随着放射性束流线装置的相继建成和升级改造，越来越多的不稳定原子核在实验室中被合成，奇特的原子核性质不断被发现，比如：皮和晕结构、低能矮共振、新的壳层演变等等。合理解释这些新的物理现象是对现有核理论的挑战，必须提出新的方法来发展和完善。不稳定核的最大特点是弱束缚，连续谱和对关联在描述原子核性质中起到重要作用，如何严格处理连续谱的贡献是理论研究的难点。本申请在已有的工作基础上,拟开展以下研究：将相对论连续无规位相近似方法通过考虑对关联的贡献推广到开壳核集体激发态性质的研究中，实现对连续谱和对关联贡献的严格处理，应用到不稳定核电磁和自旋-同位旋集体响应方程的描述中。通过本项目的研究，可发展和完善相对论核多体理论，改善对不稳定核结构的微观描述，提升预言能力，为该方法在核天体物理中的进一步应用打下基础。

With the construction of new generation of radioactive beam facilities and the production of high quality radioactive beam, more and more unstable nuclei are produced in the laboratory, and many exotic properties are found experimentally, which are different from the properties of nuclei in the β stability line, such as: skin and halo phenomena, Pygmy dipole resonances, new shell structure, di-nucleon decay and so on. To understand those new properties, it is a challenge for the present nuclear theory, and new theoretical approaches must be considered and developed. The most prominent feature of the unstable nuclei is weakly bound, the continuum and pairing play important role in describing the properties of unstable nuclei, how to treat exactly the contribution of continuum is one of the problems associated with unstable nuclei. Based on the work we have done, in this proposal we will build relativistic continuum quasiparticle random phase approximation method to describe the collective giant resonances of open shell unstable nuclei by considering the contribution of pairing correlation, develop the formalism and construct the numerical codes, and apply our new method to depict the electric and spin-isospin response functions of unstable nuclei. Finally, we can improve the relativistic many-body theory within the help of this proposal, and it can give a proper description on nuclear structure, it can help us in understanding the physics mechanism of the formation of Pygmy dipole resonances. The method can be further applied to investigate some problems in nuclear astrophysics in the future, such as nucleosynthesis and abundance distribution of elements in the stars.