The Λ-core model for studying the binding energies of Λ-hypernuclei under pseudo-spin symmetry using the Hellmann potential

Abstract

We have studied the binding energies of a group of single Λ-hypernuclei in a relativistic approach and modeled the single Λ-hypernuclei as a Λ-core binary system. Since the Hellmann potential is ideal for defining nucleon-core interaction and the single Λ-hypernuclei can be assumed as a single nucleon coupled to the whole nuclei but does not suffer from Pauli blocking, we have selected this potential for interaction between the Λ particle and the core. The time-independent Dirac equation is a reasonable option for defining the relativistic bound states that correspond to a spin-1/2 Λ hyperon in the hypernuclei. We solved this equation by using the Hellmann potential under the presence of pseudo-spin symmetry in terms of the generalized parametric Nikiforov-Uvarov method, a way to make the application of the Nikiforov-Uvarov method as plain as possible. Our results were in good agreement with experimental values and other theoretical works. Hence, this model is applicable for the Λ-hypernuclei.