Continuum function, photoionization

A related but somewhat different approach has been suggested by the recently introduced MS Xa method. Calculation of the continuum functions within this method is relatively straightforward,51 52 and the method has been applied to the AT-shell X-ray absorption spectrum53 of N2 and very recently to photoionization of N2 and CO near threshold.54 This last... 

In order finally to derive the differential cross section of photoionization one inserts equ. (8.26) in equ. (8.24) and replaces the number nph of incident photons by nPh = ce0Alo)/2ti (see equs. (8.4b) and (8.8a) and (8.8b)) and the interaction operator by equ. (8.21). Then one removes the factor h2/m0 resulting from the normalization of the continuum function from the matrix element and incorporates it in the final prefactor (see footnote concerning equ. (7.28d)), and one introduces the fine structure constant a using a = el/4ne0hc. This leads to (for the summations over magnetic quantum numbers see below)... 

S,2 1FP 2.3, (12) ionization continuum. Inset, photoionization cross-section for formation of the dimer ion Cs as a function of photon energy. 

For the purposes of this review it is convenient to focus attention on that class of molecules in which the valence electrons are easily distinguished from the core electrons (e.g., -n electron systems) and which have a large number of vibrational degrees of freedom. There have been several studies of the photoionization of aromatic molecules.206-209 In the earliest calculations either a free electron model, or a molecule-centered expansion in plane waves, or coulomb functions, has been used. Only the recent calculation by Johnson and Rice210 explicitly considered the interference effects which must accompany any process in a system with interatomic spacings and electron wavelength of comparable magnitude. The importance of atomic interference effects in the representation of molecular continuum states has been emphasized by Cohen and Fano,211 but, as far as we know, only the Johnson-Rice calculation incorporates this phenomenon in a detailed analysis. 

Figure 2.1 Plot of the radial functions Pls(r) and Pep(r) for the bound Is and a photoionized sp electron in neon as functions of the square root of the radial coordinate r (all quantities are in atomic units). The parameter s indicates the kinetic energy of the continuum electron. The radial functions have been calculated for Pl8(r) and Pep(r) using the HF potentials of the electron configurations ls22s22p6 and ls2s22p6, respectively. From [Sch95],...

The combined effect of the individual energy distribution functions which are of relevance for the photoionization process and for the detection of photoelectrons, can now be discussed. As a first step, the photoionization process alone, i.e., without any detection device, is discussed with the help of Fig. 2.9. The y-axis represents an energy scale with respect to the ground state, and different states of neon are plotted along the x-direction. For photons with sufficient energy hv and with a distribution function GB( ph, Eph), one reaches the continuum above the Is... 

Figure 5.22 Reduced matrix elements dy, in atomic units, and relative phases (<5y — <5V), in radians, as functions of photon energy for 5p photoionization in xenon leading to the 5p5 2P3/2 final ionic state. The dashed vertical lines give the 2P3/2 and 2P,/2 ionization thresholds at 12.13 and 13.44 eV, respectively. The data in the continuous range above the 2P1/2 threshold are shown as full circles with error bars. The curves below the 2P3/2 and 2P1/2 ionization thresholds are expected to approach the values in the continuum continuously (for details see the discussion and references in the original publication). From [HSS86] the dt given here are larger by /3 in order to adapt them to the cross section...

Figure 13 shows a pictorial view of the final-state radial wave functions relevant to core transitions in a molecule. Core transitions take place in an effective molecular potential seen by the excited photoelectron. Whereas for E < E0, that is, below the continuum threshold (where E0 is the energy of the core ionization potential), discrete transitions occur to the unoccupied valence states, photoelectrons excited in the photoionization process with... 

A model of the spectral dependence of the photoionization spectrum of group-III acceptors in silicon has been presented by Edwards and Fowler [52]. This model uses hydrogenic continuum states and hydrogenic ground-state wave functions scaled to account for central-cell corrections, and it provides a good description of the energy dependence of the cross-sections, as can be seen from Fig. 7.8. 

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