Screening many-body effects

When the material condensed system contains mobile charges, the electrostatic interactions, which are strong and with the slowest decay with the distance, are severely damped. Every charged component of the system tends to attract mobile components bearing the op- 

Jacopo Tomasi, Beaedetta Memucci, Chiara Cappelli 

A similar screening effect is present for dipolar liquids each molecule bearing a permanent dipole tends to organize around itself other dipolar molecules with the orientation which optimizes stabilization energy and screens the field produced by the singled out molecule. 

For the dispersion contributions there is no screening. We arrive to the apparently paradoxical situation that for relatively large bodies, even when bearing net charges, the interactions at large distances are governed by the dispersion forces, weak in comparison with others, and having a more rapid decrease with the distance. 

Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli 

---

It is worth noting that the electron gas model is a continuum model which is valid at low energy, so the connection with the parameters U and V of the lattice model can only be considered as approximate. For example, in the high-temperature range or for sufficiently large couplings the curvature of the band may become relevant and it is not clear if a continuum theory will work well quantitatively [116, 117]. The point at issue is the input parameters of the electron gas model. These are likely to enter in the theory as screened quantities due to non-logarithmic many-body effects and they should then differ from the bare parameters of the lattice model. 

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]. 

ES contributions are strictly additive there are no fluee- or many body terms for ES. The term many-body correction to ES introduced in some reviews aetually regards two other effects. The first is the electron correlation effects which come out when the starting point is the HE description of the monomer. We have already considered this topie that does not belong, strictly speaking, to the many-body effects related to the eluster expansion [8.9]. The second regards a screening effeet fliat we shall discuss later. 

Prototypical heavy fermion systems are UBCij or UPtj. Photoemission studies have associated the uranium 5f contribution with the density of states in a narrow region at the Fermi level. This indicates only that there is a large density of states at p in a one-electron or band picture, subject to all of the interpretational problems of the 4f levels in Ce. Hence, photoemission shows the presence of a 5f photohole screened by conduction electrons that essentially reoccupy it during the photoemission process. All other many-body effects which give rise to the heavy-fermion ground state are broken by the photoemission process. Several other uranium-based heavy-fermion systems do not show an analogous narrow 5f-derived peak at the Fermi level. 

The importance of electron correlation effects were taken into account in ab initio band structure calculations based on GW approximation which explicitly included many-body effects. In this approach, the electron self energy was computed via a truncated expansion in terms of a Green s function G and the screened Coulomb interaction W. 

The fact that the repulsive barrier does not evolve as we increase the volume fraction beyond a certain point seemingly indicates that at this point the addition of counterions does not lead to a decrease in the screening length. This evokes that the added counterions are located in space where there are no particles. This interpretation is somewhat reminiscent of the one implied by Sogami and Ise [41], who report the existence of an effective attraction between two macroions, because the counterions can be attracted simultaneously by neighboring particles. Such counterion-mediated attraction is only possible if the space between two particles is somewhat depleted of counterions. Our experimentally determined potentials are in fact very similar to the one reported by Sogami and Ise, such that we could conceive that both the effective attraction and the cessation of the evolution of the repulsive barrier are caused by the fact that counterions migrate to the space with a low particle concentration. This interpretation is obviously very speculative and our data do not exclude the possibility that the appearance of effective attractions is due to many body effects... 

The hydrodynamic interaction is introduced in the Zimm model as a pure intrachain effect. The molecular treatment of its screening owing to presence of other chains requires the solution of a complicated many-body problem [11, 160-164], In some cases, this problem can be overcome by a phenomenological approach [40,117], based on the Zimm model and on the additional assumption that the average hydrodynamic interaction in semi-dilute solutions is still of the same form as in the dilute case. 

As with the solution of other many-body electronic structure problems, determination of the unperturbed eigenvalues is numerically challenging and involves compromises in the following areas (1) approximations to the hamiltonian to simplify the problem (e.g., use of semi-empirical molecular orbital methods) (2) use of incomplete basis sets (3) neglect of highly excited states (4) neglect of screening effects due to other molecules in the condensed phase. 

Concluding this section, we are confident that the present treatment of the many-body polarization gives transferable and reliable effective polarizabilities and screening factors. 

In concentrated suspensions many body interactions between the colloidal particles determine the effective colloid-colloid interaction. Beresford-Smith and Chan (1983) [37] showed that in that case the effective colloid-colloid interaction can nevertheless be described by an effective pair interaction energy to characterise the electrical double layer interaction. This pair interaction energy also has a screened Coulomb form just as in the classical DLVO theory but the Debye screening parameter k now depends on the intrinsic coxmterion concentration and the concentration of added electrolyte in the system. This makes the effective pair energy dependent on the volume fraction of the particles (see general discussion of the paper of Beresford-Smith and Chan [38]. 

---