New effective interactions for hypernuclei in a density-dependent relativistic mean field model

New effective $\mathrm{\Lambda }N$ interactions are proposed for the density-dependent relativistic mean-field model. The multidimensionally constrained relativistic mean-field model is used to calculate ground-state properties of eleven known $\mathrm{\Lambda }$ hypernuclei with $A\ge 12$ and the corresponding core nuclei. Based on effective $NN$ interactions DD-ME2 and PKDD, the ratios $R_{\sigma }$ and $R_{\omega }$ of scalar and vector coupling constants between $\mathrm{\Lambda }N$ and $NN$ interactions are determined by fitting calculated $\mathrm{\Lambda }$ separation energies to experimental values. We propose six new effective interactions for $\mathrm{\Lambda }$ hypernuclei: DD-ME2-Y1, DD-ME2-Y2, DD-ME2-Y3, PKDD-Y1, PKDD-Y2, and PKDD-Y3 with three ways of grouping and including these eleven hypernuclei in the fitting. It is found that the two ratios $R_{\sigma }$ and $R_{\omega }$ correlate well and a good linear relation exists between them. The statistical errors of the ratio parameters in these effective interactions are analyzed. These new effective interactions are used to study the single-$\mathrm{\Lambda }$ excited states, the equation of state of hypernuclear matter, and neutron-star properties with hyperons.

Figure 1

(a) The relative deviations of the calculated binding energies of ${}^{11,12}\mathrm{C}, {}^{15}\mathrm{O}, {}^{27}\mathrm{Si}, {}^{31}\mathrm{S}, {}^{39}\mathrm{Ca}, {}^{50,51}\mathrm{V}, {}^{88}\mathrm{Y}, {}^{138}\mathrm{La}$, and ${}^{207}\mathrm{Pb}$ from the experimental values [125] and (b) the quadrupole deformation parameters of these nuclei. The MDC-RMF calculations are carried out with density-dependent interactions DD-ME2 and PKDD, respectively.

Figure 2

(a) The calculated $\mathrm{\Lambda }$ separation energies compared with the experimental values and (b) the calculated quadrupole deformation parameters with DD-ME2-Y1, DD-ME2-Y2, and DD-ME2-Y3. The experimental values of $B_{\mathrm{\Lambda }}$ are taken from Ref. [7] except for ${}_{\mathrm{\Lambda }}{}^{40}\mathrm{Ca}$ [126]. The inset in panel (a) shows the results for ${}_{\mathrm{\Lambda }}{}^{51,52}\mathrm{V}$. The “Core” in panel (b) represents the quadrupole deformation parameters of the corresponding core nuclei calculated with DD-ME2.

Figure 3

The correlation between $R_{\sigma }$ and $R_{\omega }$ in DD-ME2-$\mathrm{Y}i$ and PKDD-$\mathrm{Y}i$ ($i=1$, 2, and 3). The blue line shows the linear relation (10) obtained by a linear fitting of $R_{\sigma }$ and $R_{\omega }$ in these six parameter sets. Predictions from the quark model (QM), NL effective interactions NLSH-B [72], PK1-Y1 [121], and TM1-A [120] and DD effective interactions DDME2D-a [57] and DDME2-a [57] are also shown for comparison.

Figure 4

The $\mathrm{\Lambda }$ separation energies in the $s_{\mathrm{\Lambda }},p_{\mathrm{\Lambda }},d_{\mathrm{\Lambda }},f_{\mathrm{\Lambda }}$, and $g_{\mathrm{\Lambda }}$ single-particle states for ${}_{\mathrm{\Lambda }}{}^A\mathrm{Z}$ hypernuclei calculated with (a) DD-ME2-Y2 and (b) PKDD-Y2, respectively. The theoretical values are average separation energies of the deformed levels from $s_{\mathrm{\Lambda }},p_{\mathrm{\Lambda }},d_{\mathrm{\Lambda }},f_{\mathrm{\Lambda }}$, and $g_{\mathrm{\Lambda }}$ single-particle states. The experimental values in black dots are taken from Refs. [7, 126] and shown for comparison.

Figure 5

(a) The equations of state and (b) the mass-radius relations for neutron stars with hyperons. The solid curves are calculated with DD-ME2-$\mathrm{Y}i$ ($i=1$, 2, and 3) and the shaded areas are calculated with the corresponding upper and lower boundaries of $R_{\sigma }$ in the correlated direction defined by Eq. (10). Results without hyperons (calculated with DD-ME2) are also shown for comparison.