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In this work, we report the latest developments in the beyond mean-field methods applied to the shell-model framework for the description of heavy deformed nuclei. We extend our recent DNO-SM approach within the \textit{Variation-After-Projection} (VAP) scheme, dubbed as DNO-SM(VAP). This approach naturally enables to \textit{a priori} capture correlations more efficiently than the \textit{Projection-After-Variation} (PAV) scheme which is commonly used in current theoretical modelings of nuclei. Using the Kuo-Herling effective interaction, we first examine the extended method by a systematic comparison of the binding energies, the \textit{yrast} spectra and electromagnetic moments of some representative nuclei of masses ranging from $A=251$ to $A=256$. The results show that the VAP scheme variationally provides more bound solutions with respect to the PAV scheme, reflecting the additional correlations that were captured. Both spectra, dipole and spectroscopic quadrupole moments are reproduced favorably. We then focus on the case of $^{254}$No, one of the most studied elements experimentally, which can be considered as the portal to the superheavy region. The calculations show a striking agreement with the complete experimentally known spectroscopy: the \textit{yrast} band, isomers and associated $K$ bands, and the newly observed 0$^+$ and ($K=4$) 4$^+$ states, providing for the first time the complete shell-model description of $^{254}$No. The present successful achievement opens a new way for forthcoming spectroscopic studies of heavy and superheavy nuclei.

This paper reports on the measurement of the ground-state spin and nuclear magnetic dipole moment of $^{61}$Cr. The radioactive ion beam was produced at the CERN-ISOLDE facility and was probed using high-resolution resonance ionization laser spectroscopy with the CRIS apparatus. The present ground-state spin measurement $I = \frac{1}{2}$, differing from the previously adopted $I =(\frac{5}{2})$, has significant consequences on the interpretation of existing beta decay data and nuclear structure in the region. The structure and shape of $^{61}$Cr is interpreted with state-of-the-art Large-Scale Shell Model and Discrete-Non-Orthogonal Shell Model calculations. From the measured magnetic dipole moment $\mu(^{61}$Cr$)=+0.539(7)~\mu_N$ and the theoretical findings, its configuration is understood to be driven by 2 particle - 2 hole neutron excitations with an unpaired $1p_{1/2}$ neutron. This establishes the western border of the $N=40$ Island Of Inversion (IoI), characterized by 4 particle - 4 hole neutron components. We discuss the shape evolution along the Cr isotopic chain as a quantum phase transition at the entrance of the $N=40$ IoI.

The neutron-rich unbound fluorine isotope $^{30}$F$_{21}$ has been observed for the first time by measuring its neutron decay at the SAMURAI spectrometer (RIBF, RIKEN) in the quasi-free proton knockout reaction of $^{31}$Ne nuclei at 235 MeV/nucleon. The mass and thus one-neutron-separation energy of $^{30}$F has been determined to be $S_n = -472\pm 58 \mathrm{(stat.)} \pm 33 \mathrm{(sys.)}$ keV from the measurement of its invariant-mass spectrum. The absence of a sharp drop in $S_n$($^{30}$F) shows that the ``magic'' $N=20$ shell gap is not restored close to $^{28}$O, which is in agreement with our shell-model calculations that predict a near degeneracy between the neutron $d$ and $fp$ orbitals, with the $1p_{3/2}$ and $1p_{1/2}$ orbitals becoming more bound than the $0f_{7/2}$ one. This degeneracy and reordering of orbitals has two potential consequences: $^{28}$O behaves like a strongly superfluid nucleus with neutron pairs scattering across shells, and both $^{29,31}$F appear to be good two-neutron halo-nucleus candidates., Comment: 9 pages, 2 figures, accepted for publication in Physical Review Letters

The first systematic experimental study of the neutron-rich Br isotopes with two complementary state-of-the-art techniques is presented. These isotopes have been populated in the fission process at two different facilities, GANIL and ILL. New spectroscopic information has been obtained for odd-even $^{87-93}$Br isotopes and the experimental results have been compared with state-of-the-art Large-Scale Shell-Model and DNO Shell-Model calculations. As a result of such theoretical approaches, a transition from prolate ($^{87,89}$Br) to oblate ($^{91,93}$Br) shapes is obtained from the subtle balance between proton and neutron quadrupole deformations, as a clear signature of pseudo-SU3 quadrupole regime., Comment: 17 pages, 24 figures, 5 tables

Isomers close to the doubly magic nucleus $^{78}$Ni ($Z=28$, $N=50$) provide essential information on the shell evolution and shape coexistence far from stability. The existence of a long-lived isomeric state in $^{76}$Cu has been debated for a long time. We have performed high-precision mass measurements of $^{76}$Cu with the JYFLTRAP double Penning trap mass spectrometer at the Ion Guide Isotope Separator On-Line facility and confirm the existence of such a isomeric state with an excitation energy $E_x=64.8(25)$ keV. Based on the ratio of detected ground- and isomeric-state ions as a function of time, we show that the isomer is the shorter-living state previously considered as the ground state of $^{76}$Cu. The result can potentially change the conclusions made in previous works related to the spin-parity and charge radius of the $^{76}$Cu ground state. Additionally, the new $^{76}$Cu$(n,\gamma)$ reaction $Q$-value has an impact on the astrophysical rapid neutron-capture process., Comment: 8 pages, 4 figures