Description of single-$\Lambda$ hypernuclei with a relativistic point-coupling model

We extend the relativistic point-coupling model to single-$\Lambda$ hypernuclei. For this purpose, we add $N$-$\Lambda$ effective contact couplings to the model Lagrangian and determine the parameters by fitting to the experimental data for $\Lambda$ binding energies. Our model well reproduces the data over a wide range of mass region although some of our interactions yield the reverse ordering of the spin-orbit partners from that of nucleons for heavy hypernuclei. The consistency of the interaction with the quark model predictions is also discussed.

Figure 1

Comparison between the experimental data and the calculated $\Lambda$ binding energies $B_{\Lambda }$ [Fig. 1(a)] and spin-orbit splittings of $\Lambda$ single-particle energies $\Delta E_{\mathrm{so}}$ [Fig. 1(b)] obtained with the parameter set PCY-S1. The experimental data are taken from Refs. [45, 46, 47].

Figure 2

Same as Fig. 1, but with the parameter set PCY-S2.

Figure 3

Same as Fig. 1, but with the parameter set PCY-S3.

Figure 4

Same as Fig. 1, but with the parameter set PCY-S4.