In this paper we use the microscopic "double well-cluster shell model" to discuss the existence of spurious states of motion of the center of mass during nuclear fission and heavy ion reactions. We outline the derivation of the general formulae with which the ,wave functions of the motion of the center of mass can be separated. Taking Be8 as an example, the existence of the spurious states is illustrated, and the components of these states and their corrections to the energy matrix elements are quantitatively evaluated.Through the analysis of the results of Be8 mentioned above, we conclude: although the propartion of the spurious states is only several per cent, their corrections to the fission barrier are significant, even larger then the corrections due to coulomb energy, and it is necessary to take them into account in accurate quantitative calculations. For a heavier nucleus, or higher excited states, the spurious states of the motion of the center of mass should be considered in more detail.
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