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We obtain the nuclear proximity potential by using semiclassical extendedThomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), and useit in the extended $\ell$-summed Wong formula under frozen densityapproximation. This method has the advantage of allowing the use of differentSkyrme forces, giving different barriers. Thus, for a given reaction, we couldchoose a Skyrme force with proper barrier characteristics, not-requiring extra``barrier lowering" or ``barrier narrowing" for a best fit to data. For the$^{64}$Ni+$^{100}$Mo reaction, the $\ell$-summed Wong formula, with effects ofdeformations and orientations of nuclei included, fits the fusion-evaporationcross section data exactly for the force GSkI, requiring additional barriermodifications for forces SIII and SV. However, the same for other similarreactions, like $^{58,64}$Ni+$^{58,64}$Ni, fits the data best for SIII force.Hence, the barrier modification effects in $\ell$-summed Wong expressiondepends on the choice of Skyrme force in extended ETF method.

Barrier modification in sub-barrier fusion reactions using Wong formula with Skyrme forces in semiclassical formalism