Spin-Wave Excitations and Superconductivity

We study in terms of the effective two-particles $T$-matrix pairing by exchanging spin-wave excitations near the ferromagnetic or antiferromagnetic instability. We show that near the ferromagnetic instability the paring due to the exchange the paramagnetic excitations can occur in the $p$-wave state (\textit{$\ell $} = 1) and $m=\pm $1. We show that near the antiferromagnetic instability the pairing due the exchange the paramagnetic excitations occurs also in the $p$-wave state (\textit{$\ell $} = 1) but with $m$ = 0 and that there is no pairing in $d$-wave state.