Evolution of Photoionization Studies: From Classical Predictions to Quantum Triumph
Tracing the journey of photoionization studies from classical predictions to experimental rejections, quantum interpretations by Einstein, and current understanding through a classical approach. Highlighting key experiments, laws of photoeffect, and limitations faced in describing strong field situations.
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Theory Theory of of photoionization by low photoionization by low and high intensity and high intensity photon beams photon beams M. Ya. Amusia Racah Institute of physics, The Hebrew University, Jerusalem, Israel.
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 Meckler, now retired professor of the TA university. Came back to the problem, namely, photoeffect in 1967, and stay with it till now. student Yu. to Atomic
Contents I. II. 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 Introduction First experiments
I. Introduction 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.
II a. First experiments Definition of external photoeffect and experimental set-up
II b. First experiments 1887 - H. Hertz - discovery of the photoeffect 1888-1891 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 1905 "for his work on cathode rays" , Nobel prize, ?~?
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!
III a. Einsteins theory 1905 Concerning an Heuristic Point of View Toward the Emission and Transformation of Light. Annalen der Physik 17 (1905): 132-148. Central Idea: light exists as a beam of particle- like objects quanta, later named photons. Nobel prize, 1921- "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect"
III b. Einsteins theory 1905 E = 1905 I el ion is the photon frequency = / k c k k- photon momentum 1916 = p k p el rec Conservation laws are correct in an in
IV a. Atomic photoeffect One-electron approximation + 2 One-electron photoionization d amplitude: 2 1 1
IV b. Atomic photoeffect Many-electron correlations: intra- and inter-shell collective interactions
IV c. Atomic photoeffect Random phase approximation with exchange RPAE diagrams Dynamic collective response of a system upon an external field 2 3 2 = + + 4 1 1 2 b 1 2 3 + + + 4 4 3 4 2 1 3 2 1 1 c d e
IV d. Atomic photoeffect Random phase approximation with exchange RPAE formulas Amplitude: ( ) D U ( ) 3 4 4 1 3 2 3 4 d D = + 1 2 1 2 + + E E i F F 3 4 F F 3 4 U V V = ' 1 ' ' 1 ' ' ' 1 1 2 2 1 2 2 1 2 2 Crosssection: 2 4 2 ( ) ( ) ( ) F i D = + i E E id c
IV e. Atomic photoeffect Powerful maxima in photoabsorption cross sections, angular distributions, spin polarization etc ( b ) a = ( ) ( ) A a 1 [ ( )] -resonance frequency
IV f. Atomic photoeffect . Giant Resonance 40 Photoionization cross section, Mb 30 4d Xe 20 10 0 4 6 8 10 Photon energy, Ry Photoionization of 4d10 in Xe
IV f. Atomic photoeffect . Interference resonance 0.8 RPAE GRPAE exp.1 exp.2 exp.3 0.7 0.6 5s Xe Cross section (Mb) 0.5 0.4 0.3 0.2 0.1 0.0 2 3 4 5 6 7 8 9 Photon energy (Ry) Photoionization of 5p6 in Xe
IV g. Atomic photoeffect Two-electron photoionization + 2 For He at high frequency ++ + / 1.4% 1
V a. Photon momentum effects Non-dipole corrections ( ) ( )1 4 d + d = + ( ) (cos ) P + nl nl 2 nl + ( ) (cos ) P ( ) (cos ) P 1 3 nl nl c / c Lowest order in , quadrupole corrections Photon momentum Detection at magic angle , = / c = 2(cos P ) 0 0 54.7 m m
V b. Photon momentum effects Drug currents in photoeffect Current: ( ) ( ) ( ) tr k ( ) = e ph | | e Wmv d d j en dr ( ) 1 ( ) = ph cos d ( ) ph The current is able to change sign due to ion recoil: P P P = + P ph e ion e
V c. Photon momentum effects Drug currents in photoeffect Current: 3 0 -1 2) -12a/cm He 2 -2 Xe Ar I5p (10 I3p -3 0 5 10 15 Xe I5s 1 2) -11amp/sm 0 -1 *10 j (10 -2 Ar -3 Xe -4 1,0 1,5 2,0 2,5 Photon energy (Ry)
V d. Photon momentum effects Drug currents in plasma Low-charged plasma Absorb radiation , creating current, Current: 2 8 15 (0) ( E e N ( ) | | e W j e s 2 laser ) c E A L Laser current ~0.01A 10 cm sec W = 30 2 1
V e. Photon momentum effects Mechanism of light pressure Linear Momentum transfer Flux: ( ) ~ ( )/ ( ) BA AA el W k f , 2 2 ( ) Z ( ) ~ 4 ln [ sec], cm BA c 0 V drag 1/4 = (0) / 2 2 . Z E 0 AB light pressure dominates: ordinary Example: 0.1 = 4 2 2 or AB eV ~ ( ) / P N c 2 2 2 ) = ~ ( / O P Z Mc , AB 5 eV E P P cm 12 3 10 N AB O
VI a. Endohedrals Big atoms (CNshell, reality) This is a system with a big classical multi-electron shell. Example C60with 240 electrons Electrons Photons
VI b. Endohedrals Big atoms (C540shell) 220px-Fullerene_c540 Electrons Photons
VI c. Endohedrals Big atoms (CN1@CN2- onion - type) Electrons Photons
VI d. Endohedrals Big atoms (CNshell, scheme) Atom A Fullerene CN
VI e. Endohedrals Big atoms (by CN1and CN2shells) CN1 CN 2 C A
VI f. Endohedrals Big atoms = ( ) ( ) V r V r R 0 = 2 AC nl A nl ( ) | ( | ) k ( ) F , , l l l = 2 k R l sin 2 V u ( ) k R k = ( ) , F k l 2 ( ) 0 l 2 ( ) ( ) R u R = R l tan ( ) k , l + ( ) R / 2 u k V 0 l l
VI g. Endohedrals Big atoms Confinement 4d Xe 60 Xe free Xe@C60, FRPAE Xe@C60 50 +, experiment 40 Cross section (Mb) 30 4d Xe 20 10 0 6 7 8 9 10 Photon energy (Ry)
VI h. Endohedrals Big atoms (Giant resonance 4d) 70 Xe, free Xe@C60, FRPAE Xe@C60@C240, FRPAE2 Xe@C60@C240, FRPAE2 with polarization 60 50 Cross section, Mb 40 4d Xe I4d=75.59 eV 30 20 10 0 80 100 120 140 160 Photon energy, eV Photoionization cross-sections of 4d in Xe@C60 @ C240
VI i. Endohedrals Big atoms (CNshell polarization) Atom A Fullerenes electron density
VI j. Endohedrals Big atoms (C CN1 N1and CN2shells, in anti - phase)
VI k. Endohedrals Big atoms (Intershell interaction) = + D@ D D A A C C N N 1 ) ( ) C ( ) ( D D N @ A C A 3 R N Here, is the F radius, is its polarizability R ( ) C N 2 ( ) C = 2 2 A s A s ( ) ( | ) ( | ) 1 ( | ) ( | ) ( ) F F S N R s A A C 3 N
VI k. Endohedrals Big atoms Giant Endohedral Resonances ( ) np kd s = = AC , 2 A np ( ) ( ) k F , , kd s d s 2 ( ) ( ) d s F G C ( ) ( ) 2 d F A np k S , , kd s Total GER oscillator strength 40-100!
VI k. Endohedrals Big atoms Giant Endohedral Resonances 1800 Ar, free Ar@C60, FRPAE Ar@C60@C240, FRPAE2 Ar@C60@C240, FRPAE2 with polarization 1600 1400 1200 Cross section, Mb 1000 800 3p Ar, I3p=16.05 eV 600 400 200 0 20 25 30 Photon energy, eV 3p electrons in Ar, Ar@C60, Ar@C60@C240
VII a. Interaction with laser beam First experiments 1975-1977 Observation of two-electron ionization of Sr and Ba (V. Suran et al) Beam intensity was 1014Watt/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
VII b. Interaction with laser beam First surprises 1982-1984 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 1.17eV
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.
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
VIII b. Re-scattering Response From M. Yu. Kuchiev
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) 2 ~ / E el 2 ~ + / a / 20 W cm 2 ~ / a e I 10 2 = 200 ! E Mev = 2 / el
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
IX a. Role of exchange Undeveloped direction Atomic and external electric field combination. Barriers for two, inner i and outer o atomic levels. 2 ~ ( ) ir Probability to find outside for inner electron i
IX b. Role of exchange Undeveloped direction Exchange modifies the inner wave function drastically No exchange iI r 3/4 i ( ) r I e i r N C I r I r I r + 3/4 i 3/4 o ( ) r I e I e o With exchange i o i 2 r i N CI I r I r 3/4 o e o o 2 i I I 0 i No number of outer electrons
IX c. Role of exchange Undeveloped direction Exchange modifies the probability to find an inner electron outside the atom drastically: 2 ( ) r 3/2 2 2 E N I C 3/2 i , i ex i 2 /E I o o e 2 3 i I ( ) r i i Example: Ii= 5, Io= , E = 1 in atomic units (1016Watt/cm2) 14 10 !
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 ( I ) If classics come back ~ / el A E I 2 2 ~ / E I Does it mean that if multiphoton processes are improbable? No! el A
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! 2 ~ / E I el A Xe+ 19
