Determining the dynamic deformation of $^{140}$Ce by constraining coupled-channels parameters for fusion
We present a systematic study of the dynamic deformation of 140Ce using 16O and 36S projectiles in heavy-ion fusion reactions, combining experimental data, a Gaussian analytic-barrier framework and coupled-channels calculations. Fusion cross sections for 16O+140Ce are measured from ~17% above to ~12.4% below the Bass barrier. Fusion data for 36S+140Ce are obtained from the literature. Deformation parameters of 140Ce are extracted via chi-square minimization and Bayesian analysis, with independent Bayesian Model Averaging yielding beta_2 = 0.09 +/- 0.03 and beta_3 = 0.18 +/- 0.02, consistent across both systems. The extracted parameters are tested in the 28Si+140Ce system, where coupled-channels calculations including transfer of a pair of neutrons (2n) reproduce both the fusion excitation function and the barrier distribution. The positive Q-value 2n-pickup channel enhances fusion in this reaction, while the projectile's vibrational or rotational nature results in similar structure of the barrier distribution. This study demonstrates that the Gaussian analytic recipe is quite effective in deriving the fusion barrier distribution which proves to be a sensitive probe of intrinsic nuclear deformation. Further, coupled-channels analysis across multiple systems ensures robustness of the extracted deformation parameters.