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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 12C+12C, 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 58Ni+58Ni and 40Ca+58Ni systems, and discuss the role of anharmonicity of the low-lying vibrational motions. [ABSTRACT FROM AUTHOR]

The coupled-channels method has been a standard tool in analyzing heavy-ion fusion reactions at energies around the Coulomb barrier. We investigate three simplifications usually adopted in the coupled-channels calculations. These are i) the exclusion of non-collective excitations, ii) the assumption of coordinate independent coupling strengths, and iii) the harmonic oscillator approximation for multi-phonon excitations. In connection to the last point, we propose a novel microscopic method based on the beyond-mean-field approach in order to take into account the anharmonic effects of collective vibrations. [ABSTRACT FROM AUTHOR]

The covariant density functional theory (CDFT) with a few number of parameters allows a very successful description of the properties of nuclei all over the nuclear chart. The recent progress on the application of the CDFT as well as its extensions for a series of interesting and hot topics in nuclear structure and nuclear astrophysics are summarized. In particular, the newly proposed point-coupling parametrization PC-PK1 and the application of the CDFT to the single particle level of the radioactive neutron-rich doubly magic nucleus 132Sn, the deformed halo in nuclei, and the β decay life-time of neutron rich nuclei are discussed in details. [ABSTRACT FROM AUTHOR]

The structure of low-energy collective states in the neutron-rich nucleus 44S is analyzed using a microscopic collective Hamiltonian model based on energy density functionals (EDFs). The calculated triaxial energy map, low-energy spectrum and corresponding probability distributions indicate a coexistence of prolate and oblate shapes in this nucleus. [ABSTRACT FROM AUTHOR]

Covariant Density functional theory is used as a basis for calculations of the spectra of low-lying collective nuclear excitations. In this way it provides a microscopic description of quantum phase transitions in nuclei. Since the mean field approximation breaks down in transitional nuclei, a theory is developed which uses the Relativistic Generator Coordinate Method (GCM) to perform configuration mixing calculations of angular momentum and particle number projected wave functions. As applications with show 3D-calculations of the spectrum of low-lying collective states in the nucleus 24Mg and a microscopic investigation of quantum phase transitions in transitional nuclei. [ABSTRACT FROM AUTHOR]

The density functional theory with a few number of parameters allows a very successful phenomenological description of ground state properties of nuclei all over the nuclear chart. The recent progress on the application of the covariant density functional theory (CDFT) for nuclear structure and astrophysics as well as its extensions by the group in Beijing is summarized. In particular, its application to magnetic moments is discussed in details. [ABSTRACT FROM AUTHOR]