The Baranger model is used to compute collisional broadening and shift of the D1 and D2 spectral lines of M + Ng, where M = K, Rb, Cs and Ng = He, Ne, Ar, using scattering phase shift differences which are calculated from scattering matrix elements. Scattering matrix elements are calculated using the Channel Packet Method where the collisions are treated non-adiabatically and include spin-orbit and Coriolis couplings. Non-adiabatic wavepacket dynamics are determined using the split-operator method together with a unitary transformation between adiabatic and diabatic representations. Scattering phase shift differences are thermally weighted and integrated over energies ranging from E = 0 Hartree up to E = 0.0075 Hartree and averaged over values of total angular momentum that range from J = 0.5 up to J = 400.5. Phase shifts are extrapolated linearly to provide an approximate extension of the energy regime up to E = 0.012 Hartree. Broadening and shift coefficients are obtained for temperatures ranging from T = 100 K up to T = 800 K and compared with experiment. Predictions from this research find application in laser physics and specifically with improvement of total power output of Optically Pumped Alkali Laser systems
