simple form: In the weak-coupling approximation, the partial wave components of the pairing interaction V$_{ℓ}$ follow from Eq.(12) to be where the pre-factor is 3 for spin-singlet (even ℓ ) pairing and − 1 for triplet-spin (odd ℓ ) pairing. One may analyze the consequences of the q - dependence of J ( q ) in of Eq.(13) using fig. (3 ). The ferro-magnetic interactions have a peak of − J ( q ) at q = 0, while the anti- ferromagnetic interactions have a peak at the zone-boundary. First note that if J (2 k$_{F}$ x ) is independent of x , V$_{ℓ}$ = 0 for all ℓ . This is because J ( q ) independent of q implies a delta- function interaction in real space where any finite ℓ Cooper pair wave-function has zero magnitude. On the other hand for ℓ = 0, a constant J ( q ) represents a magnetic impurity, which suppresses pairing. One also can see from Eq.(13) and the smooth variation of J ( q ) in fig. (3) that V$_{0}$ > 0 , V$_{1}$ < 0 and V$_{2}$ > 0 for ferro-magnetic interactions. In other words both isotropic and anisotropic singlet states are disfavored by such interactions, while triplet ℓ = 1 state is favored. For anti-ferromagnetic interactions, V$_{0}$ > 0 , V$_{1}$ > 0; both isotropic singlet and the triplet state is disfavored. Whether V$_{2}$ < 0 or > 0, depends on the detailed form of J ( q ). A strong enough peak in J ( q ) near the zone-boundary favors such pairing. It is straightforward to extend this analysis [19] to the more realistic case for the momen- tum dependence of the interaction taking the crystal symmetry into account. It is expected that the antiferromagnetic fluctuations peak at a point q = Q along a symmetry axis and so does J ( q ). I refer to the original paper for some details. An important point to emerge from that analysis is that the pairing symmetry depends both on how steep is the increase in J ( q ) near the zone-boundary and on the details of the electronic dispersion ϵ ( k ) near the chemical potential. For example the electronic structure may choose between extended - s or d-type pairing. This point appears relevant to the case of the recently discovered Fe-pnictide superconductors, where the band-structure with hole-pockets at the zone center and electron pockets near zone corners may favor nodeless pairing with a phase difference of 18 V$_{ℓ}$ =   3 − 1  $_{}$2 ∫ 1 0 dxxP$_{ℓ}$ (1 − 2 x $^{2}$)[ − J (2 k$_{F}$ x )] , (13) H$_{int}$ = 1 / 2 ∑ kk $^{′}$q J ( | k − k $^{′}$| ) σ$_{αβ}$ · σ$_{γδ}$c + k + q / 2 $_{,α}$c + − k + q / 2 $_{,γ}$c$_{−}$$_{k}$ $^{′}$+ q / 2 $_{,δ}$c$_{k}$ $^{′}$+ q / 2 ,β (12)