有限粒子数理想费米系统的磁化率

The Magnetic Susceptibility of An Ideal Fermi Das for A Finite Number of Particles in Weak Magnetic Field

根据弱磁场中理想费米气体(忽略轨道运动)的正则配分函数Z(N),导出粒子数N+的几率分布函数G(β,N+)。运用统计平均方法,解析出有限粒子数理想费米系统泡利顺磁性平均磁化率的表达式。然后通过计算热力学极限下不同温度范围的磁化率pχ,得到不同温度范围内的有限粒子数理想费米系统泡利顺磁性平均磁化率的解析式。研究结果表明,有限粒子数理想费米系统的平均磁化率小于热力学极限下的磁化率,温度愈高,平均磁化率愈小;在低温条件下,磁场愈强,平均磁化率愈小;在高温条件下,磁场愈强,平均磁化率愈大。系统的粒子数N也对平均磁化率有直接的影响,粒子数N愈大,系统的平均磁化率愈大。

The probability distribution function G（β,N^＋ ） of particle number N^＋ is deduced on the basis of the Canonical partition function Z（N） of an ideal Fermi gas（ The orbital motion of the fermi- ons is not considered） in weak magnetic field. The expression of average susceptibility for Pauli pa- ramagnetism of an ideal Fermi gas with finite number of particles is resolved by using statistical aver- age method. Then, the analytical expressions of average susceptibilities for Pauli paramagnetism of the system in different temperature region are derived by calculating susceptibilities Xp in the limit of thermodynamics at different temperatures. It is shown that the average magnetic susceptibility of the system with finite number of particles is less than that of thermodynamics - limit system and average susceptibility decreases with temperatures increasing. At low temperatures, the stronger magnetic filed is, the smaller average susceptibility is, but at high temperatures, the result is reversed. The particle number of the system N has a direct effect on average susceptibility, which is that the average sus- ceptibility increases with number of particles increasing.