Discrete and continuous spectrum of the lightest hypernuclei

Abstract

The dynamics of reactions in nuclear and hypernuclear systems remains relevant. Its study is necessary for solving important problems of nuclear physics and astrophysics. Among them, one can refers to the hyperon-nucleon interaction, which is important for understanding a large number of astrophysical objects, such as neutron stars. These objects, depending on energy and/or intensity of the interaction, can be either a hyperon star or have a condensate of kaons, which indicates importance of the hyperon-nucleon interaction. This work aims to study the discrete and continuous spectrum of the lightest hypernuclei: 2ΛH, 3ΛH, 4ΛH, and 5ΛHe in the cluster model, representing the nuclei under study as a corresponding two-cluster configuration: Λ+p, Λ+d, Λ+t, and Λ+4He, respectively. To achieve this goal, we used the Resonating Group Method (RGM), namely its algebraic version [1], which involves the oscillatory basis and the many-particle Schrödinger equation presented in matrix form. This method correctly treats the Pauli principle and takes into account the internal structure of the clusters. The nucleon-nucleon Hasegawa-Nagata potential [2] and the nucleon-hyperon potential of YNG [3] were employed to study light hypernuclei. The used method allowed us to study in detail the interaction of Λ particles with sshell nuclei in both coordinate and oscillatory representations. It was shown that the strongest interaction of the Λ particle and the lightest s-shell nucleus occurs in a state with zero orbital angular momentum of relative motion. The results obtained within the RGM satisfactorily reproduce the available experimental data. Our analysis confirms that the nucleus of the 2ΛH hypernucleus has no bound state. For the other hypernuclei under study, bound states were discovered and studied along with continuous spectrum states. In Table 1, we collect the main parameters of the ground states of the lightest hypernuclei, which have a bound state. These parameters include the bound state energy (E), mass root-mean-square radius (Rm), and average distance (Ac) between the lambda hyperon and the s-shell nucleus. The results, presented in Table 1, lead us to the conclusion that the hypernuclei of interest are weakly bound systems with a large distance between the lambda hyperon and the nucleus.