Spin-orbit relaxation and the Knight shift in small superconducting particles of simple polyvalent metals

Recently it has been shown that the most efficient conduction-electron-spin relaxation mechanism in Al is associated with scattering events to and from certain portions (ridges) of the Fermi surface where the spin-orbit interaction leads to electron wave functions which have a substantial admixture of spin-up and spin-down components. Those ridges arise from intersections of the Fermi surface with Brillouin boundaries and therefore this relaxation mechanism must be common to and prevail in the simple (nontransition) polyvalent metals. Here, we show that in fact this mechanism accounts for the spin-flip processes responsible for the finite Knight shift observed in small Sn and Pb superconducting particles.