  Excitation energies to isobaric states, that are analogs of ground states,
are dominated by contributions from the symmetry energy. This opens up a
possibility of investigating the symmetry energy on nucleus-by-nucleus basis.
Upon correcting energies of measured nuclear levels for shell and pairing
effects, we find that the lowest energies for a given isospin rise in
proportion to the square of isospin, allowing for an interpretation of the
coefficient of proportionality in terms of a symmetry coefficient for a given
nucleus. In the (A,Z) regions where there are enough data, we demonstrate a
Z-independence of that coefficient. We further concentrate on the A-dependence
of the coefficient, in order to learn about the density dependence of symmetry
energy in uniform matter, given the changes of the density in the surface
region. In parallel to the analysis of data, we carry out an analysis of the
coefficient for nuclei calculated within the Skyrme-Hartree-Fock (SHF)
approach, with known symmetry energy for uniform matter. While the data from
isobaric analog states suggest a simple interpretation for the A-dependent
symmetry coefficient, in terms of the surface and volume symmetry coefficients,
the SHF results point to a more complicated situation within the isovector
sector than in the isoscalar, with much stronger curvature effects in the
first. We exploit the SHF results in estimating the curvature contributions to
the symmetry coefficient. That assessment is hampered by instabilities of
common Skyrme parameterizations of nuclear interactions.
