Asymptotically Correct Shell Model for Nuclear Fission

A two-center shell model with oscillator potentials, $\overrightarrow{\mathrm{l}}·\overrightarrow{\mathrm{s}}$ forces, and ${\overrightarrow{\mathrm{l}}}^2$ terms is developed. The shell structures of the original spherical nucleus and those of the final fragments are reproduced. For small separation of the two centers the level structure resembles the Nilsson scheme. This two-center shell model might be of importance in problems of nuclear fission.