在本项目前期研究囚禁玻色气体凝聚集体激发Landau阻尼工作中，提出了在Hartree-Fock-Bogoliubov平均场理论近似框架下的Landau阻尼微扰公式应用中考虑元激发实际弛豫的新方法，比原来的通常方法更合乎物理实际，不但能正确给出阻尼的计算公式，还可以给出频移的计算公式。又尝试使动能在凝聚体基态波函数边界为零,以改进消除作为唯一解析方案Thomas-Fermi近似中发散问题的方法，预期可以得到比前期解析计算更好的成果。本项目拟应用这两种新方法研究BEC-BCS交叉中超流费米气体集体激发的Landau阻尼和频移，详细计算三模耦合矩阵元、阻尼强度、频移强度、阻尼系数和频移大小，并讨论阻尼系数和频移大小与系统温度、粒子数、囚禁频率和各向异性参量的关系，通过精确的计算探究粒子间相互作用和检验凝聚体量子多体理论.

In our prevoius work, in which we studied the Landau damping of the collective mode in traped Bose gase condensate, we put out a new method that the practical reluxation has been considered in the use of the perturbation formula for the Landau damping based on the Hartree-Fock-Bogoliubov mean-field theoritical approximation. Being more reasonable than the usual one, the new method not only deduced the formula of the damping correctively but also provided the formula of the frequency-shift. And we have improved the method eliminating the divergence in Thomas-Fermi approximation, which is only analytical approach, by trying to zero the kinetic energy at the boundary in the ground sate wavefunction of the condensate, and expect to get better analytical result than that in our prevoius work. By means of the two methods, we will investigate the Landau damping and frequency-shift of the collective mode in syperfluid Fermi gas in BEC-BCS crossover. We will calculate the three-mode coupling matrix element,daming strength, frequecy-shift strength, damping rate, and frequency-shift, discuss the relations among the Landau rate, frequency-shift, temperatue, particle number, trapping frequency, and anisotropic parameter. The precision measurment of the Landau damping and frequency-shift may be used to deduce the intreraction of the system and test the quantum manybody theory for condened matter.