Physics of Solid Surfaces pp 391-391 | Cite as

# Inverse photoemission

Chapter

## Abstract

In this chapter the theory behind the inverse photoemission process is discussed in detail.

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Inverse photoemission is a related technique that developed to allow studies of the unoccupied states in a system. It is usually considered as the time reversal of the photoemission process. Thus rather than an incident photon exciting an electron from a bound state, an incident electron is “captured” by a bound state resulting in the emission of a photon. Johnson and Davenport considered the differential cross section

*dσ*/*dΩ*for such an event. The density of final states for the emitted photons results in a differential cross section given by [85J1]$$ \frac{d\sigma}{d\Omega}=\frac{\alpha }{2\pi}\frac{\omega }{mc^2}\frac{1}{k}{\left|\left\langle b\left|A.p\right|k\right\rangle \right|}^2 $$

(91.1)

where the incident electron has momentum ħ

**k**and the outgoing photon energy ħ*ω*. Within the same framework with consideration of the density of final states for the outgoing electrons, Eq. 91.3 describing the photoemission process would be given by$$ \frac{d\sigma}{d\Omega}=\frac{\alpha }{2\pi}\frac{k}{m}\frac{1}{\omega }{\left|\left\langle k\left|A.p\right|b\right\rangle \right|}^2 $$

(91.2)

Thus for the same time-reversed transition, the ratio of the two cross sections will be given by

$$ R=\frac{{\left| d\sigma /d\Omega \right|}_{inv}}{{\left| d\sigma /d\Omega \right|}_{pes}}=\frac{\omega^2}{c^2{k}^2}=\frac{q^2}{k^2}={\left|\frac{\lambda_{elec}}{\lambda_{phot}}\right|}^2 $$

(91.3)

with *q* the wave vector of the photon. Thus in the UV range, with *R* proportional to the square of the wavelength of the incident “particle,” the cross section for inverse photoemission is lower than that of photoemission by a factor of approximately 10^{5}. This fact makes the experiment considerably more difficult, and as yet the ultrahigh resolutions available in photoemission have not been achieved in inverse photoemission.

## References

- [85J1]Johnson, P.D., Davenport, J.W.: Phys. Rev. B.
**31**, 7521 (1985)ADSCrossRefGoogle Scholar

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