Competing effects of nuclear deformation and density dependence of the $\mathrm{\Lambda }N$ interaction in $B_{\mathrm{\Lambda }}$ values of hypernuclei

Competitive effects of nuclear deformation and density dependence of $\mathrm{\Lambda }N$ interaction in $\mathrm{\Lambda }$ binding energies $B_{\mathrm{\Lambda }}$ of hypernuclei are studied systematically on the basis of the baryon-baryon interaction model ESC (extended soft core) including many-body effects. By using the $\mathrm{\Lambda }N$ $G$-matrix interaction derived from ESC, we perform microscopic calculations of $B_{\mathrm{\Lambda }}$ in $\mathrm{\Lambda }$ hypernuclei within the framework of the antisymmetrized molecular dynamics under the averaged-density approximation. The calculated values of $B_{\mathrm{\Lambda }}$ reproduce experimental data within a few hundred keV in the wide mass regions from 9 to 51. It is found that competitive effects of nuclear deformation and density dependence of $\mathrm{\Lambda }N$ interaction work decisively for fine-tuning of $B_{\mathrm{\Lambda }}$ values.

Figure 1

(a) Comparison of $B_{\mathrm{\Lambda }}$ between cases (A) (solid) and (B) (dashed). Open circles show observed values with mass numbers from $A=9$ up to $A=51$, which are taken from Refs. [2, 18, 19, 22, 23, 24, 25, 26, 27]. $B_{\mathrm{\Lambda }}^{\exp }$ values measured by $({\pi }^{+},K^{+})$ and $(K^{-},{\pi }^{-})$ reactions are shifted by 0.54 MeV as explained in text. (b) Same as panel (a), but magnified in the $5\le A\le 20$ region.