### abstract

- The effect of gravitational (elastic) encounters between stars and giant molecular clouds on the stability of small-amplitude perturbations of the Milky Way's self-gravitating disk is considered, using the exact Landau (Fokker-Planck type) collision integral, and compared with the results obtained by Griv & Peter (1996), who used the simple phenomenological Bhatnagar-Gross-Krook (Bhatnagar et al. 1954) collisional model. The present analysis is carried out for the case of a spatially inhomogeneous, highly flattened system, i.e., an inhomogeneous system in which the thickness is very small in comparison with the disk's radial extension. According to observations (Grivnev & Fridman 1990), the dynamics of a system with rare, kappa (2) >> nu_c (2) (and weak, omega (2) >> nu_c (2) ), interparticle encounters is considered, where kappa is the epicyclic frequency, omega is the frequency of excited waves, and nu_c ~ 10(-9) yr(-1) is the effective frequency of star-cloud encounters. The evolution of the stellar distribution is determined primarily by interactions with collective modes of oscillations - gravitational Jeans-type and gradient-dissipative modes - rather than by ordinary (``close") star-cloud encounters. On the basis of a local kinetic theory, it is shown that the Landau integral and the Bhatnagar et al. model give practically identical results in the case of perturbations with the wavelength lambda that is comparable to the mean epicyclic radius of stars rho , that is, in the case of the most dangerous, in the sense of the loss of stability, gravitational Jeans-type perturbations. The models, however, have essentially different qualitative and quantitative behaviors in the extreme limits of long-wavelength perturbations, (pi rho /lambda )(2) << 1, and of short-wavelength perturbations, (pi rho /lambda )(2) >> 1. Certain observational implications of the present theory are discussed.