Systematic study of macroscopic interaction models and short-range effects in $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion
The $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction is central to stellar carbon burning, yet its cross section at astrophysical energies remains uncertain and theoretical extrapolations depend sensitively on the adopted nucleus-nucleus interaction. We systematically assess 24 macroscopic interactions within a common one-dimensional fusion framework and find that their relative agreement with experimental data depends strongly on both the statistical measure and energy interval considered, with no single interaction providing a uniformly superior description across all criteria. A common phenomenological short-range repulsive modification is then applied to all interactions without refitting their underlying parametrizations. Although the external fusion barrier remains essentially unchanged, the modification substantially reorganizes the inner-potential structure and produces strongly model-dependent changes in agreement with experiment. Detailed analysis of five representative interactions shows that the resulting low-energy suppression propagates into the thermonuclear reaction rates, but does not produce the conventional logarithmic-slope signature of fusion hindrance over the calculated energy range. These results demonstrate that additional short-range repulsion does not provide a universal improvement of macroscopic fusion potentials and that the reliability of extrapolations toward stellar carbon-burning energies remains sensitive to both the choice of interaction and its short-range behavior.