弱相互作用费米气体的不稳定性判据

根据由赝势法得到的弱相互作用费米气体的自由能，利用热力学方法研究了无外场时弱相互作用费米气体的稳定性.结果表明，无外场情况下理想费米气体与存在弱排斥相互作用的费米气体是稳定的；而具有弱吸引相互作用的费米气体在一定条件下可出现不稳定性.给出了不稳定性的粒子数密度判据和温度判据，就不同逸度情况下临界粒子数密度的具体表达结果以及温度、粒子质量和吸引相互作用对临界粒子数密度的影响进行了讨论. 关键词： 费米气体 相互作用 不稳定性判据

The criterion of instability for a weakly interacting Fermi gas

Using the equation of free energy for a weakly interacting Fermi gas, the stability of a weakly interacting Fermi gas in the absence of external potential is studied by means of thermodynamics. The instability arising from the weakly attractive interacting of a Fermi gas is pointed out. The particle density criterion and the temperature criterion of instability for the imperfect Fermi gas with weakly attractive interaction are given, and the dependance of the critical density of particles on the temperature and the mass of particle and the attractive interaction is discussed.