# Angular Distributions and Correlations of Nuclear Radiations in Nuclear Spectroscopy

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## Abstract

It was exactly 30 years ago, in 1940, that Dunworth^{1} ), in a paper discussing coincidence techniques, mentioned the possibility of ‘spatial correlations of successively emitted γ-rays’. In this paper the following communication by M.H.L. Pryce was quoted: ‘Where successive γ-rays are emitted by a nucleus there will, in general, be a certain amount of correlation between the two directions of emission. The distribution in relative angle is determined by the value of the total angular momentum in the three nuclear states involved in the process of emitting of the two γ-rays. In the worst case — that when the angular momenta are 0, 1,0, respectively — the distribution is proportional to cos^{2} ϑ; the number in opposite directions is then three times what would be expected on the assumption of isotropy. In most cases, however, this ratio will be much nearer to unity’. Hence, M.H.L. Pryce was the first who predicted the existence of directional correlations of nuclear radiations and furthermore he recognized already the important rôle of nuclear angular momenta in angular correlation phenomena. In the very same year, D.R. Hamilton^{2} ) developed a theory for γ-γ directional correlations using the language of perturbation theofy. Although Hamilton’s classic work contained many of the important features of angular correlation theory, it was limited in its applicability and the full generality of the underlying general principles was not recognized until about ten years later group theoretical methods and the full formalism of the quantum theory of angular momentum was applied to the description of angular correlation phenomena (Gardner^{3}), Racah^{4}), Fano^{5}), Lloyd^{6}), Alder^{7}), Coester and Jauch^{8}), Biedenharn and Rose^{9})). Since then the theory of angular correlations and distributions^{10}) of nuclear radiations including extranuclear perturbations (Alder^{7}), Abraeam and Pound^{11} ), Alder et al.^{12} ), Steffen and Frauenfelder (review)^{13}), Gabriel^{14}), Matthias et al.^{15} )) has been fully developed and it is well understood today. It is probably the best and most comprehensive theory of nuclear phenomena, because it is based on very general symmetry principles, i.e., on three-dimensional rotation and reflection symmetries, which lead to conservation of angular momentum and parity, respectively. It is the isotropy of three-dimensional space with its implication of conservation of angular momentum that is the fundamental reason for the existence of anisotropic angular correlations and distributions.

## Keywords

Angular Momentum Density Matrix Angular Distribution Angular Correlation Nuclear State## Preview

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## References

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