Density matrix renormalization group description of the island of inversion isotopes <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">F</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>28</mml:mn><mml:mtext>–</mml:mtext><mml:mn>33</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>
K. Fossez, J. Rotureau
Abstract
Background: Recent experiments have confirmed that the neutron-rich isotopes $^{28,29}\mathrm{F}$ belong to the so-called island of inversion (IOI), a region of the nuclear chart around $Z=10$ and $N=20$ where nuclear structure deviates from the standard shell model predictions due to deformation and continuum effects. However, while the general principles leading to the IOI are relatively well understood, the details of the low-lying structure of the exotic fluorine isotopes $^{28\text{--}33}\mathrm{F}$ are basically unknown.Purpose: In this work, we perform large-scale shell model calculations including continuum states to investigate the properties of the neutron-rich isotopes $^{25\text{--}33}\mathrm{F}$, from a core of $^{24}\mathrm{O}$ and using an effective two-body interaction with a small number of adjustable parameters in the central and tensor channels.Methods: We develop two models adjusted on experimentally confirmed states in $^{25,26}\mathrm{O}$ and $^{25\text{--}27}\mathrm{F}$ based on different assumptions concerning the positions of the neutron $0{d}_{3/2}$ and $1{p}_{3/2}$ shells, and solve the many-body problem using the density matrix renormalization group (DMRG) method for open quantum systems in an $sd\text{\ensuremath{-}}fp$ model space.Results: We obtain the first detailed spectroscopy of $^{25\text{--}33}\mathrm{F}$ in the continuum and show how the interplay between continuum effects and deformation explains the recent data on $^{28,29}\mathrm{F}$. Several deformed one- and two-neutron halo states are predicted in $^{29,31}\mathrm{F}$, and we provide some information about the possible structure of the heaviest fluorine isotopes. We also suggest several experimental studies of interest to constraint models and test the present predictions.Conclusions: The complex structure of neutron-rich fluorine isotopes offers a trove of information about the formation of the southern shore of the IOI through a subtle interplay of emergent deformation via the neutron ${p}_{3/2}\text{\ensuremath{-}}{f}_{7/2}$ coupling, and continuum effects favoring the occupation of the $1{p}_{3/2}$ shell over the $0{d}_{3/2}$ shell. Further experimental studies of this region will be essential to assess the quality of future theoretical approaches.