Barrier modification in sub-barrier fusion reaction⁶⁴Ni+¹⁰⁰Mo using Wong formula with Skyrme forces in semiclassical formalism

Abstract

Abstract. We obtain the nuclear proximity potential by using semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), and use it in the extended -summed Wong formula under frozen density approximation. This method has the advantage of allowing the use of different Skyrme forces, giving different barriers. Thus, for a given reaction, we could choose 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 -summed Wong formula, with effects of deformations and orientations of nuclei included, fits the fusion-evaporation cross section data exactly for the force GSkI, requiring additional barrier modifications for forces SIII and SV. However, the same for other similar reactions, like 58,64 Ni+ 58,64 Ni, fit the data best for SIII force. Hence, the barrier modification effects in -summed Wong expression depend on the choice of Skyrme force in semiclassical ETF method. IntroductionThe unexpected behavior of some fusion-evaporation cross sections at energies far below the Coulomb barrier, has challenged the theoretical models to explain the, so called, fusion hindrance phenomenon in true coupled-channels calculations (ccc) for reactions such as 58 Ni+ 58 Ni, 64 Ni+ 64 Ni, and 64 Ni+ 100 Mo [1]. The ccc could, however, be sensitive to the so far unobserved, hence not-included, high-lying states. Misicu and Esbensen [2] were the first who succeeded in describing the above said three reactions in terms of a density-dependent M3Y interaction, modified by adding a repulsive core potential [3]. The repulsive core changes the shape of the inner part of the potential in terms of a thicker barrier (reduced curvaturehω) and shallower pocket. Here, the nuclei are considered spherical in ground-state and the dynamical quadrupole and octupole deformations (β 2 , β 3 ) are included (only β 2 in the case of 58 Ni+ 58 Ni).The dynamical cluster-decay model (DCM) of preformed clusters by Gupta and collaborators [4,5] is found recently [6,7] to have barrier modification effects as the inbuilt property, where "barrier lowering" at sub-barrier energies arise in a natural way in its fitting of the only parameter of model, the neck-length parameter. The difference of actually-calculated barrier from the actually-used barrier height, corresponding to the neck-length parameter for best-fitted fusionevaporation cross section, gives the "barrier lowering" in DCM, whose values are found to increase as the incident energy decreases to sub-barrier energies. Calculations are based on β 2 deformations and orientation θ i -dependent nuclear proximity potential of Blocki et al. [8].