The interplay of cluster structures in light nuclei: The model and the application to 7Li

Abstract

Abstract The structure of light nuclei is treated as a superposition of different cluster structures. The wave function of a nucleus contains the components describing two-cluster structures constructed out of 1p shell and/or 1s shell clusters. The model is used to study the low-lying energy levels of the nucleus 7Li, whose structure is treated as a superposition of the cluster structures ( 4 He + 3 H ) and ( 6 Li + n ) . The space of the wave functions is spanned by antisymmetrized products of shell-model wave functions describing separated clusters. The separation S of the two shell-model potentials is taken as the generator coordinate. The projection of the generator coordinate wave function onto the eigenspace of angular momentum and parity operators is performed by an algebraic method based on an algorithm which expresses the effect of the rotation of the wave function in terms of the rotation of the generator coordinate S. This method enables one to express the matrix elements in the projected basis as a finite combination of matrix elements in the unprojected basis. The application of the model to the nucleus 7Li has shown the feasibility of the calculation with 1p shell clusters. The Volkov potentials were used in the calculations. The minimal energy of 7Li in the state described by the model function with fixed separation of the clusters 4He and 3He is lowered by 1.64 MeV by solving the Hill-Wheeler equation for the cluster structure ( 4 He + 3 H ) . The coupling of both cluster structures lowers the energy in addition by 0.32 MeV. The influence of the coupling on the shape of the nucleus is a follows: In the single cluster structure ( 4 He + 3 H ) the optimal separation of the clusters in the ground state is 3.5 fm and it is 0.5 fm larger than that in the first excited state 5 2 − . However, when both cluster structures are considered simultaneously, the optimal separation between the clusters 4He and 3He and the separation between the clusters 6Li and n in the ground state are equal to the corresponding separations in the excited state.