Photoionization cross-section of

E (2n3/2) E (2n1/2). The spin-orbit interaction will appear between discrete Rydberg states of different series having the same fl value (see Section 3.4.2). 

Consider the (pn) ns J) 3IIi and 1IIi Rydberg series of O2 converging to the X2II state of 0, as described by the Rydberg formulas 

A(X2fI) is the electronic energy in the absence of spin-orbit splitting  

The spin-orbit interaction associated with the unpaired pn core electron mixes the 3IIi and 1IIi components of the same n value (AO = 0). In the case (a) basis, the secular equation is [see Eq. (3.4.14)] 

The difference between the triplet and singlet energies is approximately 2Kn, where Kn is an exchange integral proportional to (n )-3. As discussed in Section 3.4.2.1.2, the mixing between 3IIi and increases with n, and when n becomes infinite the states are completely mixed and are described by a case (c) basis that corresponds to the limiting solutions, 

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The discrete line sources described above for XPS are perfectly adequate for most applications, but some types of analysis require that the source be tunable (i.e. that the exciting energy be variable). The reason is to enable the photoionization cross-section of the core levels of a particular element or group of elements to be varied, which is particularly useful when dealing with multielement semiconductors. Tunable radiation can be obtained from a synchrotron. 

Figure 11. Multichannel quantum defect theory simulations of the photoionization cross section of Ar versus excitation wavenumber, in the presence of a DC field of magnitude (a) 0.001 V/cm, (b) 0.1 V/cm, (c) 0.2 V/cm, (d) 0.3 V/cm and (e) 2.0 V/cm.

Figure 12. Multichannel quantum defect theory simulations of the photoionization cross section of N2, field = 0.3 V/cm (a) near n - 70 and (b) near n = 80, including N = 0, 2, Mj = I channels only, with excitation from J = 2, Mj = 1.

Figure 14. Photoionization cross section of NH3 and apparent photoionization cross section for NH produced by reaction of NH3+ with NH3. Variation of reaction cross section as function of vibrational state of reactant NH3+ ion was determined by comparing relative step heights of curves for NH3+ and NH after ordinate scales of both curves were adjusted so that data points of first plateau at about 10.2 eV coincide. Ratio of a pair of corresponding step heights is then proportional to ratio of cross section for reaction of vibrationally excited NH3+ to that for NH3+ in its ground vibrational state. Step heights used to determine relative cross section for reaction of NH3+ with v = 5 are shown. Step ratio NH//NH3+ decreases with increasing e.85 ...

The photoionization cross section of a statistical mixture of m levels of the nt state to the e t continuum is then given by... 

Here hco = In[j + e, where e refers to photoelectron energy and I ij is the binding energy of the nly-electron in the atom. Performing the summation in (33.9) over j and neglecting the dependence of e on j, we arrive at the following expression for total photoionization cross-section of the closed shell ... 

F. Miiller-Plathe, G.H.F. Diercksen, Molecular photoionization cross sections by moment theory. An introduction, in S. Canuto, J. D Albuquerque e Castro, F.J. Paixao (Eds.), Electronic Structure of Atoms, Molecules and Solids, World Scientific, Singapore, 1990 F. Miiller-Plathe, G.H.F. Diercksen, Perturbative-polarization-propagator study of the photoionization cross section of the water molecule, Phys. Rev. A 40 (1989) 696. 

The thus determined wavefunctions of the continuous spectrum of the atom A encage in C60, combined with the wavefunctions of the ground state of the free atom A, are used in determining the total and differential photoionization cross sections of the encaged form. 

Thus, F(oj) has a complicated codependence. The latter will be mirrored in the photoionization cross section of the encaged atom. Correspondingly, the photoionization cross section of the encaged atom in the dynamical-cage approximation might differ greatly from that in the frozen-core approximation, both quantitatively and qualitatively. 

Figure 4 RPAE calculated results for the Xe 4d photoionization cross section of free Xe, o 4dee, as well as of Xe C6o calculated in the framework of both the 5-potential model, a s [37] and A-potential model, a4 A [33], Also shown, for comparison, are calculated data [33], marked ct4 5a, obtained for the 4d photoionization cross section of Xe Cgo with an artificially reduced thickness of the Cgg cage from A = 1.9 au to A = 0.5 au, deepened potential depth, UgQ = 25.9 eV, and changed inner radius Rc = 6.389 au, in order to simulate the 5-potential model but keep the binding strength of the cage potential unchanged (see the main text body).

Figure 5 Is and 2s photoionization cross sections of free Ne (o ee and o ee) and Ne from Ne Cgo (a 5 and a 5) calculated [34] within the 5-potential model.

The presented data illustrate the noticeable sensitivity of threshold values of the photoionization cross sections of confined atoms to the principal quantum number n. Indeed, as seen from Figure 5, the photoionization cross section anoticeably increases, whereas er 5 decreases, at threshold, compared to the free Ne atom. As a result, for confined Ne, the threshold... 

Figure 17 The Cgo dynamical screening function F (to) [40] along with the RPAE calculated 5p photoionization cross section of free Xe, CT eefei, encaged Xe both at the frozen-cage approximation...

One one occasion, for the Xe 5s photoionization cross section of Xe C(,o in a photon energy region of the encaged Xe 4d giant resonance, modified... 

Figure 18 Calculated [33] RPAE results for the Xe 5s photoionization cross section of Xe Cgo obtained in the A-potential model at the frozen-cage approximation level. (a) o 1" A iro), complete RPAE calculation accounting for interchannel coupling between photoionization transitions from the Xe 4d10, 5s2 and 5p6 subshells (b) 5 A ( >), the same as in (a) but with the 4d - f, p transitions being replaced by those of free Xe, for comparison purposes (c) o AA(

The quintessence of the reversed electron correlation effect is illustrated in Figure 20 by nonrelativistic HF and RPAE calculated data of the 4s photoionization cross section of free Ca and encaged Ca, Ca C60 near threshold, both at the frozen-cage approximation level, afs A, [20] and dynamical-cage approximation level, afsA [64]. 

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