  Due to the strongly nonlocal nature of $f_{xc}({\bf r},{\bf r}',\omega)$ the
{\em scalar} exchange and correlation (xc) kernel of the time-dependent
density-functional theory (TDDFT), the formula for Q the friction coefficient
of an interacting electron gas (EG) for ions tends to give a too large value of
Q for heavy ions in the medium- and low-density EG, if we adopt the
local-density approximation (LDA) to $f_{xc}({\bf r},{\bf r}',\omega)$, even
though the formula itself is formally exact. We have rectified this unfavorable
feature by reformulating the formula for Q in terms of the {\em tensorial} xc
kernel of the time dependent current-density functional theory, to which the
LDA can be applied without intrinsic difficulty. Our numerical results find
themselves in a considerably better agreement with the experimental stopping
power of Al and Au for slow ions than those previously obtained within the LDA
to the TDDFT.
