Coulomb catastrophe

Despite the fact that formalism of the standard chemical kinetics (Chapter 2) was widely and successfully used in interpreting actual experimental data [70], it is not well justified theoretically in fact, in its derivation the solution of a pair problem with non-screened potential U (r) = — e2/(er) is used. However, in the statistical physics of a system of charged particles the so-called Coulomb catastrophes [75] have been known for a long time and they have arisen just because of the neglect of the essentially many-particle charge screening effects. An attempt [76] to use the screened Coulomb interaction characterized by the phenomenological parameter - the Debye radius Rd [75] does not solve the problem since K(oo) has been still traditionally calculated in the same pair approximation. 

To demonstrate the charge screening importance in a many-particle system, it should be mentioned that the substitution of potentials il (r, t) entering equations (6.3.2), (6.3.3) by non-screened potentials Uu(r) = L/r leads to the Coulomb catastrophe manifesting itself by the unlimited increase of the reaction rate K(t) [24, 78],... 

The role of the non-equilibrium charge screening is emphasized by calculations neglecting such screening, i.e., when equations (5.1.54) are omitted and Uv r) — L/r is postulated. In this case mutual repulsion of similar particles accompanied by the attraction between dissimilar particles are characterized by the infinite interaction radius between particles which leads immediately to the Coulomb catastrophe - an infinite increase in K(t) in time shown in Fig. 6.47. This effect is independent of the choice of the initial defect distributions for both similar and dissimilar particles. On the other hand, incorporation of the Coulomb screening makes equations (6.4.1), (6.4.2) asymptotically valid for any initial distribution of particles. 

Fig. 6.48. The role of non-equilibrium charge screening in eliminating the Coulomb catastrophe the dimensionless reaction rate vs time. Dotted curve - the Debye theory (no screening and similar particle correlation) broken curves - the solution of kinetic equations incorporating these correlations but neglecting screening full curves, screening is taken into account. Parameters L = 5, Da = Db. Curves 1 to 3 correspond to dimensionless concentrations ...

However, as the distance between two ions approaches zero, the Coulomb expression in eqn (7.6) results in infinite values, which has been called the Coulomb catastrophe . To avoid the Coulomb catastrophe which is introduced by a point charge model, COMB potentials adopt the Streitz-Mintmire charge density function. Specifically, the charge density of an atom is taken to be a function of its charge, spatial location (r) and atomic position (/ ) ... 

Shakeup represents a fundamental many-body effect that takes place in optical transitions in many-electron systems. In such systems, an absorption or emission of light is accompanied by electronic excitations in the final state of the transition. The most notable shakeup effect is the Anderson orthogonality catastrophe [5] in the electron gas when the initial and final states of the transition have very small overlap due to the readjustment of the Fermi sea electrons in order to screen the Coulomb potential of pho-toexcited core hole. Shakeup is especially efficient when the optical hole is immobilized, and therefore it was widely studied in conjunction with the Fermi edge singularity (FES) in metals [6-8] and doped semiconductor quantum wells [9-15]. Comprehensive reviews of FES and related issues can be found in Refs. [16,17]. 

---