atomic number $A$, and $\ell$ is the observed pion momentum. In order to extract useful information on multiple scattering from the pion production, it is natural to think that the $A$-dependence of the differential cross section $d\sigma_{eA\rightarrow e\pi X}
/dx_BdQ^2d\ell_T^2$ is the physical observable to study, because the transverse momentum spectrum is more sensitive to multiple scattering [@LQS1]. But, other than a future HERA with a nuclear beam, existing fixed target facilities can not produce good data on the production of leading pions at [*large*]{} transverse momenta in DIS. On the other hand, at the small transverse momentum $\ell_T^2$, the differential cross section $d\sigma/dx_BdQ^2d\ell_T^2$ is proportional to $1/\ell_T^2$, and is not perturbatively stable. A nontrivial all order resummation of the large logarithms $\log(Q^2/\ell_T^2)$ is necessary in order to get a reliable prediction of the transverse momentum spectrum at small $\ell_T^2$ [@Guo1]. However, the inclusive moments of the transverse momentum spectrum $\int d\ell_T^2 (\ell_T^2)^n\, 
d\sigma_{eA\rightarrow e\pi X}/dx_BdQ^2d\ell_T^2$ with $n\ge 1$ are perturbatively stable, and also enhance the information in the region of large $\ell_T^2$, where the multiple scattering is most relevant. Therefore, the $A$-dependence for the moments of the transverse momentum spectrum of the leading pions is a good observable for 