1. Theory of photoionization by low and high intensity photon beams
M. Ya. Amusia
Racah Institute of physics, The Hebrew University, Jerusalem, Israel.

2. For me Photoeffect is a sort of an Ego
For me Photoeffect is a sort of an Ego. First talk about Stoletov’s work on photoeffect I gave in 1950, as a high school student, member of a circle in physics, headed in our school by Leningrad University student Yu. Meckler, now retired professor of the TA university. Came back to the problem, namely, to “Atomic photoeffect” in 1967, and stay with it till now.

3. Contents I. Introduction II. First experiments
III. Einstein’s theory 1905
IV. Atomic photoeffect
V. Photon momentum effects
VI. Endohedrals – “Big atoms”
VII. Interaction with laser beam
VIII. Re-scattering
IX. Role of exchange
X. Conclusions, Perspectives

4. I. Introduction
We will trace the whole way of photoionization studies: from classical predictions, to its experimental rejection, to Einstein’s quantum picture, to its triumph and achievements, to its inability to describe strong field situation, to an approach that helps today to understand the avalanche of new data by coming back on a new level to the classical approach on a new, to not yet verified predictions of this approach, and, finally, to its limitations.

5. II a. First experiments
Definition of external photoeffect and experimental set-up

6. II b. First experiments 1887 - H. Hertz - discovery of the photoeffect
A. Stoletov – photocurrent ~ Intensity of UV radiation
1897-J. J. Thomson – discovery of the electron, Nobel prize, 1906 "in recognition of the great merits of his … investigations on the conduction of electricity by gases"
1902 – P. Lenard – , Nobel prize, 1905 "for his work on cathode rays"
𝐸~𝜔

7. II c. First experiments Laws of photoeffect:
1. Number of emitted electrons ~ radiation intensity I,
2. Maximum electron speed depends upon radiation frequency only,
3. For each material some lowest frequency exists.
Law 2 and 3 – non-classical!

8. III a. Einstein’s theory 1905
Concerning an Heuristic Point of View Toward the Emission and Transformation of Light. Annalen der Physik 17 (1905):
Central Idea: light exists as a beam of particle-like objects – quanta, later named photons.
Nobel prize, "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect"

9. III b. Einstein’s theory 1905
is the photon frequency
k- photon momentum
Conservation laws are correct in an in

10. IV a. Atomic photoeffect One-electron approximation+
One-electron photoionization
amplitude: 2 1

11. IV b. Atomic photoeffect Many-electron correlations: intra- and inter-shell collective interactions

12. IV c. Atomic photoeffect Random phase approximation with exchange – RPAE –diagrams
Dynamic collective response of a system upon an external field 2 2 3    = + + 4 1 1 2 а b 1 2 3    + + + 4 4 1 3 4 2 3 2 1 1 c d e

13. IV d. Atomic photoeffect Random phase approximation with exchange – RPAE – formulas
Amplitude:
Cross section:

14. IV e. Atomic photoeffect
Powerful maxima in photoabsorption
cross sections, angular distributions,
spin polarization etc
-resonance frequency

15. IV f. Atomic photoeffect . Giant Resonance
Photoionization of 4d10 in Xe

16. IV f. Atomic photoeffect . Interference resonance
Photoionization of 5p6 in Xe

17. IV g. Atomic photoeffect Two-electron photoionization+ 1 2
For He at high frequency

18. V a. Photon momentum effects Non-dipole corrections
Lowest order in , quadrupole corrections
Photon momentum
Detection at magic angle ,

19. V b. Photon momentum effects “Drug” currents in photoeffect
The current is able to change sign due to ion recoil:

20. V c. Photon momentum effects “Drug” currents in photoeffect

21. V d. Photon momentum effects “Drug” currents in plasma
Low-charged plasma
Absorb radiation , creating current,
Current:
Laser current ~0.01A

22. V e. Photon momentum effects Mechanism of light pressure
 Linear Momentum transfer
 Flux:
  V ”drag”
AB light pressure dominates:
ordinary or AB
Example:

23. VI a. Endohedrals – “Big atoms” (CN shell, reality)
This is a system with a big classical multi-electron shell. Example C60 with 240 electrons
Photons
Electrons

24. VI b. Endohedrals – “Big atoms” (C540 shell)
Photons
Electrons 24

25. VI c. Endohedrals – “Big atoms” (CN1@C N2 - onion - type)
Photons
Electrons 25

26. VI d. Endohedrals – “Big atoms” (CN shell, scheme)
Atom A
Fullerene CN

27. VI e. Endohedrals – “Big atoms” (by CN1 and CN2 shells)

28. VI f. Endohedrals – “Big atoms”

29. VI g. Endohedrals – “Big atoms” Confinement 4d Xe

30. VI h. Endohedrals – “Big atoms” (Giant resonance 4d)
Photoionization cross-sections of 4d C240

31. VI i. Endohedrals – “Big atoms” (CN shell polarization)
Atom A
Fullerenes electron density

32. VI j. Endohedrals – “Big atoms” (CN1 and CN2 shells, in anti - phase)

33. VI k. Endohedrals – “Big atoms” (Intershell interaction)=
Here, is the F radius, is its polarizability

34. VI k. Endohedrals – “Big atoms” Giant Endohedral Resonances
Total GER oscillator strength –40-100!

35. VI k. Endohedrals – “Big atoms” Giant Endohedral Resonances
3p electrons in Ar,

36. VII a. Interaction with laser beam First experiments
– Observation of two-electron ionization of Sr and Ba (V. Suran et al)
Beam intensity was 1014 Watt/cm
Photon energy
One-electron ionization – 5 photons
Two-electron photoionization – 10 photons
At saturation intensities ratio A++/ A+~1
Explanation: A++ is formed via excitation of an auto-ionizing discrete atomic level

37. VII b. Interaction with laser beam First surprises
– Observed multiple ionization of noble gases (A. L’Huillier et al)
1984 – Measured photoelectron energy in Xe+,++.
Observed absorption of up to 100 photons with ionization of up to 10 electrons at 1014 Watt/cm and
Observed high energy electrons and even photons from inner shell excitations
The multi-electron processes proved to be highly probable

38. VII c. Interaction with laser beam Challenge
“…observations raise a number of questions which cannot be answered at the present time. The production of multiply charged ions is most probably induced by a collective response of the atomic shell irradiated by an intense laser pulse. Multiply excited states are expected to play an important role”.
From A. L’Huillier et al, J. Phys. B: At. Mol. Phys. 17 (1984) L817-L822.

39. VIII a. Re-scattering Response
“Atomic antenna” (M. Kuchiev, 1987)
It addressed and resolved the theory-experiment discrepancy that reached 40(!) orders of magnitude.
Main idea: primary ionized atomic electron starts to oscillate in the field of the laser beam

40. VIII b. Re-scattering Response
From M. Yu. Kuchiev

41. VIII c. Re-scattering Response
Simple and impressive:
Electron classic oscillation energy is
Oscillation amplitude
Constrains
Radiation
Example
Possible role of atomic resonances – Giant, etc
Coherent oscillation of several electrons
Best generators are fullerenes and medium-size clusters (became clear much later)

42. VIII d. Re-scattering Response
Response of the community – ZERO. In 1989, at a big meeting in New York, I spoke at a special round table on lasers I presented these results
Laser VIP said: “This is so simple that if it would be correct, everybody would know it. But nobody knows. So, this is incorrect”.
Re-scattering started its way to general acceptance since rediscovered by P. Corkum in 1993
Today re-scattering is generally accepted and step by step refined

43. IX a. Role of exchange Undeveloped direction
Atomic and external electric field combination.
Barriers for two, inner i and outer o atomic levels.
Probability to find outside for inner electron

44. IX b. Role of exchange Undeveloped direction
Exchange modifies the inner wave function drastically
No exchange
With exchange
No – number of outer electrons

45. IX c. Role of exchange Undeveloped direction
Exchange modifies the probability to find an inner electron outside the atom drastically:
Example: Ii = 5, Io = ½, E = 1 in atomic units (1016 Watt/cm2)

46. X a. Conclusions. Perspectives
We presented a number of features of photoeffect on the bases of quantum Einstein equations
We demonstrated that at high intensity the equation is not valid
If classics come back
Does it mean that if multiphoton processes are improbable? No!

47. X b. Conclusions. Perspectives
Free electron laser, photon energy 90.5 eV has very small energy However, in interaction with Xe ions were produced ions up to (M. Richter et al , 2009). The field is not exhausted and some other ideas may be of importance.
You still cannot do everything: example – the many-electron atom. R. P. Feynman, 1961
Thank You very much for attention!