International Workshop on Atomic Interactions in Laser Fields - Abstracts

Ouantum Mechanically Complete Photoionization Experiments

Hans Kleinpoppen

Atomic Physics Laboratory, University of Stirling, Stirling, U.K.

 

I. Introduction

Photoionisation processes of atoms (A) are traditionally investigated by the total and differential cross section (Becker and Shirley 1996):

  1. A + hν → A+ + e, with the total cross section σ(hν) as a function of the photon energy
  2. with the differential cross section dσ(Θ,hν)/dΩ, where Θ is the angle between the electric field vector of the incoming radiation and the direction of the photoelectron.

Another type of photoionization studies has been developed in connection with the possibility that both atoms and electrons can be restricted to the fact that the atoms may be oriented or aligned and the photoelectrons spin-polarized. This possibility leads to new types of photoionization investigations which can be associated to so-called "quantum mechanically complete photoionization experiments". Fano (1957) and Bederson (1969) proposed the complete atomic collision experiments. Eminyan et al. (1973) and Standage and Kleinpoppen (1976) reported the first experiments for electron atom excitation processes. Heinzmann (1980) reported complete photoionization experiments of atoms by spin analysis of the photoelectrons.

Fano (1957) discussed general principles for so-called ideal atomic collision experiments. It follows from Fano's arguments that the linearity of the Schrodinger equation describing the collision process results in a method for quantum mechanically complete experiments. An initial state of colliding atomic particles may be prepared such that it is described by a quantum mechanically pure state: |Ψin> = |P>|A>, where |P>, |A> are state vectors of the projectile and atomic target, respectively. Due to the linearity of the Schrodinger equation, the initial state |Ψin> = |P>|A> is "transferred" to the final state |Ψout>. According to such a scheme the knowledge represented by the state vector |Ψout> represents maximum information on the atomic collision process. For the photoionization process this scheme for complete photoionization experiments is described by |Ψin> = |hν>|A> → |Ψout> = |A+>e>. Becker (1998) published a more complete summary of applications of related investigations; Cherepkov et al. (1995) discussed in detail photoionization of polarized atoms.

II. Applications of Photoionization with Polarized Atoms

Several groups have reported photoionization studies with polarised atoms: Becker (1998) and Schmidt (1997) have summarized their results in particular. We will however restrict ourselves here only to the papers published by the Becker group at the Fritz-Haber-Institüt of the Max-Planck-Gesellschaft. The theoretical formalism linking the experimental data with quantum mechanical amplitudes and phases is based upon the theoretical paper of Klar and Kleinpoppen (1982). The scheme of the apparatus required is as follow:

The atomic beam is polarised by a magnetic hexapole magnet. Their polarisation at the target area (crossing between the synchrotron and the atomic beam) is finally made up by the small magnetic field of a pair of Helmholtz coils. A rotateable electron spectrometer detects the photoelectrons at an angle Θ between the electric vector of incoming radiation and the propagation vector of the photoelectron. A Rabi magnet combined with a quadrupole mass spectrometer is applied to measure the degree of polarisation of the atomic beam. The problem of selecting atoms for photoionization studies of polarised depends on technical possibilities and scientific aspects which is discussed in the original and summarising papers. In this talk we will restrict ourselves to approaches of quantum mechanically complete photoionization experiments with polarised open shell atomic oxygen (Plotzke et al., and Prümper et al. 1997) and thallium atoms (Prümper et al. 1999).

a) Polarized Oxygen Atoms

The polarised oxygen atom is in the state O(1s22s22p4)3P2 with Stern-Gerlach profiles of % occupation of the magnetic substates Mj of the 3P2 atom state as follows:

Mj = -2(3%), -1(7%), 0(13%), 1(24%), 2(53%). The relevant photoreactions studied are:

O(1s22s22p4)3P2 + hν → O+(1s22s22p4) 4P2 + e

O+(1s22s22p3) 4S3/2, P1/2,3/2, 2D3/2,5/2

A substantial difference in the angular distributions (magnetic dichroism) of 2p photoelectrons from polarised oxygen atoms was found for antiparallel atomic polarisations as a function of photon energy from 25 to 52eV. In particular, the magnetic dichroism in the photoelectron angular distributions for the final ionic states 2D and 2P is examined and compared with predictions made from measurements on. s. For comparison with other techniques concerning complete photoionization experiments the photoelectron spin polarisation to be expected under a special experimental geometry is derived.

b) The Thallium 5d- and 6p- Photoionization

Polarized thallium atoms (degree of polarization was 0.33 +- 0.03 have been applied to study the linear magnetic dichroisms of the following photoionizations processes in the low photoelectron energy range (< 40 eV):

Tl 5d10 6s2 6p2 P1/2 + hν → Tl+ 5d9(2D5/2,3/2) 6s2 6p(2P1/2) + e-

Tl 5d10 6s2 6p(2P1/2) + hν → Tl+ 5d10 6s2 (1S0) + e-

The Tl+ 5d3(2D3/2)6s2 6p(2P1/2)J = 1 state (J combines the vector addition of the 2D3/2 and 2P1/2 states) has been particularly useful for the magnetic dichroism and partial wave analysis of the Tl 5d - ionization. Measurements and a partial wave analysis resulted in the angular distribution parameter β, the phase differences Δfp between the f and the p waves the asymmetry (the antiparallel polarization intensities of the electron intensities) and the amplitude ratios γfp = Rf/Rp between the two photoelectron waves.

Similar linear magnetic dichroism measurements of the 6p-photo-electrons of thallium according to the second reaction above resulted in measurements of the angular distribution parameter β the phase difference Δsd between the s- and d- partial waves of the photoelectrons, the asymmetry (the antiparallel amplitudes as above) and the ratio γds = Rd/Rs of the two photo-electron waves.

Comparisons are made between the experimental Tl-data and the Hartree-Fock-(HF) and random-phase-approximation-exchange (RPAE) method are made and will be discussed.

III. Conclusions

The combination of polarized atoms. linearly polarized VUV-light and angle resolved photoelectron spectrometry provides sufficient data information to analyse the photoionization process "quantum mechanically complete", i.e. a partial photoelectron wave analysis. While in certain cases a β-measurement may not distinguish between HF- and RPAE- methods a study with polarized atoms can be powerful enough to distinguish between them.

References

  1. Becker, U. and Shirley, D.A., eds of "VUV and Soft X-Ray Photoionisation", Plenum Press, New York and London, 1996.
  2. Becker, U., J. Electr. Spectroscopy 96, 1105 (1998).
  3. Bederson, B., Comments At. Mol.. Phys. 1, 41 and 65 (1969).
  4. Cherepkov, N.A., Kuznetsov, V.V. and Verbitskii, V.A., J. Phys. B 28, 1221 (1995).
  5. Eminyan, M., MacAdam, K., Slevin, J. and Kleinpoppen, H., Phys. Rev. Lett. 31, 576 (1973 ).
  6. Fano, U., Rev. Mol. Physics 29, 74 (1957).
  7. Heinzmann, U., J. Phys. B 13, 4353 and 4367 (1980).
  8. Klar, H. and Kleinpoppen, H., J. Phys. B 15, 933 (1982).
  9. Plotzke, O., Prümper, G., Zimmermann, B., Becker, U. and Kleinpoppen, H., Phys. Rev. Lett. 77, 2642 (1996).
  10. Prümper, G., PhD. Thesis, Technical University, Berlin 1998, D83 No. 11 of "Studies of Vacuum Ultraviolet and X-Ray Processes", ed. U. Becker, Fritz-Haber-Institut, Berlin.
  11. Prümper, G., Zimmermann, B., Plotzke, O., Becker, U. and Kleinpoppen, H., Europhys. Lett. 38 (1), 19 (1997).
  12. Prümper, G., Zimmermann, B., Langer, B., Becker, U. and Kleinpoppen, H., in BESSY Jahresbericht 1998 P.152 - 154 and to be published.
  13. Schmidt, V., "Electron Spectrometry of Atoms Using Synchrotron Radiation", University Press, Cambridge (1997).