Green's function relativistic mean field theory for $\Lambda$ hypernuclei

Abstract

The relativistic mean-field theory with Green's function method is extended to study $\Lambda$ hypernuclei. Taking hypernucleus ${}_{\Lambda }^{61}$Ca as an example, the single-particle resonant states for $\Lambda$ hyperons are investigated by analyzing density of states and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow $1f_{5/2}$ and $1f_{7/2}$ states are very similar as bound states while that of the wide $1g_{7/2}$ and $1g_{9/2}$ states are like scattering states. Besides, the impurity effect of $\Lambda$ hyperons on the single-neutron resonant states are investigated. For most of the resonant states, both the energies and widths decrease with adding more $\Lambda$ hyperons due to the attractive $\Lambda N$ interaction. Finally, the energy level structure of $\Lambda$ hyperons in the Ca hypernucleus isotopes with mass number $A=53-73$ are studied, obvious shell structure and small spin-orbit splitting are found for the single-$\Lambda$ spectrum.

10pages, 6 figures,2 tables

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Cited by in corpus (10)

• Green's function method for the single-particle resonances in a deformed Dirac equation
• New effective interactions for hypernuclei in density dependent relativistic mean field model
• Green's function method for the spin and pseudospin symmetries in the single-particle resonant states
• Continuum Skyrme-Hartree-Fock-Bogoliubov theory with Green's function method for odd-$A$ nuclei
• Searching for single-particle resonances with the Green's function method
• $\Lambda \Lambda$ pairing in multi-strange hypernuclei
• Study of single-particle resonant states with Green's function method
• Density-dependent relativistic mean field approach and its application to single-$\Lambda$ hypernuclei in Oxygen isotopes
• Probing spin and pseudospin symmetries in deformed nuclei by the Green's function method
• Charge symmetry breaking in hypernuclei within RMF model