impact energy. 1 Collisional Excitation by Electron Impact 35 is a more convenient quantity to use, since it removes the primary energy dependence for most atomic transitions. In this equation, me is the electron mass, E is the electron energy, and g1 is the statistical weight of the ground state.

Ionised magnesium, (Mg+ or Mg ii), which is isoelectronic with sodium and has one optically active electron in its outer shell will have the ground state, defined by the electron configuration and the ground term; 1s2 2s2 2p6 3s 2 S1/2 . While one optically active electron only allows us one way of forming the total angular momentum by combining the spin and the orbital angular momentum, with two or more electrons life gets much more complicated. Consider the case of two electrons. For light atoms, as first shown by Russell & Saunders, the angular momentum vectors are coupled by electrostatic interaction to form the total orbital angular momentum, and the spins are also coupled by electrostatic interaction to give the total spin: L = l1 + l2 = (l1 + l2 ), (l1 + l2 − 1), ...

If the operator O is anti–symmetric like the dipole operator D then the symmetry of the integrand is determined using simple product rules. 2 Molecular Spectra 29 S be any symmetric function and A be any anti–symmetric one, then the following apply: SS → S SA → A AS → A AA → S So, for the transition probability to be non–zero, with an anti–symmetric operator like D, the wavefunctions Ψ1 and Ψ2 must be of opposite symmetry. This can be confirmed by taking triplets of S s and As with the middle term being A and multiplying through with the above rules.