“L+1 rule” for continuous electron-hole excitations in photoemission spectra
V. I. Grebennikov, T.V. Kuznetsova.
Institute of Metal Physics, UD RAS, Ekaterinburg 620041, Russia
Low-energy excitations in valence bands arestudied by means of XPS spectroscopy. The analysisof a form of core levels spectra gives the size of effectsof electron-hole interactions on atoms of different
chemical elements in the compound Ni0.5TiTe2. The
rule for many-electron excitations in solids underaction of core-level photo holes is offered.
Ti2p and Te3d XPS spectra in the intercalated
compound Ni0.5TiTe2 are shown in fig. 1. Thelines of the Ti2p spin-orbital doublet arebroadened asymmetrically due to many-bodyexcitations of valence-band electrons generated
by sudden creation of the 2p photo holes [1]. At
the same time such effects on the Te3d lines aremush smaller. To extract the quantitative
information the experimental spectra wereapproximated by a sum of two spin-orbital lines
andaninelastic
background
Ibg: I ( Е ) = I1 ( E ) + I 2 ( E ) + I bg ( E ) . The form of each

These effects are smaller on nickel atoms because of
the almost filled Ni 3d-shell does not respond on
external perturbations. The Te 3d- and 4d-spectra are
narrow symmetric lines like in an isolated atom
because of f-electrons absence.

Ni0.5Ti Te2
Ti 2pline I j ( E ) = Aj Im g ( E − E j − iΓ j ) is determined455

by an imaginary part of the power function [2]1g ( z) =[1 − (1 − b / z )1−α ](1)(1 − α )bHere Aj is line weights; α is the asymmetrycoefficient, shown intensity of the valence electron
excitations accompanying creation of the photo hole;b is their maximal energy; Ej and Гj stand for binding
energy and decay of the lines. The power ofelectron-hole interaction for different XPS lines in
Ni0.5TiTe2 has the following magnitudes:
Lineα

Ti2p0.33

Te3d0.06

Ti 3s0.23460465

Ni0.5Ti Te2
Te 3dTe4d0.08

The asymmetry of a spectrum (dynamic screeningof the photo hole) in titanium is much more, than inother components of compound. It is characterized byα = 0.33 (the values of α in nickel and tellurium aresmall, see table and spectra). The important conclusion
follows. Despite of a collective character of thevalence band electrons in solids, their reactions on
photo holes, arising on core levels of various elements,
are completely different. Exaggerating, it is possible totell, that in this case there is no common band
excitations, each atom in itself.
Analyses of XPS spectra of Ni0.5TiTe2 and othercompounds allow us to conclude that the many-bodyexcitations in solids are followed by the “l + 1 rule”:
photo-hole with the moment l shakes up the band
electrons of l + 1 states, mainly. So, for example,
3d-electrons react basically on 2p-hole, therefore themany-electron effects are strongest on titanium atoms.

570

575

580

585

Binding energy, eVFig. 1. Ti2p and Te3d XPS spectra in the compound
Ni0.5TiTe2 and their decomposition on sum of two
standard lines (1) and a background.

The origin of the rule is connected to prevalence ofthe dipole matrix elements in coulomb interactionl' = l ± 1. However the probability of a transition
with reduction of the orbital moment in solids ismuch less than that in free atoms because of strong
delocalization of electron states with the momentl - 1. In result the l + 1 transition dominate, as it isclearly visible in experimental spectra.
[1] S. Doniach, M. Sundjic, J. Phys. C 3 (1970) 285.
[2] V. I. Grebennikov, J. Electr. Spectr. Rel.
Phenom. 137137-140 (2004) 741.