Effects of a hyperonic many-body force on $B_{\mathrm{\Lambda }}$ values of hypernuclei

The stiff equation of state (EoS) giving the neutron-star mass of $2M_{\odot }$ suggests the existence of strongly repulsive many-body effects (MBE) not only in nucleon channels but also in hyperonic ones. As a specific model for MBE, the repulsive multi-Pomeron exchange potential (MPP) is added to the two-body interaction together with the phenomenological three-body attraction. For various versions of the Nijmegen interaction models, the MBE parts are determined so as to reproduce the observed data of $B_{\mathrm{\Lambda }}$. The mass dependence of $B_{\mathrm{\Lambda }}$ values is shown to be reproduced well by adding MBE to the strong MPP repulsion, assuring the stiff EoS of hyperon-mixed neutron-star matter, in which $P$-state components of the adopted interaction model lead to almost vanishing contributions. The nuclear matter $\mathrm{\Lambda }NG$-matrix interactions are derived and used in $\mathrm{\Lambda }$ hypernuclei on the basis of the averaged-density approximation (ADA). The $B_{\mathrm{\Lambda }}$ values of hypernuclei with $9\le A\le 59$ are analyzed in the framework of antisymmetrized molecular dynamics with use of the two types of $\mathrm{\Lambda }NG$-matrix interactions including strong and weak MPP repulsions. The calculated values of $B_{\mathrm{\Lambda }}$ reproduce the experimental data well within a few hundred keV. The values of $B_{\mathrm{\Lambda }}$ in $p$ states also can be reproduced well, when the ADA is modified to be suitable also for weakly bound $\mathrm{\Lambda }$ states.

Figure 1

$U_{\mathrm{\Lambda }}$ as a function of $k_F$. Solid, dashed, dotted, and dot-dashed curves are for ESC14, ESC12, ESC08a, and ESC08b, respectively.

Figure 2

$S$-state contributions to $U_{\mathrm{\Lambda }}$ as a function of $k_F$. Also see the caption of Fig. 1.

Figure 3

$P$-state contributions to $U_{\mathrm{\Lambda }}$ as a function of $k_F$. Also see the caption of Fig. 1.

Figure 4

(a) $U_{\mathrm{\Lambda }}$ curves with ESC14. The solid (dashed) curve shows $U_{\mathrm{\Lambda }}$ with (without) the MPP+TBA contributions. The dot-dashed (dotted) curve shows $U_{\mathrm{\Lambda }}$ only with MPP (TBA). (b) The same as (a), but for ESC12.

Figure 5

Excitation spectra of ${}^{12}\mathrm{C}$ and ${}_{\mathrm{\Lambda }}{}^{13}\mathrm{C}$ with (a) ESC12 + MBE and (b) ESC14 + MBE. The observed energy spectrum of ${}_{\mathrm{\Lambda }}{}^{13}\mathrm{C}$ by $\gamma$-ray spectroscopy experiments [27] is also displayed.

Figure 6

(a) Comparison between $B_{\mathrm{\Lambda }}$ from full-basis GCM (solid) and spherical GCM (dashed) calculations. Open circles show observed data with mass numbers from $A=9$ up to $A=51$, which are taken from Refs. [28, 29, 30, 31, 32, 33, 34, 35, 36]. $B_{\mathrm{\Lambda }}^{\exp }$ measured by $({\pi }^{+},K^{+})$ and $(K^{-},{\pi }^{-})$ reactions are shifted by 0.54 MeV as explained in the text. (b) The same as (a), but magnified in the $5\le A\le 20$ region.