Doubly Excited States ofH−of High Principal Quantum Number: Implications for Electron-Atom Ionization

Abstract

It is pointed out that insight into the threshold region of electron-atom ionization can be gained by examination of the nature of the doubly excited states of the compound ion. A study of these states for ${\mathrm{H}}^{-}$ has been initiated with two types of variational wave functions. One, ${\Psi }_W$, has the two electrons at roughly equal distances from the nucleus; the other, ${\Psi }_D$, has one electron at a very much farther distance so that it sees the dipole potential caused by the inner electron and the nucleus. Both functions are constructed to be eigenfunctions of the operator $Q_N$, which projects out all states of the target of principal quantum number less than $N$, and renders the energy subject to a minimum principle. If the number of states for which ${\Psi }_W$ yields a lower energy than ${\Psi }_D$ is proportional to $N^{\gamma }$, then an extrapolation argument shows that the threshold yield curve will be effectively proportional to $E^{\frac{(3-\gamma )}{2}}$. Calculations have been done to $N=5\mathrm{}$ for ${\Psi }_D$ and $N=9\mathrm{}$ for ${\Psi }_W$. Only the lowest of the ${\Psi }_W$ states is lower than the corresponding ${\Psi }_D$ state. The results suggest $\gamma$ in the range $0<\mathrm{}\gamma <~\frac{1}{2}$. Some comments on Wannier's theory of ionization are made.