Transverse Momentum Broadening in Semi-inclusive DIS on Nuclei

Using a three stage model of hadron formation we calculate the change of the transverse momentum distribution of hadrons produced in semi-inclusive deep inelastic scattering (SIDIS) on nuclei. In the first stage after its interaction with the virtual photon, the struck quark propagates quasi free in the nuclear environment undergoing multiple collisions with nucleons. During this stage it can acquire transverse momentum. In the second stage a prehadron is formed which has a very small elastic cross section with the nucleons. In the third stage the prehadron turns into a hadron. For HERMES energies, prehadron elastic scatterings contribute little to $p_\perp$-broadening. The acquired extra $\Delta p_\perp^2$ of hadrons can therefore be deduced entirely from the first stage of quasi free quark propagation with quark-nucleon collisions. We use this model to describe $\pi$-production on Ne, Kr, Xe and compare with the most recent HERMES preliminary data.