Challenges for first-principles nuclear structure: $^{11}$Li and $^{29}$F

Abstract

Ab initio calculations of atomic nuclei have had many successes in recent years. Nonetheless, important challenges that resist even brute-force calculation remain. As archetypal examples of these challenges, we consider $^{11}$Li and $^{29}$F, well known halo nuclides situated on islands of inversion. The deformed intruder levels, which are primarily two-particle, two-hole neutron excitations with respect to naive spherical shell model configurations, are slow, with respect to increases of the model space, to take their rightful place among, and potentially mix with, the lowest levels. We suggest these systems prototype the challenges for other important intruder states, and can serve as useful testbeds for potential approaches.

Figures (7)

• Figure 1: Schematic of normal (left side) versus two-particle, two-hole intruder (right side) configurations. Dashed lines represent spherical shell closures. For our example of $^{11}$Li, the filled proton orbital (hashed fill) is $0s$ while the filled neutron orbitals (solid fill) consist of $0s$-$0p$. For $^{29}$F, the filled proton and neutron orbitals are $0s$-$0p$ and $0s$-$0p$-$1s0d$, respectively.
• Figure 2: Relative energies for the normal $1/2^-$ and $3/2^-$ (blue, shaded symbols) and first intruder $1/2^-$ through $7/2^-$ (red, open symbols) levels of $\isotope[11]{Li}$, for (a) a chiral N3LO interaction and (b) the Daejeon16 interaction, shown as functions of ${N_\text{max}}$ (at fixed ${\hbar\omega}$, as indicated). Although states are designated as normal or intruder in this figure according to what might naively be expected for the level given the energy evolution, the first two $1/2^-$ levels start to undergo an avoided crossing at higher ${N_\text{max}}$ in the Daejeon16 calculations (see text).
• Figure 3: Decompositions by ${N_\text{ex}}$ (left) and by $\mathrm{SU}(3)$ jointly with ${N_\text{ex}}$ (right), for the normal (bottom) and intruder (top) $3/2^-$ levels of $\isotope[11]{Li}$, for the Daejeon16 interaction, in calculations with $N_\mathrm{max}=8$ and ${\hbar\omega}=12.5\,{\mathrm{MeV}}$. The $\mathrm{SU}(3)$ decompositions are shown arranged by the Bohr deformation variables corresponding to the given $\mathrm{SU}(3)$ quantum numbers, and include contributions from the $0{\hbar\omega}$ (blue, shaded circles) and $2{\hbar\omega}$ (red, open circles) spaces. Contributions from irreps which are degenerate with respect to the $\mathrm{SU}(3)$ Casimir operator (connected by dotted lines) cannot be distinguished (and, for plotting purposes, such contributions have, arbitrarily, been distributed equally between these irreps).
• Figure 4: Dimensionless ratio $Q/r^2$ for normal (blue, shaded symbols) and intruder (red, open symbols) $3/2^-$ levels of $\isotope[11]{Li}$, for the protons (left) and neutrons (right), calculated with the chiral N3LO (top) and Daejeon16 (bottom) interactions. Calculated values are shown as functions of ${N_\text{max}}$, at fixed ${\hbar\omega}$ (as indicated). The experimental value for $Q_p/r_p^2$stone2016:e2-momentsangeli2013:charge-radii for the $3/2^-$ ground state is shown for comparison (solid square), with the point-proton radius deduced from the charge radius as detailed in Ref. caprio2025:emnorm2-part1.
• Figure 5: Relative energies for the normal $1/2+$ and $5/2+$ (blue, shaded symbols) and first intruder $1/2+$ through $5/2+$ (red, open symbols) levels of $\isotope[29]{F}$, for (a) a chiral N3LO interaction and (b) the Daejeon16 interaction, shown as functions of $N_\mathrm{max}$ (at fixed ${\hbar\omega}$, as indicated).