Ab initio study in the island of inversion within the two-major-shell valence space

TL;DR

The study addresses the island of inversion around $N=20$ in light nuclei by deriving ab initio multishell valence-space Hamiltonians that span the $sd$, $sdf_{7/2}p_{3/2}$, and $sdfp$ shells. These Hamiltonians are obtained with the valence-space IMSRG (VS-IMSRG) from chiral NN and 3N forces and are used in a quantum-number projected generator coordinate method (PGCM) to sample deformed configurations. Expanding the valence space from $sd$ to $sdf_{7/2}p_{3/2}$ and finally to $sdfp$ substantially improves the description of quadrupole collectivity; the calculated $2^+_1$ energies are lowered and $B(E2;0^+_1\rightarrow2^+_1)$ values increase, indicating intruder-driven deformation. Neutron occupancies show cross-shell mp-mh excitations into the $fp$ shell, with roughly $1.5$ to $2$ neutrons promoted in the Mg isotopes near $N=20$, consistent with intruder configurations, while $^{34}$Si remains largely $sd$-shell dominated. The VS-IMSRG+PGCM framework provides a scalable, parameter-free ab initio approach to describe deformation and collectivity across multiple major shells, offering a path toward reliable predictions for heavier open-shell nuclei.

Abstract

We present an \textit{ab initio} study of nuclear structure in the island of inversion around neutron number $N=20$, using multishell effective Hamiltonians derived from the valence-space in-medium similarity renormalization group approach combined with the quantum-number projected generator coordinate method. By progressively expanding the valence space from the \textit{sd} shell to the intermediate $sdf_{7/2}p_{3/2}$ space and, for the first time, to the full \textit{sdfp} shell, we investigate low-lying spectra, $E2$ transition strengths, deformation properties, and neutron occupancies in even-even Ne, Mg, and Si isotopes around $N=20$. Our results show that enlarging the valence space significantly improves the description of quadrupole collectivity, yielding better agreement with experimental data for key observables such as the lowered $2^+$ energies and the enhanced $B(E2;0^+_1\rightarrow2_1^+)$ values. The analysis reveals the critical role of cross-shell multi-particle multi-hole excitations in breaking the $N=20$ shell closure and establishing intruder-dominated ground states. It also demonstrates the ability of the VS-IMSRG+PGCM framework to capture both dynamical (short range) and static (long range) correlations across multiple major-oscillator shells.

Figures (5)

• Figure 1: Calculated low-lying spectra of $^{32}$Mg obtained within the $sd$, $sdf_{7/2}p_{3/2}$, and $sdfp$ valence spaces, compared with experimental data. The arrows indicate the $B(E2)$ transition strengths from $0^{+}_{1}$ to $2^{+}_{1}$ in units of $e^2fm^4$. The experimental data are taken from the atomic mass evaluation (AME 2020) Wang_2021 and the National Nuclear Data Center (NNDC) NNDC.
• Figure 2: (a) Projected potential energy of $^{32}$Mg with particle-number projection and angular-momentum projection onto $J=0$ against axial deformation $\beta_2$, calculated in the $sd$, $sdf_{7/2}p_{3/2}$, and $sdfp$ spaces. For clarity, the spherical configuration energy has been set to zero. (b) The distributions of the collective wavefunction of the $0^{+}_{1}$ state in 3 different model spaces. (c) Same as panel (b) but for $2^{+}_{1}$ states.
• Figure 3: Neutron occupancies calculated within the $sd$, $sdf_{7/2}p_{3/2}$, and $sdfp$ spaces. Note that "0d" denotes the occupation of the neutron $0d_{5/2}$ and $0d_{3/2}$ orbitals.
• Figure 4: Calculated low-lying spectra of $^{30}$Ne, $^{30-34}$Mg, and $^{34}$Si within $sdfp$ model space, compared with experimental data. The arrows indicate the $B(E2;0^+_1\rightarrow2^+_1)$ values in units of $e^2fm^4$. The experimental data are taken from the AME 2020 Wang_2021 and NNDC NNDC. The calculations are done with $e_{max}=12$ and $E_{3\mathrm{max}}=16$.
• Figure 5: Neutron occupancies calculated within the full $sdfp$ space for the ground states of $^{30-34}$Mg and the adjacent $N=20$ isotones $^{30}$Ne, $^{34}$Si. Note that "0d" denotes the occupation of the neutron $0d_{5/2}$ and $0d_{3/2}$ orbitals.