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The nuclear fusion is a reaction to form a compound nucleus. It plays an important role in several circumstances in nuclear physics as well as in nuclear astrophysics, such as synthesis of superheavy elements and nucleosynthesis in stars. Here we discuss two recent theoretical developments in heavy-ion fusion reactions at energies around the Coulomb barrier. The first topic is a generalization of the Wong formula for fusion cross sections in a single-channel problem. By introducing an energy dependence to the barrier parameters, we show that the generalized formula leads to results practically indistinguishable from a full quantal calculation, even for light symmetric systems such as $^{12}$C+$^{12}$C, for which fusion cross sections show an oscillatory behavior. We then discuss a semi-microscopic modeling of heavy-ion fusion reactions, which combine the coupled-channels approach to the state-of-the-art nuclear structure calculations for low-lying collective motions. We apply this method to subbarrier fusion reactions of $^{58}$Ni+$^{58}$Ni and $^{40}$Ca+$^{58}$Ni systems, and discuss the role of anharmonicity of the low-lying vibrational motions.
Complete fusion excitation functions of reactions involving breakup are studied by using the empirical coupled-channel (ECC) model with breakup effects considered. An exponential function with two parameters is adopted to describe the prompt-breakup
The cross sections of complete fusion and incomplete fusion for the $ ^{9} $Be + $ ^{197} $Au system, at energies not too much above the Coulomb barrier, were measured for the first time. The online activation followed by offline $gamma$-ray spectros
In this paper we revisit the one-dimensional tunnelling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the barrier s
The present understanding of reaction processes involving light unstable nuclei at energies around the Coulomb barrier is reviewed. The effect of coupling to direct reaction channels on elastic scattering and fusion is investigated, with the focus on
We carefully compare the one-dimensional WKB barrier tunneling model, and the one-channel Schodinger equation with a complex optical potential calculation of heavy-ion fusion, for a light and a heavy system. It is found that the major difference betw