Generalized Fermi–Dirac functions and derivatives: properties and evaluation
Generalized Fermi–Dirac functions and derivatives: properties and evaluation
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DOI：
10.1016/s0010-4655(01)00145-x
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发表时间：
2001-02
影响因子：
6.3
通讯作者：
Zhi-gang Gong;L. Zejda;Werner DappenJosep M. Aparicio
中科院分区：
文献类型：
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作者：
Zhi-gang Gong;L. Zejda;Werner DappenJosep M. Aparicio
广义Fermi-Dirac函数及其导数对于计算稠密恒星等离子体中部分简并电子的热力学量具有重要意义。本文建立了广义Fermi-Dirac函数的新的递推关系，并根据Aparicio [Ap.J.S.S.]的方法，提出了一种计算广义Fermi-Dirac函数三阶导数的有效数值方法。117（1998）627]。基于这种方法的Fortran程序，连同一个示例测试用例，提供。研究了一些其它的、常用的广义Fermi-Dirac函数在极端条件下的解析近似的精度和可靠性域，并与我们的结果进行了比较。
The generalized Fermi–Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi–Dirac functions have been found. An effective numerical method to evaluate the derivatives of the generalized Fermi–Dirac functions up to third order with respect to both degeneracy and temperature is then proposed, following Aparicio [Ap.J.S.S. 117 (1998) 627]. A Fortran program based on this method, together with a sample test case, is provided. Accuracy and domain of reliability of some other, popularly used analytic approximations of the generalized Fermi–Dirac functions for extreme conditions are investigated and compared with our results.