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Very weak alpha branching in heavy elements was studied by a recently developed coincidence technique. This technique makes it possible to measure the energies and intensities of both alpha -particle groups and de-exciting radiation, even when the transition intensities are as low as 10/sup -8/ relative to the most intense alpha group. Twenty alpha -particle emitters from Po/sup 214/ to Fm were examined. 00+ states (beta vibrations) were observed in six even-even nuclei, and analogous states were found in three odd-mass nuclei. They are in general characterized by low alpha-decay hindrance factors and roughly equal de-excitation by electric monopole and quadrupole transitions. However, the deexcitation of these states is in disagreement with vibrational model predictions in certain cases; more important, the de-excitation and other properties of the states exhibit some irregular variations from nucleus to nucleus which are evidence for some particle character in the states. Information was also obtained about some other types of levels. A number of 1- states (octupole vibrations) were observed, and a possible 2- state was observed in U/sup 236/. A state that appears to be analogous to the 1-octupole states of even-even nuclei was observed in U/sup 235/. In Pu/sup 239/, a K = …