Collective Modes in Light Nuclei from First Principles

Results for ab initio no-core shell model calculations in a symmetry-adapted SU(3)-based coupling scheme demonstrate that collective modes in light nuclei emerge from first principles. The low-lying states of ${}^6\mathrm{Li}$, ${}^8\mathrm{Be}$, and ${}^6\mathrm{He}$ are shown to exhibit orderly patterns that favor spatial configurations with strong quadrupole deformation and complementary low intrinsic spin values, a picture that is consistent with the nuclear symplectic model. The results also suggest a pragmatic path forward to accommodate deformation-driven collective features in ab initio analyses when they dominate the nuclear landscape.

Figure 1

Probability distributions across $(S_p{S}_{n}S)$ and $(\lambda \mu )$ values (horizontal axis) for the calculated $1_{gs}^{+}$ of ${}^6\mathrm{Li}$ obtained for $N_{\max }=10$ and $\hslash \Omega =20\mathrm{MeV}$ with the JISP16 interaction (left) and the $0_{gs}^{+}$ of ${}^8\mathrm{Be}$ obtained for $N_{\max }=8$ and $\hslash \Omega =25\mathrm{MeV}$ with the chiral ${\mathrm{N}}^3\mathrm{LO}$ interaction (right). The total probability for each $N\hslash \Omega$ subspace is given in the upper left-hand corner of each histogram. The concentration of strengths to the far right demonstrates the dominance of collectivity.

Figure 2

The ground-state binding energies of ${}^6\mathrm{Li}$ (a) and ${}^6\mathrm{He}$ (b), excitation energies of $T=0$ states of ${}^6\mathrm{Li}$ (c), $2_1^{+}$ excited state of ${}^6\mathrm{He}$ (d), shown for the complete $N_{\max }$ (dashed black curves) and truncated $⟨N_{\max }^{\perp }=N_{\max }⟩12$ (solid red lines) model spaces. Results shown are for JISP16 and $\hslash \Omega =20\mathrm{MeV}$. Note the relatively large changes when the complete space is increased from $N_{\max }=2$ to $N_{\max }=12$ as compared to nearly constant $⟨N_{\max }⟩12$ SA-NCSM outcomes.

Figure 3

Electric quadrupole transition probabilities and quadrupole moments for $T=0$ states of ${}^6\mathrm{Li}$ calculated using the JISP16 interaction without using effective charges are shown for the complete $N_{\max }$ (dashed black lines) and truncated $⟨N_{\max }^{\perp }=N_{\max }⟩12$ (solid red lines) model spaces [(a) and (c)], and as a function of $\hslash \Omega$ for the complete $N_{\max }=12$ space and $⟨6⟩12$ truncated space (solid blue lines) [(b) and (d)]. Experimentally, $B(E2;1_1^{+}\to 3_1^{+})=25.6(20)e^2{\mathrm{fm}}^4$ [39].