Scattering matrix elements of the inelastic fine structure transition M(P-2(1/2)) + Ng <-> M(F-2(3/2)) + Ng are,computed using the channel packet method (CPM) for alkali-metal atoms M = K, Rb, and Cs, as they collide with noble-gas atoms Ng = He, Ne, and Ar. The calculations are performed within the block Born-Oppenheimer approximation where excited state V-A(Pi 1/2)2(R), V-A(Pi 3/2)2(R), and V-B(Sigma 1/2)2(R) adiabatic potential energy surfaces are used together with a Hund's case (c) basis to construct a 6 x 6 diabatic representation of the electronic Hamiltonian. Matrix elements of the angular kinetic energy of the nuclei incorporate Coriolis coupling' and,- together with the diabatic representation of the electronic Hamiltonian, yield a 6 x 6 effective potential energy matrix. This matrix is diagonal in the asymptotic limit of large intertmclear separation with eigenvalues that correlate to the P-2(j) alkali atomic energy levels. Scattering matrix elements are computed using the CPM by preparing reactant and product wave packets on the effective potential,energy surfaces that correspond to the excited P-2(j) alkali states of interest. The reactant wave racket is then propagated forward in time Wing the split operator method together with a unitary transformation between the adiabatic and diabatic representations. The Fourier transformation of the correlation function between the evolving reactant wave packet and stationary product wave packet yields state-toLstate scattering matrix elements as a function of energy for a particular choice of total angular momentum J. Calculations are performed for energies that range from 0.0 to 0.01 hartree and values of j that start with a Minimum of J = 0.5 for all M + Ng pairs up to a maximum that ranges from J = 450.5 for KAr to J = 100.5 for CsAr. A sum over J together with an average over energy is used to compute thermally averaged cross sections for a temperature range of T = 0-400 K.