Photoelectron Spectroscopy

BY A. HAMNETT AND A. F. ORCHARD

There has been intense activity in the general field of photoelectron (p.e.) spectroscopy, especially as regards the low-energy aspect of the technique which normally involves photoionisation in the vapour phase using u.v. radiation sources. A very important book on u.v.–p.e. spectroscopy by Turner et al. has appeared, the fruit of many years research by the pioneering Imperial College-Oxford group. P.e. spectroscopy using X-ray sources (X–p.e. spectroscopy or ESCA*) has in the past been almost entirely confined to the solid state, but in late 1969 an authoritative monograph by Siegbahn et al. on the X–p.e. spectroscopy of gases was published. The proceedings of a Royal Society discussion on p.e. spectroscopy held in February 1969 has now appeared in print : this provides a most interesting variety of articles on both u.v.–p.e. and X–p.e. studies. A very useful recent review by Brundle' should also be mentioned.

We report on u.v.–p.e. and X–p.e. spectroscopy in separate sections below. But first of all, a brief review of theoretical work on photoelectron emission is appropriate.

1 The Theory of Photoelectron Emission from Atoms and Molecules

Theoretical work on gas-phase phenomena falls naturally into two categories : (i) the angular distribution of photoelectrons and (ii) the calculation of total photoionisation cross-sections. Photoelectrons show an intensity variation with angle of emission because the plane of polarisation of the exciting radiation defines an axis of quantisation. For unpolarised radiation the direction of the photon beam provides such an axis. It has been known for many years that the angular dependence for electric-dipole induced transitions obeys the general law

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where x is the axis of polarisation, φx is the angle between the momentum vector of the ejected electron and this axis. and β is the asymmetry parameter which has been defined in various ways. P2(cos φ) is the second Legendre polynomial and is given by the expression 1/2(3 cos2 φ - 1).

Peshkin has shown how the above equation may be derived from quite general considerations of symmetry and has elaborated the theory to cover cross-pole and multipole ionisations. The assumptions underlying his derivation may be listed as:

(a) the target atoms are oriented at random,

(b) the influence of external fields is neglected,

(c) when more than one electron is emitted, the direction of emission of the

An expression for the asymmetry parameter β was first given by Bethe for the hydrogen atom and generalised recently by Cooper and Zare and also by Berry et al. to many-electron atoms, a central spherical potential field and LS coupling being assumed. Calculations using this formula have been made for the inert gases by Manson and Cooper, who show how β varies with the energy of the exciting radiation. Buckingham et al. have extended equation (1) to the case of diatomic molecules and have found that its form is unaltered save that the value of β will depend on the specific Hund coupling case involved. The equation derived by Cooper and Zare can be seen as a special case of the more general expression given by Buckingham et al. Sichel has extended this work to the situation where rotational fine structure can be resolved.

Experimental verification of the general form of equation (1) is difficult since, in normal photoelectron work, the ionising radiation is unpolarised. The corresponding expression for unpolarised radiation is given by Peshkin as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where φ, is now the angle between the trajectory of the ejected electron and the photon beam. This formula has been shown to hold for argon by Morgenstern et al., for argon, xenon and various small molecules by Vilesov and Lopetin, and for zinc and cadmium atoms (in an atomic beam) by Harrison. Samson has discussed the form of the equation for partially polarised radiation (obtained from a grating) and has measured values of the asymmetry parameter β for argon and molecular nitrogen. He finds that β is very nearly 2 for helium, indicating that at an observation angle φ, given by cos φ = [square root of 2/3] the troublesome selfabsorption by helium in He" spectra might be eliminated.

The calculation of photoionisation cross-sections poses many problems, not least of which is the fact that the true forms of the continuum wavefunctions are not known for polyelectronic species. It is usually assumed that continuum functions for many-electron atoms differ from those of the hydrogen atom simply by a phase factor, δ, which can be shown theoretically to relate to the quantum defect, obtainable from Rydberg analysis of atomic spectra, extrapolating to positive energy. However, this information is not available for most molecules, nor indeed has the theory been shown to hold in the molecular (non-spherically symmetrical) case. Another major problem concerns the accuracy with which the ground state of the neutral atom or molecule is described. To evaluate properly the scope of the theory the best wavefunctions to hand should of course be used : but this is easier said than done, and most workers have been forced to compromise this requirement by using rather inaccurate wavefunctions. Tuckwell has, with some measure of success, calculated photoionisation cross-sections for molecular N2 and 02, making use of a transformation into prolate spheroidal co-ordinates: in the case of O2, however, the quantum defect data were not available so that only relative cross-sections could be estimated. Similar calculations have been performed for atoms by Henry and also by McGinn, while a more empirical approach has been described by Zilitis. Perhaps the most sophisticated many-electron treatment was reported by Brown, who has computed ab initio photoionisation cross-sections for the helium atom, using a correlated atomic wavefunction. The agreement with experimental data was disappointingly poor at high photon energies.

A further complicating factor, in the theory of molecular photoionisation, is the variation of cross-section with energy over the vibrational structure of a photoelectron band. The calculation of the Franck–Condon factors continues to interest many workers. In particular, Tuckwell has shown for O2, that similar cross-sections are obtained by direct integration, without separation of the electronic and vibrational problems, and also by independent calculation of Franck–Condon factors. This provides justification for the customary use of the Franck–Condon principle in molecular photoelectron...