Effective $\Lambda N$ potential from relativistic Brueckner-Hartree-Fock theory

The effective $\Lambda N$ potentials are derived from one-boson-exchange hyperon-nucleon interaction such as Juelich potentials, Juelich94a (Jul94) and Juelich05 (Jul05), within the relativistic Brueckner-Hartree-Fock theory. The Jul94 effective $\Lambda N$ potential $U_{\Lambda }$ ($p_{\Lambda }$) with $p_{\Lambda }=0$ is $-27.63$ MeV at the nuclear saturation density, which is in good agreement with the observed data, whereas for the Jul05 effective $\Lambda N$ potential, $U_{\Lambda }$ is $-47.85$ MeV, which is bound more than the observed data. We then compare the effective $\Lambda N$ potential energies obtained in nonrelativistic and relativistic frameworks. With the $\Lambda$ momentum $p_{\Lambda }$ increasing, the relativistic effect becomes obvious and provides more repulsive contribution. We also derive the scalar and vector potentials of the $\Lambda$ hyperon from the effective $\Lambda N$ potential in the relativistic framework. With these potentials, the coupling constants between mesons and the $\Lambda$ hyperon are determined for each density in the framework of relativistic mean-field theory. Finally, we calculate the $\Lambda$ single-particle energies of hypernuclei with these density-dependent coupling constants in the relativistic mean-field theory. We find that the single $\Lambda$ binding energies of $\Lambda$ hypernuclei from ${}_{\mathrm{\Lambda }}{}^{16}\mathrm{O}$ to ${}_{\mathrm{\Lambda }}{}^{208}\mathrm{Pb}$ by using the Jul94 potential compare well with the experimental data.

Figure 1

The effective $\Lambda N$ potentials at $p_{\Lambda }=0$ as a function of density with different $YN$ interaction and methods.

Figure 2

The effective $\Lambda N$ potentials at (a) $k_F^N=1.35$ ${\mathrm{fm}}^{-1}$ for the Jul05 potential and (b) $k_F^N=1.65$ ${\mathrm{fm}}^{-1}$ for the Jul94 potential as a function of momentum in the relativistic (RBHF) and nonrelativistic (BHF) frameworks.

Figure 3

The scalar and vector components of single $\Lambda N$ potentials with (a) Jul94 and (b) Jul05 potentials in the RBHF theory.

Figure 4

The density-dependent coupling constants of $\sigma$ and $\omega$ mesons between two nucleons from Bonn-A potential in the RBHF theory.

Figure 5

The ratio between the $\sigma \Lambda$ and $\sigma N$ coupling constants as a function of density obtained from (a) Jul94 and (b) Jul05 potentials.

Figure 6

The single $\Lambda$ energy in finite nuclei with DDRMF through the RBHF theory with Jul94 potential. Experimental data are shown by black squares.