We should also note the important fact that when the effective e-e interactions in the pairing channels are expressed so that they are retarded only over the same range, < ω > , as the e-ph interactions they are reduced to µ ∗ = µ/ (1 + µ ln( E$_{f}$ / < ω > ) . (11) In an interesting paper Kohn and Luttinger [8] showed that the effective electron-electron interactions must, due to the sharpness of the fermi-surface, always be oscillatory in the momentum transfer 2 k$_{F}$ cos( θ ) where cos( θ ) = ˆ k$_{f}$ · ˆ k ′ $_{f}$, with both k and k ′ are close to the fermi-surface. From this it follows that there is always attraction in the pairing channel at some or the other angular momentum angular momentum ℓ . The issue then is whether it is of sufficient magnitude to give T$_{c}$ larger than that from typical e-ph interactions. Kohn and Luttinger also provide an estimate for the effective interaction when the bare interaction is weak. The direct (screened for e-e interactions) repulsive interaction falls of exponentially in ℓ , while the oscillatory exchange attractive interactions fall off only as 1 /ℓ $^{4}$, the latter therefore wins for large enough ℓ . The same is true for hard-core interaction of finite radius. For He $^{3}$, taking this radius equal to the diameter of the He atoms, ℓ = 1 channel is already attractive and provides using a BCS type expression, a T$_{c}$ ≈ ω$_{c}$ exp( − 2 . 5). Here ω$_{c}$ is the cut-off. If one takes ω$_{c}$ ≈ E$_{f}$ , one gets a factor 10 2 too large a value compared with the experiments. There are several things wrong with this. For ℓ = 0 pairing, one must include the repulsion in the ℓ = 0 channel in the normal self-energy, even in the weak-coupling limit. This cuts down the estimate by about two orders of magnitude. The leading effect over the weak-coupling limit is that, the quasi-particle renormalization, due to increasing interactions, also renormalizes the attractive coupling constants in the exponent downwards as well as the cut-off ω$_{c}$ . An important point is that for any reasonable interactions, the Kohn-Luttinger result that the attractive interaction falls off as 1 /ℓ 4 is unlikely to change much in more com- plicated calculations with incoherent particle-hole interactions. Then, for example, for the parameters of He $^{3}$, the ℓ = 2 pairing has a transition temperature of about 10 − $^{17}$K , even without considering the s-wave repulsion. One may conclude that incoherent particle-hole fluctuations are not a very good way to get to high T$_{c}$ . How then to make use of the 16 3. Pairing in ℓ = 0 through Incoherent particle-hole fluctuation exchange