中文摘要：

在壳模型的框架下引入了密度依赖的Gogny相互作用以研究有限核的核结构性质.文中详细地讨论了密度依赖核力的性质和在壳模型中的运用.通过迭代求解的方法可以得到任意模型空间下的两体矩阵元和单粒子能.经过p壳和sd壳的计算我们发现Gogny相互作用可以在跨度较大的核区内有效计算能谱和结合能等核结构信息.并且在各套Gogny参数中D1S的表现最好,与实验数据进行对比能给出很好的计算结果.

英文摘要：

Shell model has been an important and powerful tool for describing the structures of finite nuclei. In shell-model calculations, one of the most important questions is to construct the effective Hamiltonian in the truncated model space. One way is to start from realistic nuclear forces and then use perturbation theory to get the effective interaction. However, these calculations are complicated. If one wants to gain better quantitative descriptions one will have to take the high-order correlations （e.g., three-nucleon force, 3NF） into consideration. High-order correlations make calculations even more complicated and give rise to a significant growth of the model dimension. Another way is to start form an empirical TBMEs which will provide more quantitative results with simpler shell-model calculations. In empirical methods, the TBMEs are usually derived from realistic interactions originally and then are modified by fitting the experimental data coming from nuclear structures（including nuclear binding energies, excitation spectra and transition properties）. Effects of the missing high-order correlations （e.g., 3NFs） are assume to be equivalently taken into account by fitting procedure. Yet the fitting can be a troubled process while there are too many TBMEs to be fitted. Meanwhile there will be large uncertainties in evaluating the TBMEs since some of matrix elements （especially for off-diagonal matrix elements） are insensitive to the data fitting. When it come to cross-shell cases, i.e. the model space including two or more major shells, the fitting process will be even more intricate. Not only because the large number of TBMEs to be fitted, but also that it is difficult to obtain the SPEs in such cases. We cannot distinguish the collective core excitations and single-particle excitations because they can get really close for cross-shell cases while the energy for the system is high. To deal with the above problems and to discuss the cross-shell situation properly, in the present work, we introdu