Part I contains the solution of the problem of a particle for which the potential energy $V\left(r\right)\mathrm{}$ is a simple rectangular hole of finite depth, such a model being of interest in connection with the spacing of nuclear energy levels. Formulae are given by which a numerical determination of energies can be carried out for any assumed depth of the hole. In part II the results are extended to finite holes of different shape, and an argument is presented which proves the inadequacy of any such model to explain the arrangement of $\alpha$-ray levels in Ra C'.

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