Theoretical Description of the SEFS Process

In this section we shall use the atomic (Hartree-Fock) system of units where ft = e = m = 1, the energy unit is e /ao = 2 Ry 27.2 eV, and the unit of length is the Bohr radius ao 0.52 A. 

The emission current, of 7 ( p, p), of secondary electrons with energies ranging from Ep to Ep + dEp and a momentum direction from p = p/p to p + dffis written as 

In the process under study, the energy conservation law is given by i ( , — E/), where , is the energy of the system in its initial state t), and / is the energy of the system in its final state /). The initial state of the system, [/), is characterized by the nonexcited electron subsystem of the sample and an incident electron io). The final state, /), is characterized by the incident electron that has lost energy, ), and a secondary electron (Ep, p), which is just detected in the experiment, as well as by a hole either on the sample atom core level or in the valence band. Summation over all final states that are not detected in the experiment is implied in Eq. (2). 

Consider the process of secondary electron emission from an atom whose electron subsystem consists of a core level, a), with 2na electrons, and the valence states, )8 , involving 2np electrons. In the case of the secondary electron emission from the core level la) the energy conservation law gives — Eu = Ep + Ea, where E — is the energy loss of the incident elecron, is the binding energy of the core level a), and Ep is the energy of the secondary electron detected in the experiment. Then, after the summation in Eq. (2) over the states i ) and 1 that are not detected in the experiment, the cross section of the secondary electron emission from the core level a) takes the form 

In the case of the secondary electron emission from the valence state P) its cross section is also defined by Eq. (3) with ) instead of la). The matrix element Tfi determines the amplitude of the transition from the initial state i) into the final 

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