1. 1 EFFECT OF EXITING PHOTON INELASTIC SCATTERING IN PHOTOIONIZATION OF ATOMS V.A. Kilin, R.Yu. Kilin Tomsk Polytechnic University

2. 2 1.Multi-step physical models in theoretical studies of atomic processes and properties 2.Model physical processes studied in our previous works as steps in multiple ionization of atoms 3.Post-photoexcitation fluorescent photons as inelastic scattered exciting photons 4.PT approach to inelastic photon scattering 5.Conclusion

3. 3 1. MULTI-STEP PHYSICAL MODELS IN THEORETICAL STUDIES OF ATOMIC PROCESSES AND PROPERTIES External perturbation (EM field, accelerated charged particles, etc.) Reaction products (excited atom, ions, photons) Isolated atom ? What we have in reality: 1.Probably, not all the reaction products observed 2.Experiment uncertainty 3.Interpretation of experimental data

4. 4 1. MULTI-STEP PHYSICAL MODELS IN THEORETICAL STUDIES OF ATOMIC PROCESSES AND PROPERTIES What we imagine (modeling) : To understand physics (main physical mechanisms) and, in many cases, carry out necessary evaluation of physical properties we need to decompose a complicated many- electron process into “elementary” steps, of which each could be explained in a language of “single-particle events”. KrI+  res  KrI 3d 9 np  (b)  KrII 4s 1 4p 4 n’l’ np +e 1  (  2 )  KrIII 4s 2 4p 3 np + e 1 + e 2   KrIII 4s 2 4p 3 ns/d+ e 1 + e 2 +  fl  KrIII 4s 2 4p 4 + e 1 + e 2 +  fl +  vis EXAMPLE: Multi-step Double Photoionization with excitation Photoexcitation of the resonant state KrI 3d 9 np and its further decay pathways  vis

5. 5 2. Model physical processes studied in our previous works as steps in multiple ionization of atoms 1. Many-electron Auger effects Three-electron (doubled) Auger effect Double Auger effect Satellite Auger transitions

6. 6 3d -1 →4s -1 4p -2 [ 4 P, 2 D] nl[LS] +q 3d -1 → 4p -3 [ 4 S, 2 D, 2 D] nl[LS] +q n=1,2,…,9; l=0,1,2,3; ε~2-35 eV Calculated superposition of the continuous spectra of double Auger transitions and discrete spectra of satellite Auger transitions in Kr 0 5 10 15 20 25 30 35 40 200 400 600 800 1000 1200 1400 Kr ×10 -6

7. 7 2. Model physical processes studied in our previous works as steps in multiple ionization of atoms 2. Autoionization transitions Double autoionization decay of a resonantly excited state Autoionization decay of a doubly excited state

8. 8 Calculated total electron spectrum of Double Autoionization transitions from KrI 3d 9 5p resonantly excited state

9. 9 i 1 i 2 i 3 nl  i 1,2,3 f n'l' 2. Model physical processes studied in our previous works as steps in multiple ionization of atoms Two-electron radiation transitions 3. Many-electron radiation transitions Three-electron radiation transitions

10. 10 2. Model physical processes studied in our previous works as steps in multiple ionization of atoms 4. Multiple photoionization (PI) Direct double PI Two-step double PI Triple PI

11. 11 Calculated and experimental DPI total cross sections of Ne

12. 12 3. Post-photoexcitation fluorescent photons as inelastic scattered exciting photons Principal possibility of an irradiation transition in a multi-step sequence, Slide 4, as well as the observation of resonant and background photons in PIFS experiments demonstrates that the effect of inelastic exciting photon scattering (IEPS) takes place in photo-ionization/excitation. (s): 2s 2 2p 6 +  1  2s 1 2p 6 +e p (s’): 2s 2 2p 6 +  1  2s 1 2p 6 +e s,d +  2 Examples (Ne) : (p): 2s 2 2p 6 +  1  2s 2 2p 5 + e s,d (p’): 2s 2 2p 6 +  1  2s 2 2p 5 + e p,f +  2 - The IEPS effect influences, in a measure, on both the measured and calculated PI cross sections and photoelectron angular distribution, especially in the region close around the resonant energy. - One may expect to observe and explain new features in fluorescence and photoelectron spectra as well as in photoelectron angular distribution taking into account the IEPS.

13. 13 3. Post-photoexcitation fluorescent photons as inelastic scattered exciting photons PIFS spectra of Kr

14. 14 4. PT approach to Inelastic Photon Scattering Conventionally, the photoionization (PI) of atoms is considered as a process of driving an atomic electron out because of interaction of a N-electron atom with EM field. Here the vector potential monochromatic plane waves of frequency ω, wave vector is a superposition of, (ω=с ), and polarization EM field intensity, atoms are able to absorb a single photon. Therefore, only one component with k = k 1, ω = ω 1 can be taken into account in calculation of PhI cross sections.. In case of low Let us consider the influence of inelastic exciting photon scattering (IEPS) on PI cross sections. It means that we consider the exciting photon energy region satisfying the following equation ω 1 = ω 2 + I f + ε q, where ω 1 and ω 2 are the exciting and scattered photon energies, respectively, I f is the ionization potential of a f-shell, and ε q is the photoelectron q energy. The transition energy E tr = ω 1 - I f = ω 2 + ε q can be continuously distributed (shared) between photoelectron q and scattered photon ω 2. This is very similar to the continuous energy distribution between two electrons in such processes as double PI, double Auger transitions, double autoionization of resonantly excited states, and so forth, considered in our previous works. Therefore, the contributionof IEPS into total PI cross section is the integral

15. 15 4. PT approach to Inelastic Photon Scattering To develop the theory of IEPS within the framework of perturbation theory (PT), now one needs to take into account two terms in the vector potential, which describe two monochromatic plane waves of frequencies ω 1 and ω 2. This lead to the formula for differential IEPS cross section In the lowest non-vanishing PT order the IEPS amplitude of the following two partial amplitudes: could be presented as the sum = = + + PT

16. 16 4. PT approach to Inelastic Photon Scattering It is seen that the partial amplitudes M 1 and M 2 can contribute significantly in cases : (a), i.e., if an intermediate state k is a hole or discrete excited one and (b), i.e., if an intermediate state k is a state of continuum. In case (a) the two opportunities of IEPS with PI of f-shell may be held via two steps, of which the first step is: (1) photoionization of intermediate k-shell followed by the second step irradiation transition k -1  f -1 + ω 2, left top in figure above, (2) excitation of intermediate hole-particle discrete spectrum state (f -1 k) due to the interaction with electromagnetic field and irradiation of the photon ω 2, which then followed by photoionization of (f -1 k), right top in figure above. Both in (1) and (2) the second step transition changes the photoelectron energy because of correlation interactions, which are not included yet within the considered order of PT. In case (b) the left bottom figure corresponds and describes the photoionization of f-shell with the ejection of intermediate photoelectron k on the first step. Then photoelectron k gives out a part of its energy irradiating the photon ω 2. = = + +

17. 17 4. PT approach to Inelastic Photon Scattering Higher PT order amplitudes, and so on

18. 18 4. PT approach to Inelastic Photon Scattering RPAE higher order PT diagrams RPAE higher order PT diagrams accounted through calculation of photoelectron WF in the field of vacancy i

19. 19 Conclusion 1.Background photoelectrons and fluorescent photons observed in PES and PIFS experiments could be related, at least partly, to the IEPS effect. 2. To accurately calculate the photoionization cross section nearby a resonance one needs take the IEPS effect into account. 3. Photoelectrons of “unusual” orbital momentum can be observed in PI superinducing new features in their angular distribution. 4. Additional term in vector potential of EM field responsible for irradiation of secondary photon allows new Interchannel Interactions in Photoionization and Photoexitation.