Hypernuclear constraints on $ΛN$ and $ΛNN$ interactions

TL;DR

The work develops a density-dependent optical potential for Λ hypernuclei that includes both ΛN two-body and ΛNN three-body terms and fits it to Λ s.p. binding energies across a wide mass range. The two- and three-body strengths are tightly constrained, yielding $D^{(2)}_{\Lambda} \approx -37$ to $-39$ MeV and $D^{(3)}_{\Lambda} \approx +9$ to $+13$ MeV, giving a total depth $D_{\Lambda} \approx -27$ to $-28$ MeV, with a correlated determination of the underlying parameters $b_0$ and $B_0$. An isospin-suppression mechanism reduces the ΛNN contribution for neutron-rich systems, aligning with observed data and enabling a repulsive ΛNN term of order ~10 MeV that helps resolve the hyperon puzzle. Overall, the density-dependent framework yields results consistent with EFT and femtoscopy studies and provides a robust decomposition of Λ-induced forces with implications for hypernuclear spectroscopy and neutron-star matter.

Abstract

Recent work on using density dependent $Λ$-nuclear optical potentials in calculations of $Λ$-hypernuclear binding energies is reviewed. It is found that all known $Λ$ binding energies in the mass range $16 \leq A \leq 208$ are well fitted in terms of two interaction parameters: one, attractive, for the spin-averaged $ΛN$ interaction and another one, repulsive, for the $ΛNN$ interaction. The $ΛN$ interaction term by itself overbinds $Λ$ hypernuclei, in quantitative agreement with recent findings obtained in EFT and Femtoscopy studies. The strength of the $ΛNN$ interaction term is compatible with values required to resolve the hyperon puzzle.

Figures (4)

• Figure 1: A three-parameter Woods-Saxon potential fit of all known $\Lambda$ single-particle binding energies from various experiments across the periodic table marked by different colors. Figure adapted from Ref. GHM16, updating the original figure in Ref. MDG88.
• Figure 2: $B_{\Lambda}^{1s,1p}(A)$ values across the periodic table, $12\leq A \leq 208$ as calculated in models X (upper) and Y (lower), compared with data points, including uncertainties. $^{16}_{~\Lambda}$N is the third point on each line. Continuous lines connect calculated values. Figure updating Fig. 3 in Ref. FG23a. The upper part, model X, uses the full $\rho^2$ term. The lower part, model Y, replaces $\rho^2$ with a reduced form, decoupling $(N-Z)$ excess neutrons from $2Z$ symmetric-core nucleons, see text. The dashed lines are for $\rho^2$ replaced with $F\rho^2$, with a suppression factor $F$, Eq. (\ref{['eq:F']}).
• Figure 3: $\chi^2$ fits to the full 1$s_\Lambda$ and $1p_\Lambda$ data (solid black lines) and when excluding $^{12}_{~\Lambda}$B and $^{13}_{~\Lambda}$C (dashed red lines). Also shown are predictions of 1$d_\Lambda$ and 1$f_\Lambda$ binding energies for the latter choice.
• Figure 4: $B_\Lambda(^{48}_{~\Lambda}{\rm K})-B_\Lambda(^{40}_{~\Lambda}{\rm K} )$ values for $1s_{\Lambda}$ and $1p_{\Lambda}$ states, with and without applying the suppression factor $F$, as a function of the neutron-skin of $^{48}_{~\Lambda}$K, see text.