  In this paper, a detailed analysis on normal modes of the linearized Hermite
collision operator is presented, which follows from linearizing spin Boltzmann
equation for massive fermions proposed in \cite{Weickgenannt:2021cuo} with the
non-diagonal part of the transition rate neglected and approximating what we
got with a mutilated operator. With the assumption of total angular momentum
conservation, the collision term is proved to well describe the equilibrium
state and gives proper interpretation for collisional invariants, thus is
relevant for the research on local spin polarization. Following the familiar
fashion as used in quantum mechanics, we treat the problem of solving normal
modes as a degenerate perturbation problem and calculate the dispersion
relations for intriguing eleven zero modes, which form one-to-one
correspondence to all collisional invariants. We find that the results of
spinless modes appearing in ordinary hydrodynamics are consistent with
available conclusions in textbooks. As for spin-related modes, we obtain the
frequencies up to second order in wave vector and relate them with the
dissipation of spin density fluctuation. In addition, the ratio of two
relaxation time scales for spin and momentum is shown as a function of reduced
mass, which reads that based on present framework spin equilibration is almost
as slow as momentum equilibration as far as the strange quark spins in quark
gluon plasma (QGP) are concerned.
