On the shape of light nuclei in the translationally invariant shell model

In the framework of the method of generalized hyperspherical functions, multicomponent collective functions corresponding to an oscillator interaction between the nucleons are constructed for a number of states of light nonmagic nuclei. The functions characterizing the shape of the nuclei in the coordinate system associated with the principal axes of the inertia ellipsoid are found. For the nucleus $\operatorname{Be}^8$ it is shown that the shape changes on the transition from the state with orbital angular momentum $L=2$ to the state with $L=4$. The quadrupole moments of these states are calculated, and the mean deformation of light nuclei is considered.