  Four quantities deducible from nuclear structure experiments have been
claimed to correlate to the slope parameter $L$ of the symmetry energy; the
neutron skin thickness, the cross section of low-energy dipole (LED) mode,
dipole polarizability $\alpha_D$, and $\alpha_D S_0$ (i.e. product of
$\alpha_D$ and the symmetry energy $S_0$). By the calculations in the
Hartree-Fock plus random-phase approximation with various effective
interactions, we compare the correlations between $L$ and these four
quantities. The correlation derived from different interactions and the
correlation from a class of interactions that are identical in the symmetric
matter as well as in $S_0$ are simultaneously examined. These two types of
correlations may behave differently, as exemplified in the correlation of
$\alpha_D$ to $L$. It is found that the neutron skin thickness and
$\alpha_DS_0$ correlate well to $L$, and therefore are suitable for narrowing
down the value of $L$ via experiments. The LED emergence and upgrowth makes the
$\alpha_DS_0$-$L$ correlation strong, although these correlations are
disarranged when neutron halo appears in the ground state.
