  In ultrarelativistic heavy-ion collisions, in the 2 GeV$<p_\perp<$ 6 GeV
transverse momentum region, the soft and semi-hard multiple scattering of the
incoming nucleons in the nuclear medium results in the broadening of the
expected hadronic (e.g. pion) $p_\perp$ spectra relative to proton-proton
($pp$) collisions. Thus, higher transverse-momentum regions are populated than
in $pp$ collisions. In a perturbative QCD based calculation we include the
intrinsic transverse momentum ($k_\perp$) of the partons in the nucleon
(determined from $pp$ collisions), augmented by the extra broadening obtained
via a systematic analysis of proton-nucleus ($pA$) collisions in the energy
range 17$<\sqrt{s}<$ 39 AGeV. The original polynomial spectra are modified, and
a nearly exponential spectrum appears in the region 2$\lesssim p_\perp\lesssim
3.5$ GeV. At present RHIC energies ($\sqrt{s}=$130 AGeV), the slope of the
calculated spectra is reminiscent of that of fluid-dynamical descriptions, but
lacks any thermal origin. We determine and discuss the size of the
modifications originating in multiple scattering, which lead to this state of
affairs.
