One-hole state

Ekin(electron from autoionization decay) = hv, — Ef(one-hole state), (1.29c)... 

We now introduce the very important concept of a one-hole state. Th is a state i) of the weak-coupling basis y) that is formed by annihilatin an electron in the target ground state 0). Clearly (y a(q) 0) in (11.13) is zero if ) is not a one-hole state. A one-hole state a) is denoted by the orbital of the annihilated electron. In the context of the many-electron ion space this notation cannot be confused with that of the orbital. 

The weak-coupling approximation is made by taking only the leading term a) of the expansion (11.13) in one-hole states. Its validity can be experimentally verified. In the overwhelming majority of cases it turns out to be valid. In this approximation... 

The orbital energy is the expectation value for the one-hole state a) of the ion Hamiltonian Hj. 

The spectroscopic factor (11.16) is the absolute square of the coefficient of the one-hole state a) in this expansion. Determination of one coefficient in each of several eigenstates of Hi in the representation is a strong constraint on the calculation. Furthermore the determination of spectroscopic factors depends only on the validity of the weak-coupling... 

The sensitivity of fragmentation to the nature of resonances was shown for tetramethylsilane by using the photoion photoion coincidence technique (Morin et al. 1986). In this technique, fragmentation channels are identified by the coincidences of pairs of ions in the time-of-flight mass spectrometer. For tetramethylsilane, two resonances were observed in the ion pair yield curves. The lower energy resonance, below the ionization edge, had been shown from electron spectra to decay into a one-hole state, but the production... 

Although we usually do not write a hole explicitly in the occupied MO level in the energy level scheme but two electrons, the scheme always means that the occupied MO level corresponds to that of one-hole state and the unoccupied MO level to one-electron state by assuming Koopmans theorem [30]. The valence band is thus called the hole band and the conduction band is called the electron band. For ionization, Koopmans theorem gives... 

We now generalize our previous development to obtain a diagrammatic representation of RS perturbation theory as applied to an N-state system. Consider the problem of finding the perturbation expansion for the lowest eigenvalue of such a system. Here we still have only one hole state, 1>, but there are now N - 1 particle states n>, n = 2, 3,..., AT. We draw the same set of diagrams as before. However, now we can label the particle lines with any index n. For example, the diagram... 

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