Partial-wave decomposition of the $p$--$^{5}_Λ\mathrm{He}$ correlation function: a femtoscopic route to the $^{6}_Λ\mathrm{Li}$ resonance

Abstract

The hypernucleus $^{6}_Λ\mathrm{Li}$ is unbound against proton emission, so its resonances appear in the low-momentum $p$--$^{5}_Λ\mathrm{He}$ correlation function, which femtoscopy can measure. We compute this correlation function in an $α+Λ$ folding model of $^{5}_Λ\mathrm{He}$: phenomenological $pα$ and $pΛ$ interactions are averaged over the internal $α$--$Λ$ motion, and a single $ΛN$ strength factor is fixed by the measured $^{6}_Λ\mathrm{He}$ binding energy. The model places the $^{6}_Λ\mathrm{Li}$ $1^{-}$ state at $E_{R}=0.60^{+0.11}_{-0.10}$~MeV with $Γ=0.18\pm0.05$~MeV and produces a pronounced peak in $C(k^{*})$ near $31~\mathrm{MeV}/c$. The predicted peak position, $k^{*}_{\rm peak}=\sqrt{2μE_{R}}=30.8\pm2.6~\mathrm{MeV}/c$, is uncertain mainly because of the measured $B_Λ(^{6}_Λ\mathrm{He})$, not because of the $ΛN$ interaction. An exact partial-wave decomposition shows that the $P$ wave accounts for the entire enhancement over the Coulomb baseline, $79\%$ of it from the $1^{-}$ channel. A Lednický--Lyuboshitz analysis restricted to $S$ waves therefore cannot describe this system. The maximum of the $1^{-}$ channel lies within $1\%$ of $k^{*}_{\rm peak}$, but the unresolved $2^{-}$ state and the momentum resolution shift the measured maximum upward by $2.4~\mathrm{MeV}/c$ at $σ_{k^{*}}=3~\mathrm{MeV}/c$.