超镄核以及超重核的结构性质是目前原子核理论研究中的前沿热点问题之一。由于这些原子核核子数较多，费米面附近的能级较密，因此其结构非常复杂，能否正确描述这些原子核的性质，是检验一个核理论模型是否成功的重要依据。本项目拟采用最近发展的基于推转协变密度泛函理论的类壳模型方法（CDFT-SLAP），系统研究超镄核、超重核区高K同核异能态以及形状同核异能态的性质。首先，进一步发展推转CDFT-SLAP，采用更加适合的有限力程可分离对力代替目前模型中采用的零程单极对力；其次，系统研究超镄核区高K同核异能态以及形状同核异能态的性质，着重研究其组态结构、能谱、转动惯量、形状随原子核转动的演化、对关联以及高阶形变的影响等，并探索长寿命同核异能态的形成机制；进一步，探索质子数Z=108，中子数N=162附近的形变超重核，以及超重稳定岛附近原子核中可能存在的长寿命同核异能态的性质。

The property of the transfermium and superheavy nuclei is one of the most important frontier issues in present theoretical nuclear physics research. Due to so many nucleons in these nuclei, the energy levels close to the Fermi surface are crowded together, and their structures are very complicated, which provide a good benchmark for testing a nuclear model. In the present program, the recently developed cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) will be adopted to investigate the properties of the high-K isomers and the shape isomers in the transfermium and superheavy nuclei. Firstly, as a further development of the cranking CDFT-SLAP, the more reasonable finite range separable pairing will be adopted to replace the zero range monopole pairing in the present model. Secondly, systematic investigation will be performed for the high-K and shape isomers in the transfermium region. The research will focus on the configuration, energy spectra and moment of inertia, shape evolution with rotation, the effects of pairing and high-order deformations, etc. Furthermore, the mechanism of forming long-lived isomers will be investigated. At last, the properties of the isomers in the deformed superheavy nuclei around proton number Z=108 and neutron number N=162, and the isomers in the nuclei around the superheavy island will be investigated.