\begin{table}%t9 %\centering \par \caption {\label{LVG}H$_2$ volume densities and molecular column densities of H$^{13}$CO$^+$ and HN$^{13}$C derived assuming extended emission for both the ambient and the precursor components of L1448-mm. } \begin{tabular}{lcccc} \hline \hline \noalign{\smallskip} & \multicolumn{2}{c} { H$_2$ density (cm$^{-3}$)}&\multicolumn{2}{c} { Column density (cm$^{-2}$)} \\ \cline{2-3} \cline{4-5} Molecule & Ambient & Precursor & Ambient & Precursor\\ \hline \multicolumn{5}{c}{(0,~20)}\\ H$^{13}$CO$^+$ & $1.4\times10^5$ & $3.5\times10^5$ &$4.8\times10^{11}$ & $4.0\times10^{11}$ \\ HN$^{13}$C & $\la$$ 1.9\times10^5$ & $\la$$ 9.2\times10^5$ & $\la $$6.4\times10^{11}$ & $\la $$1.5\times10^{11}$ \\ \hline \multicolumn{5}{c}{(20,~0)}\\ H$^{13}$CO+ & $\la $$8.8\times10^4$ & $1.8\times10^5$ & $\la $$5.1\times10^{11}$ & $4.3\times10^{11}$ \\ HN$^{13}$C & $\la $$1.8\times 10^5$ & $\la$$ 3.3\times10^5$ & $\la$$ 7.2\times10^{11}$ & $\la$$ 4.1\times10^{11}$ \\ \hline \multicolumn{5}{c}{(--20,~0)}\\ H$^{13}$CO$^+$ & $\la $$8.7\times10^4$ & $7.1\times 10^4$ & $\la$$ 3.5\times10^{11}$ & $6.4\times10^{11}$\\ HN$^{13}$C & $1.2\times10^5$ & $\la$$ 6.1\times10^5$ & $1.4\times10^{12}$ & $\la$$ 2.0\times10^{11}$ \\ \hline \par \end{tabular} \par \end{table}