- Autor(in)
- Referenz
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1 H. A. Buchdahl, Ann. Physik (7) 3, 345 (1959).
2 H. A. Buchdahl, Physic. Rev. 116, 1027 (1959); especially Section 4.
3 S. Chandrasekhar, An Introduction to the Study of Stellar Structure, (University of Chicago Press, 1939), Chapter X. References to equations in this chapter are indicated by X.
- Seitenbereich
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0031 - 0046
- Zusammenfsg.
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The exact equation of state and total energy function of a perfect Fermi-Dirac gas for arbitrary degree of degeneracy, and when relativistic effects are fully taken into account, can be exhibited only in a rather unsurveyable parametric form. It is therefore desirable to have approximations available which provide the pressure <I>P</I> and the total energy density <I>u</I> explicitly as functions of the temperature <I>T</I> and the particle density <I>n</I>. Such „heuristic“ approximations are constructed in this paper, that is to say, approximations which tend asymptotically to the correct functions in certain extreme regions (e. g. that of complete degeneracy and either very small or very large density), and which numerically reproduce them sufficiently closely throughout the entire ranges of values which the variables <I>T</I> and <I>n</I> can take. Numerical investigations of the approximations considered here suggest that they should be sufficiently good to be useful in some astrophysical problems.
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- Forschungsartikel