Can Ab Initio Theory Explain the Phenomenon of Parity Inversion in ${}^{11}\mathrm{Be}$?

The weakly bound exotic ${}^{11}\mathrm{Be}$ nucleus, famous for its ground-state parity inversion and distinct $n+{}^{10}\mathrm{Be}$ halo structure, is investigated from first principles using chiral two- and three-nucleon forces. An explicit treatment of continuum effects is found to be indispensable. We study the sensitivity of the ${}^{11}\mathrm{Be}$ spectrum to the details of the three-nucleon force and demonstrate that only certain chiral interactions are capable of reproducing the parity inversion. With such interactions, the extremely large $E1$ transition between the bound states is reproduced. We compare our photodisintegration calculations to conflicting experimental data and predict a distinct dip around the $3/2_1^{-}$ resonance energy. Finally, we predict low-lying $3/2^{+}$ and $9/2^{+}$ resonances that are not or not sufficiently measured in experiments.

Figure 1

Spectrum of ${}^{11}\mathrm{Be}$ with respect to the $n+{}^{10}\mathrm{Be}$ threshold. The NCSM (left) and NCSMC (right) calculations are carried out for different model-space sizes ($N_{\max }=5$, 7, 9). Light boxes of experimental and NCSMC spectra indicate resonance widths. Experimental energies are taken from Ref. [1]. See the text and Supplemental Material for details of the calculations [46].

Figure 2

NCSMC spectrum of ${}^{11}\mathrm{Be}$ with respect to the $n+{}^{10}\mathrm{Be}$ threshold. Dashed black lines indicate the energies of the ${}^{10}\mathrm{Be}$ states. Light boxes indicate resonance widths. Experimental energies are taken from Refs. [1, 51].

Figure 3

The $n+{}^{10}\mathrm{Be}$ phase shifts as a function of the kinetic energy in the center-of-mass frame. NCSMC phase shifts for the ${\mathrm{N}}^2{\mathrm{LO}}_{\mathrm{SAT}}$ interaction are compared for two model spaces indicated by $N_{\max }$.

Figure 4

Comparison of the cluster form factors with the ${\mathrm{N}}^2{\mathrm{LO}}_{\mathrm{SAT}}$ interaction at $N_{\max }=9$. Note the coupling between the ${}^{10}\mathrm{Be}$ target and neutron in the cluster state $|{\mathrm{\Phi }}_{\nu ,r}^{J^{\pi }T}⟩\sim [(|{}^{10}\mathrm{Be}:I_1^{{\pi }_1}{T}_1⟩{|n:1/2^{+}1/2⟩)}^{sT}{Y}_{\ell }(\widehat{r}){]}^{J^{\pi }T}$.

Figure 5

Dipole strength distribution $dB(E1)/dE$ of the photodisintegration process as a function of the photon energy. Theoretical dipole strength distributions for two chiral interactions with (solid line) and without (dashed line) the phenomenological energy adjustment are compared to the experimental measurements at GSI [58, 61] (black dots) and RIKEN [58, 59, 60] (violet dots).