\begin{table}%t1
\caption{The stellar structure before and after mass transfer$^a$.} \label{mincore}
%\centerline
{
\begin{tabular}{cl|ccrccc|cc}
\hline\hline
&&\multicolumn{6}{c}{pre-CE}&\multicolumn{2}{c}{post-CE}\\
\hline
$\frac{M_{\rm{ZAMS}}}{M_{\odot}}$&&$\frac{M_{*}}{M_{\odot}}$&$\frac{M_{\rm{core}}}{M_{\odot}}$&$\frac{R_{*}}{R_{\odot}}$&$\lambda_{\rm{gr}}$&$\lambda_{\rm{tot}}$&$\frac{I}{M_*R_*^2}$&$\frac{M_{\rm{env}}\times 10^{-3}}{M_{\odot}}$&$\frac{M_{\rm{remnant}}}{M_{\odot}}$\\
\hline
\multicolumn{10}{l}{helium flash}\\
1.00&min&0.821&0.460&168&0.55&4.61& 0.052&$\leq$$1.3$&0.46 \\
 &tip&0.791&0.472&185&0.53&4.28&0.051&$\leq$$10$&0.47--0.48\\ 
1.50&min&1.401&0.454&136&0.64&3.74&0.084&$\leq$$1.4$&0.45 \\ 
 &tip&1.395&0.466&148&0.57&3.36&0.082&$\leq$$9$&0.47--0.48\\ 
1.75&min&1.695&0.434&107&0.69&2.92&0.097&$\leq$$1.7$&0.43 \\  
&tip&1.687&0.446&118&0.62&2.70&0.095&$\leq$$7$&0.45--0.46\\   
1.95&min&1.926&0.394&65&0.73&2.18&0.113&$\leq$$2.7$&0.39 \\  
&tip&1.926&0.394&65&0.72&2.14&0.113&$\leq$$6$&0.39--0.40\\  
\multicolumn{9}{l}{non-degenerate helium ignition}\\
2.05&min&2.045&0.317&26&0.83&1.90&0.135&$\leq$$14$&0.32--0.33\\ 
 &tip&2.043&0.320&26&0.83&1.92&0.135&$\leq$$13$&0.32--0.33\\ 
2.50&min&2.494&0.322&5&0.25&0.47&0.022&$-$&$-$\\  
&tip&2.493&0.372&36&0.85&2.02&0.134&$\leq$$34$&0.37--0.41\\  
3.00&min&2.993&0.411&6&0.24&0.46&0.021&$-$&$-$ \\  
 &tip&2.993&0.444&45&0.84&2.00&0.132&$\leq$$61$&0.44--0.50\\  
4.00&min&3.991&0.596&8&0.26&0.48&0.022&$-$&$-$\\   
 &tip&3.990&0.623&74&0.78&1.94&0.125&$\leq$$116$&0.62--0.74\\   
\hline
\end{tabular}}
\medskip
\par
$^a$ For each ZAMS mass, the first line gives the stellar structure corresponding to the minimum core mass for helium ignition. The second line corresponds to the tip of the RGB. The columns are respectively: $M_{\rm{ZAMS}}$ = zero-age main-sequence mass; $M_*$ = total mass of giant; $M_{\rm{core}}$ = helium core mass of giant, $R_*$ = radius of giant; $\lambda_{\rm{gr}}$ and  $\lambda_{\rm{tot}}$ are dimensionless parameters indicating respectively the gravitational binding energy and the total (including thermal) binding energy of the ejected envelope (see Sect.~\ref{ALPHA}); $I$ = the moment of inertia; $M_{\rm{env}}$ = hydrogen envelope left after CE ejection; $M_{\rm{remnant}}$ = remnant mass after CE ejection. 
\end{table}