Discrete and continuous spectrum of lightest hypernuclei

TL;DR

The paper develops an algebraic two-cluster resonating group method to study the discrete and continuous spectra of light $_{\Lambda}$ hypernuclei formed with s-shell cores. By employing Gaussian folding potentials for the $NN$ and $N\Lambda$ interactions and expanding relative motion in a harmonic-oscillator basis with a common length $b$, the authors compute bound-state energies, wave functions, phase shifts, and low-energy scattering parameters, adjusting a Fermi-momentum parameter $k_F$ to reproduce known binding energies. They find that several hypernuclei ${}_{\Lambda}^{3}$H, ${}_{\Lambda}^{4}$H, ${}_{\Lambda}^{4}$He, and ${}_{\Lambda}^{5}$He possess bound ground states, while the two-cluster continuum shows no resonances, consistent with a weaker $\Lambda$N interaction compared to $n$N. Comparisons with ab initio and multi-cluster models show general agreement, supporting the validity of the two-cluster approach and providing inputs for extended three-cluster studies such as ${}_{\Lambda}^{7}$Li.

Abstract

We analyze the peculiarities of the interaction of the lambda hyperon with s-shell nuclei. The spectra of bound and scattering states are studied in the hypernuclei $_Λ^{2}$H, $_Λ^{3}$H, $_Λ^{4}$H, $_Λ^{4}$He and $_Λ^{5}$He, which is considered as two-cluster configurations $p+Λ$, $d$+$Λ$, $^{3}$H+$Λ$, $^{3}$He+$Λ$, $^{4}$He+$Λ$, respectively. The explicit form of the folding potentials of such an interaction is presented in coordinate and oscillator representations, which help us to understand the structure of hypernuclei of interest. We compare energies of bound states, phase shifts of the elastic lambda hyperon, and neutron scattering from s-shell nuclei.

Figures (19)

• Figure 1: Folding potentials of interaction of the lambda hyperon and neutron with $^{4}$He.
• Figure 2: 3D presentation of matrix elements of the $\Lambda$+$^{4}$He interaction (top) and $n$+$^{4}$He interaction (bottom).
• Figure 3: Diagonal matrix elements of potential energy of the $n$+$^{4}$He and $\Lambda$+$^{4}$He interactions.
• Figure 4: Matrix elements of the potential energy operator for the $\Lambda+d$ interaction (top) and $n+d$ interaction the (bottom).
• Figure 5: Folding potentials of the $\Lambda$+d, $\Lambda$+$^{3}$H, $\Lambda$+$^{3}$He and $\Lambda$+$^{4}$He interaction.