Absorption threshold

Definition

In the literature there is much confusion, even in modern papers, concerning the definition of the absorption threshold. The absorption threshold should indicate the first allowed transition in an absorption spectrum. Many definitions are used in common parlance. In practice, they yield very different values in common analysis. We present and comment upon the most commonly used:

(1) The energy at which the open continuum channel for photo-electric absorption becomes available, producing a continuum photo-electron. This has an exact value from theory, subject to convergence issues (see Fermi energy).

(2) A (higher) energy at which a secondary (two-step) photoionization channel becomes energetically possible (see shake-up, shake-off); in general this is more challenging to compute theoretically, and is less easily separable in conventional XAS experimental data, but can be investigated incisively in RIXS, XFS and related spectroscopies.

(3) Experimentally, the absorption threshold is sometimes defined as the inflection point in the first derivative of the experimental edge spectrum (the point of maximum slope on the rising edge for a particular sub-shell); this is a convenient marker for experimentalists but &ndash' (a) it is source (beam-line) and band-width dependent; (b) it is affected by pre-edge structure and the Fermi level (cross link) due to potential contributions from bound-bound channels; (c) the experimental edge may contain two or more such inflection points, and the determination depends upon instrumental resolution.

(4) Experimentally, the absorption threshold is sometimes defined as the point exactly 50% of the jump ratio from the background absorption (from other shells, including scattering) to the peak absorption coefficient of the XANES spectrum, defined either by the clear maximum or by the smooth line representing the background to be subtracted in the determination of [math]\chi(k)[/math] (see XAFS); this is a problematic measure, since it depends upon beam-line dependent effects [(3) above], and a wide variety of different predictions of the 'true background level’ [math]\mu_0[/math] above the edge ((see XAFS).

(5) Computationally, an absorption threshold is defined for XAFS fitting (and occasionally XANES fitting) as [math]E_0[/math] which is considered either as an arbitrary fitting coefficient or the starting point of the [math]k[/math] transform, which in turn generates the Fourier transform for the XAFS structure [math]\chi(k)[/math]; as the latter, it should be defined as per (1) above; as the former, this will often yield a function of [math]r[/math] and errors in [math]E_0[/math] of order 10 eV or more which can result in bond length errors of order 0.02 Å or more.

Both computationally and experimentally, the energy axis is often not defined except in a relative sense, so that inconsistencies between the implementations of these definitions are at this point relatively common.

See also

Fermi level/Fermi energy