is where g$_{scr}$ ( q ) is the screened electron-phonon coupling function, related to the bare el-ph interaction function g ( q ) by and the average is over the same states as in 5. For jellium, g ( q ) is given by where the bare ion plasma frequency Ω$_{p}$ is related to the actual frequency of the ions in jellium by the Bohm-Staver relation, We therefore have [15] In view of the fact that jellium is completely characterized by one parameter r$_{s}$ , such a relation should not be surprising. One could go further and say that, this relation could be projected onto any angular momentum pairing channel ℓ of electrons scattering from k , − k to k $^{′}$, − k ′ and therefore that such a relation exists in each channel, λ e − ph ℓ ≈ µ$_{ℓ}$ . For Fermi- Thomas screening ϵ ( q ) ∝ q $^{2}$/ ( q $^{2}$+ q 2 $_{T F}$), where q − 1 T F is the inverse screening length. One may project the interactions on to pairing channel ℓ and find that the effective dimensionless direct repulsion as well as e-ph induced attraction parameters both are proportional to exp( − q$_{TF}$ k$_{F}$ ℓ ). Cohen and Anderson [16], in a not easily accessible paper, which has several interesting ideas, have discussed how in a lattice, Umklapp scattering which in effect is due to the modulation of the charge density within a unit-cell due to phonons or local field effects, increases the coupling constant λ e − ph relative to µ . This paper emphasizes that strong e-ph interactions mean the modulation of electronic bonds. This point will be discussed further in Sec. (III) in the context of transition metals and compounds, where this idea is most prominently borne out in the empirical data and implemented efficiently through the tight- binding representation of e-ph interactions to provide a theory of e-ph interactions as well as a quantitative theory of the anomalies in the phonon spectra [17, 18] in transition metal and compounds. 15 λ e − ph = µ. (10) ω $^{2}$( q ) = Ω 2 $_{p}$/ϵ ( q ) . (9) g $^{2}$( q ) / ( M Ω 2 $_{p}$) = 4 πe $^{2}$/q$^{2}$, (8) g$_{scr}$ ( q ) = g ( q ) /ϵ ( q ) , (7) λ e − ph = N (0) < g 2 $_{scr}$( q ) > /M < ω ( q ) 2 >, (6)