Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST AB Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article:

Phys. Rev. 95, 249–262 (1954)

[Issue 1 – 1 July 1954 ]

[ Previous article | Next article | Issue 1 contents ]

Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles

Léon Van Hove

Institute for Advanced Study, Princeton, New Jersey

A natural time-dependent generalization is given for the well-known pair distribution function g(r) of systems of interacting particles. The pair distribution in space and time thus defined, denoted by G(r, t), gives rise to a very simple and entirely general expression for the angular and energy distribution of Born approximation scattering by the system. This expression is the natural extension of the familiar Zernike-Prins formula to scattering in which the energy transfers are not negligible compared to the energy of the scattered particle. It is therefore of particular interest for scattering of slow neutrons by general systems of interacting particles: G is then the proper function in terms of which to analyze the scattering data.

After defining the G function and expressing the Born approximation scattering formula in terms of it, the paper studies its general properties and indicates its role for neutron scattering. The qualitative behavior of G for liquids and dense gases is then described and the long-range part exhibited by the function near the critical point is calculated. The explicit expression of G for crystals and for ideal quantum gases is briefly derived and discussed.

©1954 The American Physical Society

URL: http://link.aps.org/abstract/PR/v95/p249
DOI: 10.1103/PhysRev.95.249

[ Previous article | Next article | Issue 1 contents ]

References

1. I. Waller, Z. Physik 51, 213 (1928).
2. N. F. Mott, Proc. Roy. Soc. (London) A127, 658 (1930).
3. I. Waller and D. R. Hartree, Proc. Roy. Soc. (London) A124, 119 (1929) [CAS].
4. P. M. Morse, Physik. Z. 33, 443 (1932).
5. I. Waller, dissertation, Uppsala, 1925 (unpublished).
6. F. Zernike and J. Prins, Z. Physik 41, 184 (1927); P. Debye and H. Memke, Ergeb. Tech. Röntgenk. 2 (1931).
7. D. J. Hughes, Pile Neutron Research (Addison-Wesley Publishing Company, Cambridge, 1953).
8. G. Placzek, Phys. Rev. 86, 377 (1952) ; G. C. Wick, Phys. Rev. 94, 1228 (1954) .
9. L. Van Hove, Phys. Rev. 93, 268 (1954) .
10. R. J. Glauber (private communication); Phys. Rev. 87, 189 (1952); 94, 751 (1954), and forthcoming paper.
11. H. Palevsky and D. J. Hughes, Phys. Rev. 92, 202 (1953) ; G. L. Squires (to be published).
12. A. Akhiezer and I. Pomeranchuk, J. Phys. (U.S.S.R.) 11, 167 (1947); G. C. Wick, reference 8.
13. Omitted endnote.
14. J. M. Cassels, Progr. Nuclear Phys. 1, 185 (1950).
15. O. Chamberlain, Phys. Rev. 77, 305 (1950) .
16. Placzek, Nijboer, and Van Hove, Phys. Rev. 82, 392 (1951) .
17. L. Goldstein, Phys. Rev. 84, 466 (1951) .
18. P. C. Sharrah and G. P. Smith, J. Chem. Phys. 21, 288 (1953).
19. Henshaw, Hurst, and Pope, Phys. Rev. 92, 1229 (1953) .
20. P. Egelstaff, Nature 168, 290 (1951); B. N. Brockhouse and D. G. Hurst, Phys. Rev. 88, 542 (1952) ; R. D. Lowde, Proc. Roy. Soc. (London) A221, 206 (1954) [CAS].
21. Kirkwood, J. Chem. Phys. 3, 300 (1935) [CAS]; B. R. A. Nijboer and L. Van Hove, Phys. Rev. 85, 777 (1952) ; B. R. A. Nijboer and R. Fieschi, Physica 19, 545 (1953) [CAS].
22. L. Landau and G. Placzek, Physik. Z. Sowjetunion 5, 172 (1934); J. Frenkel, Kinetic Theory of Liquids (Clarendon Press, Oxford, 1946), pp. 244 ff.
23. L. S. Ornstein and F. Zernike, Proc. Acad. Sci. Amsterdam 17, 793 (1914); Physik. Z. 19, 134 (1918).
24. L. Onsager, Phys. Rev. 37, 405 (1931) ; 38, 2265 (1931) .
25. L. Landau and G. Placzek (reference 22).
26. Omitted endnote.
27. Omitted endnote.
28. G. Placzek, Physik. Z. 31, 1052 (1930).
29. G. Placzek and L. Van Hove, Phys. Rev. 93, 1207 (1954) ; The unpublished work of R. J. Glauber (reference 10).
30. Omitted endnote.
31. F. Bloch, Z. Physik 74, 295 (1932).
32. Omitted endnote.
33. Omitted endnote.
34. G. Placzek and L. Van Hove, reference 29.
35. G. Klein and I. Prigogine, Physica 19, 1053 (1953) [CAS].
36. L. Van Hove, Phys. Rev. 89, 1189 (1953) .
37. Omitted endnote.
38. reference 34.
39. G. Placzek, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, 1951), pp. 581-588.
40. G. C. Wick, Physik. Z. 38, 689 (1937); J. M. Cassels, Progr. Nuclear Phys. 1, 185 (1950).
41. F. London, J. Chem. Phys. 11, 203 (1943) [CAS].
42. A. Akhiezer and I. Pomeranchuk, J. Phys. (U.S.S.R.) 9, 461 (1945) [CAS]; Goldstein, Sweeney, and Goldstein, Phys. Rev. 77, 319 (1950) ; L. Goldstein and D. W. Sweeney, Phys. Rev. 80, 141 (1950) .

[ Previous article | Next article | Issue 1 contents ]