extracting information on multiple scattering.

We define the first moment of the transverse momentum spectrum - the averaged pion transverse momentum squared, as $$\langle \ell_{T}^2\rangle^{eA} = \left.
\int d\ell_{T}^2 \, \ell_{T}^2 \, 
\frac{d\sigma_{eA\rightarrow e\pi X}}{dx_B  dQ^2 d\ell_{T}^2} 
\right/ \frac{d\sigma_{eA\rightarrow eX}}{dx_B  dQ^2} \, ;
\label{LTavg}$$ where $d\sigma_{eA\rightarrow eX}/dx_B dQ^2$ is the total inclusive DIS cross section normalized by the atomic weight $A$. In Eq. (\[LTavg\]), the Bjorken variable $x_B=Q^2/(2p\cdot q)$, and $q=k_1-k_2$ is the four-momentum of the virtual photon. The transverse momentum $\ell_{T}$ of the leading pion depends on our choice of the frame. In this paper, we choose the photon-nucleus frame, and choose the $z$-axis along the momentum line of the nucleus and the virtual photon.

To separate the multiple scattering contribution from the single scattering contribution, we define the nuclear broadening of the transverse momentum square as $$\Delta\langle \ell_T^2\rangle \equiv  
\langle \ell_T^2\rangle^{eA} - \langle \ell_T^2\rangle^{eN} \, .
\label{DLT2}$$ As we will demonstrate below, the nuclear broadening of the transverse momentum square defined in Eq. (\[DLT2\]) can be parameterized as [@E683; @E609] $$\Delta\langle \ell_T^2\rangle =
a + b\, A^{1/3}\ ,
\label{BA13}$$ where $bA^{1/3}$ represents the contribution directly from the multiple scattering which is explicitly proportional to the nuclear size ($\propto 