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The potential sub-shell closures N = 32 and N = 34 are analyzed at high spins in the titanium isotopes within the generalized beyond mean field theory considering triaxial deformations and the angular frequency as generator coordinates together with the particle number and the angular momentum conservation. A good description of bulk properties, high angular momenta spectra and transition probabilities is obtained. The outcome at high spin in these nuclei is consistent with the magic number character of N = 32 but not of N = 34., Comment: Published: Phys. Lett. B804 (2020) 135359

We present a self-consistent theory for the description of the spectroscopic properties of odd nuclei which includes exact blocking, particle-number and angular-momentum projection and configuration mixing. In our theory the pairing correlations are treated in a variation-after-projection approach and the triaxial deformation parameters are explicitly considered as generator coordinates. The angular-momentum and particle-number symmetries are exactly recovered. The use of the effective finite-range density-dependent Gogny force in the calculations provides an added value to the theoretical results. We apply the theory to the textbook example of 25Mg and, although this nucleus has been thoroughly studied in the past, we still provide a novel view of nuclear phenomena taking place in this nucleus. We obtain an overall good agreement with the known experimental energies and transition probabilities without any additional parameter such as effective charges. In particular, we clearly identify six bands, two of which we interpret as collective gamma bands., Comment: 12 pages, 10 figures, accepted for publication in Phys. Rev. C

The deformation parameters beta and gamma together with the two-quasiparticle excitations are taken into account, for the first time, as coordinates within a symmetry conserving (angular momentum and particle number) generator coordinate method. The simultaneous consideration of collective as well as single particle degrees of freedom allows us to describe soft and rigid nuclei as well as the transition region in between. We apply the new theory to the study of the spectra and transition probabilities of the 156-172Er isotopes with a Pairing plus Quadrupole residual interaction. Good agreement with the experimental results is obtained for most of the observables studied and with the same quality for the very soft and the strongly deformed nuclei., Comment: 14 pages, 11 figures, accepted for publication in Phys. Rev. C

We present a self-consistent theory for odd nuclei with exact blocking and particle number and angular momentum projection. The demanding treatment of the pairing correlations in a variation-after-projection approach as well as the explicit consideration of the triaxial deformation parameters in a projection after variation method, together with the use of the finite-range density-dependent Gogny force, provides an excellent tool for the description of odd-even and even-even nuclei. We apply the theory to the Magnesium isotopic chain and obtain an outstanding description of the ground-state properties, in particular binding energies, odd-even mass differences, mass radii and electromagnetic moments among others., Comment: 8 pages, 6 figures, accepted for publication in Phys. Let. B

We present an overview of beyond mean field theories (BMFT) based on the generator coordinate method (GCM) and the recovery of symmetries used in nuclear physics with effective forces. After a reminder of the Hartree-Fock-Bogoliubov (HFB) theory a discussion of the shortcomings of any mean field approximation (MFA) is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. The lack of fluctuations around the average values of the MFA is a shortcoming of this approach. To build in correlations in BMFT one selects the relevant degrees of freedom: quadrupole, octupole and the pairing vibrations as well as the single particle ones. In the GCM the operators representing these degrees of freedom are used as coordinates to generate a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill-Wheeler equation. We discuss the classical beta and gamma vibrations by considering the quadrupole operators as coordinates. We present pairing fluctuations by considering the pairing gaps as generator coordinates. Lastly the explicit consideration of the time reversal symmetry breaking in the HFB wave function by the cranking procedure allows the alignment of nucleon pairs opening a new dimension in the BMFT calculations. Abundant calculations with the Gogny force illustrate the state-of-the-art of BMFTs with density functionals. We conclude with a thorough discussion on the potential poles of the theory., Comment: To be published in Physica Scripta as an invited comment in a focus issue to celebrate the 40-year anniversary of the 1975 Nobel Prize to Aage Niels Bohr, Ben Roy Mottelson and Leo James Rainwater

The ground and first excited 0+ states of the {156-172}Er isotopes are analyzed in the framework of the generator coordinate method. The shape parameter beta is used to generate wave functions with different deformations which together with the two-quasiparticle states built on them provide a set of states. An angular momentum and particle number projection of the latter spawn the basis states of the generator coordinate method. With this ansatz and using the separable pairing plus quadrupole interaction we obtain a good agreement with the experimental spectra and E2 transition rates up to moderate spin values. The structure of the wave functions suggests that the first excited 0+ states in the soft Er isotopes are dominated by shape fluctuations, while in the well deformed Er isotopes the two-quasiparticle states are more relevant. In between both degrees of freedom are necessary ., Comment: 11 pages, 11 figures, accepted for publication in Physical Review C

We present a novel nuclear energy density functional method to calculate spectroscopic properties of atomic nuclei. Intrinsic nuclear quadrupole deformations and rotational frequencies are considered simultaneously as the degrees of freedom within a symmetry conserving configuration mixing framework. The present method allows the study of nuclear states with collective and single-particle character. We calculate the fascinating structure of the semi-magic 44S nucleus as a first application of the method, obtaining an excellent quantitative agreement both with the available experimental data and with state-of-the-art shell model calculations., Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Lett

We present the first calculations of a symmetry conserving configuration mixing method (SCCM) using time-reversal symmetry breaking Hartree-Fock-Bogoliubov (HFB) states with the Gogny D1S interaction. The method includes particle number and tridimensional angular momentum symmetry restorations as well as configuration mixing within the generator coordinate method (GCM) framework. The nucleus $^{32}$Mg is chosen to show the performance and reliability of the calculations. Additionally, $0^{+}_{1}$, $2^{+}_{1}$ and $4^{+}_{1}$ states are computed for the magnesium isotopic chain, where a noticeable compression of the spectrum is obtained by including cranked states, leading to a very good agreement with the known experimental data., Comment: 7 pages, 5 figures, accepted in Physics Letters B

Nuclear matrix elements (NME) for the most promising candidates to detect neutrinoless double beta decay have been computed with energy density functional methods including deformation and pairing fluctuations explicitly on the same footing. The method preserves particle number and angular momentum symmetries and can be applied to any decay without additional fine tunings. The finite range density dependent Gogny force is used in the calculations. An increase of $10\%-40\%$ in the NME with respect to the ones found without the inclusion of pairing fluctuations is obtained, reducing the predicted half-lives of these isotopes., Comment: 5 pages, 3 Figures

Pairing fluctuations are self-consistently incorporated on the same footing as the quadrupole deformations in present state of the art calculations including particle number and angular momentum conservation as well as configuration mixing. The approach is complemented by the use of the finite range density dependent Gogny force which, with a unique source for the particle-hole and particle-particle interactions, guarantees a self-consistent interplay in both channels. We have applied our formalism to study the role of the pairing degree of freedom in the description of the most relevant observables like spectra, transition probabilities, separation energies, etc. We find that the inclusion of pairing fluctuations mostly affects the description of excited states, depending on the excitation energy and the angular momentum. $E0$ transition probabilities experiment rather big changes while $E2$'s are less affected. Genuine pairing vibrations are thoroughly studied with the conclusion that deformations strongly inhibits their existence. These studies have been performed for a selection of nuclei: spherical, deformed and with different degree of collectivity., Comment: 23 pages, 23 Figures, To be published in Phys. Rev. C

The influence of large amplitude pairing fluctuations is investigated in the framework of beyond mean field symmetry conserving configuration mixing calculations. In the numerical application the finite range density dependent Gogny force is used. We investigate the nucleus $^{54}$Cr with particle number and angular momentum projected wave functions considering the axial quadrupole deformation and the pairing gap degree of freedom as generator coordinates. We find that the effects of the pairing fluctuations increase with the excitation energy and the angular momentum. The self-consistency in the determination of the basis states plays an important role., Comment: 9 pages, 5 figures

We study the structure of the neutron rich $^{44}$S isotope with modern configuration mixing methods based on the Gogny interaction including beyond-mean-field effects. Restoration of particle number and rotational symmetries are taken into account as well as shape mixing in the whole triaxial $(\beta_{2},\gamma)$ plane. We obtain a qualitative agreement between the calculated spectrum and the experimental data reported recently. Very extended collective wave functions in the $(\beta_2,\gamma)$ plane are found for the lowest states, corresponding to very flat potentials, indicating strong configuration mixing and supporting the weakening of the N=28 magic number., Comment: Corrected typo (level at 3248 keV)

We study the low-lying energy spectrum of the rp-process waiting point nucleus 80Zr with state-of-the-art beyond mean field methods with the Gogny D1S interaction. Symmetry restoration and configuration mixing of axial and triaxial shapes are included in the calculations. Five 0+ states corresponding to different nuclear shapes are obtained below 2.25 MeV and several rotational and {\gamma}- bands built upon them are identified. Nevertheless, these states do not modify the {\beta}-decay half-life having a negligible effect in the rp-process. A good agreement with the available experimental data is obtained., Comment: 6 pages, 3 figures, submitted to Physics Letters B

We present the first implementation in the $(\beta,\gamma)$ plane of the generator coordinate method with full triaxial angular momentum and particle number projected wave functions using the Gogny force. Technical details about the performance of the method and the convergence of the results both in the symmetry restoration and the configuration mixing parts are discussed in detail. We apply the method to the study of $^{24}$Mg, the calculated energies of excited states as well as the transition probabilities are compared to the available experimental data showing a good overall agreement. In addition, we present the RVAMPIR approach which provides a good description of the ground and gamma bands in the absence of strong mixing., Comment: 40 pages,14 figures

Recent experimental results obtained using $\beta$ decay and isomer spectroscopy indicate an unusual behaviour of the energies of the first excited 2$^{+}$ states in neutron-rich Cd isotopes approaching the N=82 shell closure. To explain the unexpected trend, changes of the nuclear structure far-off stability have been suggested, namely a quenching of the N=82 shell gap already in $^{130}$Cd, only two proton holes away from doubly magic $^{132}$Sn. We study the behaviour of the 2$^+$ energies in the Cd isotopes from N=50 to N=82, i.e. across the entire span of a major neutron shell using modern beyond mean field techniques and the Gogny force. We demonstrate that the observed low 2$^+$ excitation energy in $^{128}$Cd close to the N=82 shell closure is a consequence of the doubly magic character of this nucleus for oblate deformation favoring thereby prolate configurations rather than spherical ones., Comment: 10 pages, 4 figures, to be publised in Phys. Lett. B

The beyond mean field approximation combined with the Gogny interaction is used to analyze the spherical to prolate deformed shape transition in the Neodymium isotopic chain. The vibrator as well as the rotor limits are nicely reproduced while the transitional region is only qualitatively described probably due to the lack of triaxial correlations in the calculations. Our results do not support the interpretation of $^{150}$Nd as a critical point nucleus and question the interpretation of shape changes as nuclear shape phase transitions., Comment: 12 pages, 9 figures, accepted in Phys. Lett. B