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Very tightly bound, abnormally-high-density states of nuclei, suggested as a possibility by Bodmer and by Lee and Wick, have been searched for as an anomalous isotope of radon. This was done by looking for high-energy γ rays following thermal-neutron capture. The limit that may be set for the atomic concentration of such nuclides on Earth is {~}10^-29 atom of Si.
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Holt et al. (1976) studied this question.
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