Il Nuovo Cimento (1955-1965)

, Volume 37, Issue 4, pp 1407–1421

The high-energy limit of the statistical model

Article

Summary

The sum over allN-particle phase space integrals forN ⩾ 3$$\Omega _R (P) = \sum\limits_{N = 3}^\infty {\frac{{(2mR^3 )^N }}{{N!}}\int {...\int {\prod\limits_{t = 1}^N {\frac{{d^3 p_i }}{{2p_{i0} }}} } } } \delta (4)(\sum\limits_{i = 1}^N {p_i - P} )$$ with interaction factorR is evaluated for high energiesW= √P2≫m, using the limit-theorem formalism of statistics. Applied to the calculation of the multiplicity our result is shown to yield asymptotically Fermi’s thermodynamic limit.

Riassunto

Si valuta la somma sopra tutti gli integrali dello spazio delle fasi perN particelle, oonN⩾3,$$\Omega _R (P) = \sum\limits_{N = 3}^\infty {\frac{{(2mR^3 )^N }}{{N!}}\int {...\int {\prod\limits_{t = 1}^N {\frac{{d^3 p_i }}{{2p_{i0} }}} } } } \delta (4)(\sum\limits_{i = 1}^N {p_i - P} )$$con il fattoreR di interazione, per alte energieW=√P2≫m, usando il formalismo statistico del teorema limite. Si mostra che il presente risultato, applicato al calcolo della molteplicità, porta asintoticamente al limite termodinamioo di Fermi.

References

1. (1).
E. Fermi:Progr. Theor. Phys. (Japan),1, 570 (1950).
2. (2).
P. P. Srivastava and G. Sudaeshan:Phys. Rev.,110, 765 (1958). For further literature see M. Kretzschmar :Ann. Rev. Nucl. Sci.,11, 1 (1961).
3. (3).
F. Lueçat and P. Mazur:Nuovo Cimento,31, 140 (1964).
4. (4).
A. I. Khinchik:Mathem. Foundations of Statistical Mechanics (New York, 1949).Google Scholar
5. (5).
P. Mazub and J. Van dee Linden:Journ. Math. Phys.,4, 271 (1963).
6. (6).
M. Neumann:An. Acad. Brasil. Cienc.,31, 361, 487 (1959); H. Satz:Forts,d. Phys.,11, 445 (1963); L. Van Hove:Nuovo Cimento,28, 798 (1963).Google Scholar
7. (7).
H. Joos and H. Satz:Nuovo Cimento,34, 619 (1964).
8. (8).
A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi:Higher Trascendental Functions, vol. 2 (New York, 1953).Google Scholar
9. (9).
Seee.g. L. Landau and E. Lifschitz:Statistical Physios (London, 1958).Google Scholar
10. (10).
Seee.g. M. G. Kendall :The Advanced Theory of Statistics I (London, 1952).Google Scholar
11. (11).
M. Frechet and J. Shohat:Trans. Am. Math. Soc., 33 (1931). The N-dimensional generalization is given by E. K. Haviland:Am. Journ. Math.,56, 625 (1934).Google Scholar
12. (12).
Seee.g. H. Cramée:Mathematical Methods of Statistics (Princeton, 1961).Google Scholar

© Società Italiana di Fisica 1965

Authors and Affiliations

• H. Satz
• 1
1. 1.Deutsches Elektronen-Synchrotron (DESY)Hamburg