Energy spectrum of neutron-rich helium isotopes: Complex made simple

We demonstrate that the intricate energy spectrum of neutron-rich helium isotopes can be straightforwardly described by taking advantage of the low-energy properties of neutron-neutron interaction and the scale separation that is present in diluted drip-line systems. By using arguments based on the halo effective field theory, we carry out a parameter reduction of the complex-energy configuration interaction framework in the $spd$ space, including resonant and scattering states. By constraining the core potential to $\alpha \text{−}n$ scattering phase shifts and adjusting the strength of the spin-singlet central neutron-neutron interaction, we reproduce experimental energies and widths of ${}^{5–8}\mathrm{He}$ within tens of keV precision. We predict a parity inversion of narrow resonances in ${}^9\mathrm{He}$ and show that the ground state of ${}^{10}\mathrm{He}$ is an $s$-wave-dominated configuration that could decay through two-neutron emission. This threshold state can be viewed as a “double-halo” structure in an analogy to the atomic ${}^3\mathrm{He}{}^4{\mathrm{He}}_2$ trimer.

Figure 1

Energy spectra of ${}^{5–10}\mathrm{He}$ with respect to the ${}^4\mathrm{He}$ core. Experimental data [20] are compared to our Gamow-density-matrix renormalization-group (G-DMRG) calculations. Decay widths are shown as shaded bars. The predicted $1/2^{-}$ resonant states in ${}^{5,7}\mathrm{He}$ are so broad that their widths are not marked. For these states as well as for states in ${}^{9,10}\mathrm{He}$, experimental information is not firm.