Skip to main content
Log in

Transport coefficients of a neutrino gas

Транспортные козффициенты гаэа нейтрино

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

A relativistic kinetic theory for massless particles is developed in which expressions for the transport coefficients in terms of the cross-section are found. Applied to a neutrino gas of temperatureT one obtains for the heat conductivityλ and the shear viscosityη the expressionsλ=5·1057 T −2 andη=9.3·1035 T −1 (cgs units). The volume viscosity vanishes.

Riassunto

Si sviluppa una teoria cinetica relativistica per particelle prive di massa in cui si trovano espressioni dei coefficienti di trasporto in funzione della sezione d’urto. Applicandola a un gas di neutrini a temperaturaT si ottengono per la conducibilità termicaλ e la viscosità di taglioη le espressioniλ=5·1057 T −2 edη=9.3·1035 T −1 (in unità cgs). La viscosità di volume si annulla.

Реэюме

Раэвивается релятивистская кинетическая теория для частиц с нулевой массой, в которой определены выражения для транспортных козффициентов череэ поперечные сечения. Применяя полученные реэультаты к гаэу нейтрино с температуройT, получаются следуюшие выражения для удельной теплопроводностиλ=5·1057 T−2 и сдвиговой вяэкостиη=9.3·1035 T−1 (в единицах СГС). Общемная вяэкость отсутствует.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cf., for instance,C. W. Misner:Nature,214, 40 (1967);Phys. Rev. Lett.,19, 533 (1967);Astrophys. Journ.,151, 431 (1968);B. Pontecorvo:Kiev Conference on High-Energy Physics (Kiev, 1970);M. Ruderman:Accad. Naz. Lincei,157, 1 (1971);S. Weinberg:Astrophys. Journ.,168, 175 (1971);Gravitation and Cosmology: Principles Applications of the General Theory of Relativity (New York, N. Y., 1972);T. de Graaf;Accad. Naz. Lincei,157, 81 (1971);R. A. Matzner andC. W. Misner:Astrophys. Journ.,171, 415 (1972);E. D. Commins:Weak Interactions (New York, N. Y., 1973);T. de Graaf:Vistas in Astronomy, Vol.15, edited byA. Beer (Oxford, 1973);C. W. Misner, K. S. Thorne andJ. A. Wheeler:Gravitation (San Francisco, Cal., 1973).

    Article  ADS  Google Scholar 

  2. W. A. van Leeuwen andS. R. de Groot:Lett. Nuovo Cimento,6, 470 (1973).

    Article  Google Scholar 

  3. W. A. van Leeuwen, P. H. Polak andS. R. de Groot:Physica,63, 65 (1973);P. H. Polak, W. A. van Leeuwen andS. R. de Groot:Physica,66, 455 (1973).

    Article  ADS  Google Scholar 

  4. This particular form of the transport equation can be found in,e.g.,Ch. G. van Weert,W. A. van Leeuwen andS. R. de Groot:Physica,69, 441 (1973).

    Article  ADS  Google Scholar 

  5. See,e.g.,W. Israel andJ. N. Vardalas:Lett. Nuovo Cimento,4, 887 (1970);W. Israel: inGeneral Relativity, Papers in Honour of J. L. Synge, edited byL. O’Raifeartaigh (Oxford, 1972).

    Article  Google Scholar 

  6. F. Jüttner:Ann. der Phys.,34, 856 (1911).

    Article  MATH  Google Scholar 

  7. This fact may be verified with the help of the asymptotic relationK n(z)∼ ∼ 2n−1(n−1)!z n which holds in the limitz→0. SeeM. Abramowicz andI. A. Stegun:Handbook of Mathematical Functions (New York, N. Y., 1965), formula 9.6.9, p. 375.

  8. Equations (8)–(52) and thus in particular eq. (38) may alternatively be found by taking the limit of vanishing mass in the corresponding equations (3,5) for the massive case, as may be checked with the asymptotic relation of footnote (7).

  9. Cf.,e.g.,J. Werle:Relativistic Theory of Reactions (Amsterdam, 1966), p. 225;W. Israel: inGeneral Relativity, Papers in Honour of J. L. Synge, edited byL. O’Raifeartaigh (Oxford, 1972), p. 217; ref.(4), p. 446.

    Article  ADS  Google Scholar 

  10. M. Abramowitz andI. A. Stegun:Handbook of Mathematical Functions (New York, N. Y., 1965), formulae 9.6.23 and 9.6.28, p. 376.

  11. S. Chapman andT. G. Cowling:Mathematical Theory of Non-Uniform Gases (Cambridge, 1970), p. 155.

  12. L. H. Thomas:Quart. Journ. Math., Oxford series,1, 239 (1930);C. W. Misner andD. H. Sharp:Phys. Lett.,15, 279 (1965).

    Article  MATH  ADS  Google Scholar 

  13. I. S. Gradshteyn andI. M. Ryzhik:Table of Integrals, Series and Products (New York, N. Y., 1965), formula 6.561.16, p. 684.

  14. ħ=1.0545919(80)·10−27 g cm2s−1,c=2.9979250(10)·1010cm s−1,k B=1.380622(59)·10−16 g cm2s−2°K−1 (Particle Data Group:Rev. Mod. Phys.,45, No. 2, Part II (1973)),G=1.4350(11)·10−49 g cm5s−2 (R. E. Marshak, Riazuddin andC. P. Ryan:Theory of Weak Interactions in Particle Physics (New York, N. Y., 1969), p. 39). The figures in parentheses indicate the uncertainty in the last two digits of the main number.

  15. P. H. Meltzer: unpublished report.

  16. W. Israel:Journ. Math. Phys.,4, 1163 (1963);W. A. van Leeuwen andS. R. de Groot:Physica,51, 32 (1971).

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Groot, S.R., van Leeuwen, W.A. & Meltzer, P.H. Transport coefficients of a neutrino gas. Nuov Cim A 25, 229–251 (1975). https://doi.org/10.1007/BF02729044

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02729044

Navigation