Ab initio mapping of the boundary of the $N=20$ island of inversion

Abstract

Starting from a chiral two- plus three-nucleon interaction, we perform a systematic study of the low-lying states of neutron-rich nuclei around $N=20$ using the in-medium generator coordinate method (IM-GCM), which combines the multi-reference in-medium similarity renormalization group (MR-IMSRG) with the quantum-number projected generator coordinate method (PGCM) defined in a full single-particle space. The main features of the energy spectra and electromagnetic properties of low-lying states in both even-even and odd-mass nuclei of this mass region are reasonably reproduced. The boundary of the $N=20$ island of inversion (IOI) is investigated, and the results indicate that $^{30}$Ne, $^{29,31,33}$Na, $^{31-34}$Mg, and $^{35}$Al lie within the IOI, whereas $^{29}$F, $^{29}$Ne, $^{30}$Mg, $^{31, 33}$Al, $^{34,35}$Si, and $^{35}$P fall outside it.

Figures (15)

• Figure 1: (Color online) Flowchart of the IM-GCM framework Yao:2020PRL. The central insets are schematic cartoons illustrating the evolution of the nuclear interaction in momentum space as a function of the SRG momentum-resolution scale (left) and the evolution of Hamiltonian matrix elements in configuration space with the MR-IMSRG flow parameter (right).
• Figure 2: (Color online) (a) Deformation energy curves of [30]Ne obtained from VAPNP+HFB calculations using IMSRG-evolved Hamiltonians with various values of the flow parameter $s$, as a function of the axial quadrupole deformation $\beta_2$. (b) Nilsson diagram for neutrons in [30]Ne calculated with the evolved Hamiltonian $\hat{H}(s)$ at $s = 0.16, \mathrm{MeV}^{-1}$, showing single-particle energies as functions of $\beta_2$. The Nilsson asymptotic quantum numbers $\Omega^\pi[Nn_z\Lambda]$ are shown for several relevant orbitals. Here, $N$ denotes the principal oscillator quantum number, while $n_z$, $\Omega$, and $\Lambda$ represent the projections of $N$, $j$, and $\ell$ onto the symmetry axis, respectively. Black squares mark the neutron Fermi levels.
• Figure 3: (Color online) (a) The low-energy spectra and (b) the $B(E2: 2^+ \rightarrow 0^+)$ values of [30]Ne from the PNAMP calculation using different $\hat{H}(s)$ based on the single HFB state with $\beta_2 = 0.5$. In panel (b), either the bare one-body transition operator (Bare) or the evolved one-body operator with (1B+2B) and without (1B) evolved two-body operators is used. The experimental data are taken from Refs. Ne30E2Doornenbal:2016NNDC.
• Figure 4: (Color online) Energy spectra and distributions of collective wave functions $|g_\alpha^{J\pi}|^2$ [Eq. (\ref{['eq:coll_wf']})] for the low-lying states of $\nuclide[30]{Ne}$ (a, b), $\nuclide[34]{Si}$ (c, d), $\nuclide[30]{Mg}$ (e, f), and $\nuclide[34]{Mg}$ (g, h), obtained from IM-GCM calculations and compared with available data NNDCsheeta=30Rotaru:2012Si34isomer. Solid arrows represent the calculated $B(E2)$ transition strengths (in units of e$^2$fm$^4$), while dashed arrows denote the $10^{3}\rho^2(E0)$ values. The collective wave functions corresponding to weakly deformed states are shown in red, and those for strongly deformed states are shown in black.
• Figure 5: (Color online) (a) Excitation energies of the $2_1^+$ state and (b) transition probabilities $B(E2: 2_1^+ \rightarrow 0_1^+)$ for [30,32,34]Mg, [30]Ne, and [34]Si. The bullets and red solid lines represent the experimental data and the IM-GCM calculations using the configuration with zero cranking frequency ($\langle J_x \rangle = 0$). Results from PNAMP calculations based on the lowest-energy configuration with zero and nonzero cranking frequencies ($\langle J_x \rangle = 0$ and $\langle J_x \rangle = \sqrt{6}$, respectively) are also provided for comparison. The three-dimensional AMP is used to restore the angular momentum of the configurations with nonzero cranking frequency.