Systematic investigation of nuclear incompressibility and finite-range exchange effects in density-dependent NN interactions on α-decay half-lives

Abstract We present a systematic investigation of $\alpha$-decay half-lives for nuclei with $52 \leq Z \leq 122$ within a microscopic double-folding framework. The $\alpha$--nucleus potentials are constructed using the Michigan three-range Yukawa (M3Y) nucleon--nucleon interaction and its density-dependent variants (DDM3Y, CDM3Y, and BDM3Y), explicitly incorporating both direct and exchange terms. Particular emphasis is placed on the role of finite-range exchange effects, which provide a more realistic description compared to the conventional zero-range approximation and lead to noticeable modifications of the Coulomb barrier region. Barrier penetrabilities are evaluated using the WKB approximation with the Bohr--Sommerfeld quantization condition. The results demonstrate that nuclear deformation generally enhances tunneling probability, resulting in reduced $\alpha$-decay half-lives. The calculations indicate that increasing the nuclear incompressibility parameter $K$ within the CDM3Y family tends to lower the predicted half-lives by slightly enhancing the barrier penetrability. The calculated isotopic trends reflect the characteristic behavior near neutron shell closures at $N=82$, 126, and 184, indicating the interplay between nuclear structure effects and decay dynamics. The results provide a systematic assessment of the sensitivity of $\alpha$-decay half-lives to finite-range exchange, density dependence, deformation, and nuclear incompressibility within the microscopic double-folding approach.