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On the statistical distribution of the widths and spacings of nuclear resonance levels

Published online by Cambridge University Press:  24 October 2008

Eugene P. Wigner
Eugene P. Wigner
Affiliation:
Palmer Physical LaboratoryPrinceton
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Abstract

If the average spacing of the resonance levels is very small as compared with the range of energy in which the spacing or width of the levels changes appreciably on the average, one can speak of a statistical distribution of the level spacings and widths. The question then comes up naturally, whether the ‘distribution law’ for width and spacing is different for protons, neutrons, etc., i.e. whether it depends on the long-range interaction of the scattered particle. It is pointed out that while the average width must depend on the long-range interaction (on account of the penetration factor) the distribution of the widths, if these are measured in terms of their average, can be expected to be independent therefrom. In the case of the level spacings, not only the distribution about the average, but the average itself is also independent of the long-range interaction. It is pointed out, incidentally, that the logarithmic derivative of the wave function at the surface of the nucleus will have, on the whole, a positive value between resonances because of the greater effect of the high-energy resonances than that of the bound states.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 4 , October 1951 , pp. 790 - 798
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

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‡ The general condition for the validity of (2a) seems to be that one can define (a) a probability density throughout space (or at least define the probability for the whole internal region r < a) and (b) a flux density at the boundary r = a of the internal region. Cf. the writer's article, Phys. Rev. 70 (1946), 15Google Scholar, especially p. 18; also Goertzel, G., Phys. Rev. 73 (1948), 1463CrossRefGoogle Scholar, where the consideration is carried out for the Dirac electron. † Cf. Blatt, J. M. and Jackson, J. D., Phys. Rev. 76 (1949), 18.CrossRefGoogle Scholar

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‡ Recently, B. L. Cohen has shown that a similar formula holds for a-particles with an additional factor ⅛

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