Lambda motion and cluster states of BeΛ9−11 predicted via neural networks guided microscopic calculation

We investigate the Λ particle motion and cluster states of BeΛ9−11 using a novel multiple cooling approach guided by the Control Neural Networks method (Ctrl.NN). The numerical results are well reproduced, and the Ctrl.NN method shows rapid convergence concerning the set of the basis states in comparison to traditional generator coordinate method (GCM) calculations. Taking advantage of this merit, we calculate ground state energies and rotational bands of BeΛ9−11 which agree well with experimental observations. By analyzing the density distributions of the main basis, a slight short-range repulsive correlation between Λ particle and α clusters in directions perpendicular to the axis of the Be8 core is revealed. The Λ particle presents a significant broad distribution as a consequence of this correlation, which we call an “analog π-orbit” structure. Furthermore, we prove that this correlation originates from the competition between kinetic energy and Λ-N interaction, as indicated by the energy curves for different configurations of BeΛ9. In the ground states of BeΛ10 and BeΛ11, the Λ particle is confined in a cage-like structure of core nuclei formed by two α clusters and valence neutrons. These structures lead to the development of more compact Λ particle configurations, and the shrinkage of α-α relative distance is also well reproduced.