Faddeev calculations for the _Λ⁹Be spectrum

¹ North Carolina Central University, Durham, NC, 27707, USA
² Saint-Petersburg State University, Petrodvorets, St. Petersburg, Russia

^a e-mail: ifilikhin@nccu.edu

Abstract

An α-cluster model is applied to study low-lying spectrum of the _Λ⁹Be hypernicleus. The ααΛ three-body problem is numerically solved by the Faddeev equations in configuration space using phenomenological pair potentials. Found is a set of the potentials that reproduces experimental data for the ground state (1⁺/2) binding energy and excitation energy of the 5⁺/2 and 3⁺/2 states, simultaneously. This set includes the Ali-Bodmer potential of version “e” for αα and modified Tang-Herndon potential for αΛ interactions. The spin-orbit αΛ interaction is given by modified Scheerbaum potential. Low-lying energy levels are evaluated applying a variant of the analytical continuation method in coupling constant, and the experimental data for excitation energies are well reproduced by our calculations. This result improves previous α-cluster calculations. It is shown that the spectral properties of _Λ⁹Be can be classified as an analog of ⁹Be spectrum with the exception of several “genuine hypernuclear states”, which agrees qualitatively with previous studies. The energy splitting of spin-flip doublet (9⁺/2 , 7⁺/2) is predicted.