EGAS41 - Swansea University

41 st EGAS CP 108 Gdańsk 2009
Shell model calculations for alkali halide molecules
S.Y. Yousif Al-Mulla
College of Engineering, University of Borås, Sweden
This work applies the shell model to study the behaviour of the internuclear interactions
of diatomic alkali halide molecules from data given by the dynamical models for alkali
halide crystals. Our interest is to test the breathing shell model when core holes have
been introduced. This will provide another source of information on the nature of the
interaction potential between anion and cation systems and give insight into the rate of
relaxation in determining shifts in Auger and photoelectron spectroscopy.
It is well known that environmental shifts in photoelectron (PES) and Auger (AES)
spectroscopies are due both to chemical shifts characterizing the initial state and to final
state relaxation shifts. In specifying shifts in elemental solids and related compounds the
free atom is often used as reference; then PES and AES are combined to isolate the so
called extra-atomic relaxation, a quantity which is independent of experimental energy
reference. The modified Auger parameter α ′ gives similar information. Alkali halide
molecules are attractive systems for investigation, because the interatomic forces are well
understood in the initial state, and it appears that chemical shift and relaxation are of
comparable importance in their electron spectroscopy[1-3].
a) Rittner model
The influential Rittner potential [1] assumes the ions to be polarisable spherical charge
distributions with full ionicity, and it is usually of the form:
U(r) = − 1 [ 1
4πε 0 r + α + + α −
+ 2α ]
+α −
− C + R(r) (1)
2r 4 r 7 r6 where α + and α − are the polarisabilities of the alkali ion and halogen ion, respectively,
R(r) is a two parameter repulsion term (usually Born-Mayer). The second and third
terms represent a dipole-dipole and a quasi-elastic energy stored in the induced dipole
moments, and are valid for internuclear separation large cornpared with ion dimension.
b) The shell modell
The diatomic molecule is considered to contain a positive ion, which to first order can
be considered as a point charge (+e)’ and a negative ion contains a rigid shell of charge
(Ye) and a core of charge (Xe), where X + Y = −1. In the presence of an electric field
the shell centre will be displaced by distance ω, and the total potential Φ(R, ω, ξ) can
be described by the different contributions; electrostatic, polarization, deformation, and
short range interactions:
Φ(R, ω, ξ) = ϕ es (r, ω) + ϕ pol (ω) + ϕ def (ξ) + ϕ int (R, ξ) (2)
where ϕ pol (ω) = 1/2kω 2 , ϕ def (ξ) = 1/2h 2 ξ 2 , ϕ def (ξ) = 1/2G 2 (ρ − ρ 0 − b) for anisotropic
deformation and ϕ int (R, ξ) = B ± exp(−α ± r) − (C ± r 6 ) − (D ± r 8 ).
References
[1] L. Sangster, Sol. Stat. Comin., 15, 471 (1974)
[2] J.E. Szymanski and A.D. Matthew, Can J. Phys. 62, 583 (1984)
[3] S.Y Yousif Al-Mulla, Acta Physica Hungarica 72, 295-301 (1992)
[4] S. Aksela, I. Aksela and S. Leinoneu, Electr. Spect. 35, 1 (1984)
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