Knowledge Bank

The Born-Oppenheimer theory of neutral diatomic molecules is based on an expansion in the parameter $K=(m/M)1/4$ (m = electron mass; M = nuclear mass). One has $K\approx 0.1$ for diatomic molecules from the first complete row of the periodic table. If R denotes the Rydberg (= 13.6 eV), then the electronic, vibrational, rotational energies are of order R, $K2R\approx 10-2R$, $K4R\approx 10-4R$. Decay by photon emission may usually be ignored in calculating the states, because the energy $\hslash \times (decayrate)\approx R(v/c)3\approx 10-8R$ is much smaller; (v = electron velocity; c = velocity of light). In unstable negative ions, the decay rate is usually much larger; how much depends on the mechanism of electron trapping. Therefore the decay can no longer be treated as a perturbation small compared with vibrational and rotational energies. In the special case of $H2-observed1$ in the scattering of electrons off $H2$ at about 3 eV one has $\hslash \times (decayrate)\approx 2eV\approx 0.15R>>K2R$. There the notion of a vibrational or rotational state becomes meaningless. One has to think of the nuclei as almost standing still during the lifetime of the $H2-$, and receiving an impluse from the extra electron, instead of being in a well-defined rotational and vibrational state. This and other physical examples of the breakdown of the familiar scheme of electronic, vibrational, rotational excitations will be discussed. Another possible difference between the excited states of neutrals and unstable negative ions arises from the mechanism of production--the absorption of radiation and electron capture. The interaction with the radiation field acts on one electron at a time; therefore, the electronic excited states of neutrals which one sees most strongly have a single excited electron. With electron-capture, there is some indication of the production of states with many excited electrons; crudely speaking, the electrons ``boil.’’ An example will be discussed. $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ F. Linder and H. Schmidt, Zeits. f. Naturforschung, 26a, 1603-17, (1971).