  Within the framework of a generalized factorization, semi-inclusive deeply
inelastic scattering (SIDIS) cross sections can be expressed as a series of
products of collinear hard parts and transverse-momentum-dependent (TMD) parton
distributions and correlations. The azimuthal asymmetry <cos\phi>$ of
unpolarized SIDIS in the small transverse momentum region will depend on both
twist-2 and 3 TMD quark distributions in target nucleons or nuclei. Nuclear
broadening of these twist-2 and 3 quark distributions due to final-state
multiple scattering in nuclei is investigated and the nuclear dependence of the
azimuthal asymmetry $<\cos\phi>$ is studied. It is shown that the azimuthal
asymmetry is suppressed by multiple parton scattering and the transverse
momentum dependence of the suppression depends on the relative shape of the
twist-2 and 3 quark distributions in the nucleon. A Gaussian ansatz for TMD
twist-2 and 3 quark distributions in nucleon is used to demonstrate the nuclear
dependence of the azimuthal asymmetry and to estimate the smearing effect due
to fragmentation.
