由弱磁场中弱相互作用费米气体的配分函数,导出有限粒子数条件下系统的配分函数G(β,N+).在此基础上,运用统计平均方法求解有限粒子数弱相互作用费米气体热力学量的解析表达式,给出各种温度条件下的热力学性质.研究结果表明,有限粒子数效应使各个热力学量都产生了一个修正项,除温度趋于0外,粒子数对化学势的修正项有直接影响,对内能和热容量的修正项并不产生直接影响.并且有限粒子数效应总是降低化学势,从而使化学势的0点向低温漂移,粒子数增大,会削弱这种效应,粒子间的相互排斥会加强这种效应.

The partition function of system with finite number of particles is derived is derived by using partition function of a weakly interacting Fermi gas trapped in weak magnetic field. Based on the derived expressions, the analytical expressions of thermodynamic quantities of a weakly interacting Fermi gas for finite particle number are solved by using statistical average method and the thermodynamic properties under different temperature conditions are given. It is shown that each thermodynamic quantity has a correctional term due to effects of a finite number of particles. The particle number has a direct effect on correction of chemical potential but has no direct effects on corrections of total energy and heat capacity except T = 0. Furthermore, effects of a finite number of particles always reduce chemical potential, thereby zero point of chemical potential shifts towards low temperatures. The increase of particle number weakens the effect, but the repulsive interactions between particles strengthen the effect.门福殿（中国石油大学(华东)物理科学与技术学院,东营,257061）刘慧（中国石油大学(华东)物理科学与技术学院,东营,257061）朱后禹（中国石油大学(华东)物理科学与技术学院,东营,257061）吕琳（中国石油大学(华东)物理科学与技术学院,东营,257061）