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Alpha and cluster decays are analyzed for heavy nuclei located above $^{208}$Pb on the chart of nuclides: $^{216-220}$Rn and $^{220-224}$Ra, that are also candidates for observing the $2 α$ decay mode. A microscopic theoretical approach based on relativistic Energy Density Functionals (EDF), is used to compute axially-symmetric deformation energy surfaces as functions of quadrupole, octupole and hexadecupole collective coordinates. Dynamical least-action paths for specific decay modes are calculated on the corresponding potential energy surfaces. The effective collective inertia is determined using the perturbative cranking approximation, and zero-point and rotational energy corrections are included in the model. The predicted half-lives for $α$-decay are within one order of magnitude of the experimental values. In the case of single $α$ emission, the nuclei considered in the present study exhibit least-action paths that differ significantly up to the scission point. The differences in alpha-decay lifetimes are not only driven by Q values, but also by variances of the least-action paths prior to scission. In contrast, the $2 α$ decay mode presents very similar paths from equilibrium to scission, and the differences in lifetimes are mainly driven by the corresponding Q values. The predicted $^{14}$C cluster decay half-lives are within three orders of magnitudes of the empirical values, and point to a much more complex pattern compared to the alpha-decay mode., 9 pages, 13 figures

International audience; Alpha and cluster decays are analyzed for heavy nuclei located above $^{208}$Pb on the chart of nuclides: $^{216,218}$Rn and $^{220-224}$Ra, that are also candidates for observing the $2 \alpha$ decay mode. A microscopic theoretical approach based on relativistic Energy Density Functionals (EDF), is used to compute axially-symmetric deformation energy surfaces as functions of quadrupole, octupole and hexadecupole collective coordinates. Dynamical least-action paths for specific decay modes are calculated on the corresponding potential energy surfaces. The effective collective inertia is determined using the perturbative cranking approximation, and zero-point and rotational energy corrections are included in the model. The predicted half-lives for $\alpha$-decay are within one order of magnitude of the experimental values. In the case of single $\alpha$ emission, the nuclei considered in the present study exhibit least-action paths that differ significantly up to the scission point. The differences in alpha-decay lifetimes are not only driven by Q values, but also by variances of the least-action paths prior to scission. In contrast, the $2 \alpha$ decay mode presents very similar paths from equilibrium to scission, and the differences in lifetimes are mainly driven by the corresponding Q values. The predicted $^{14}$C cluster decay half-lives are within three orders of magnitudes of the empirical values, and point to a much more complex pattern compared to the alpha-decay mode.

International audience; Background: The study of additional terms in functionals is relevant to better describe nuclear structure phenomenology. Among these terms, the tensor one is known to impact nuclear structure properties, especially in neutron-rich nuclei. However, its effect has not been studied on the whole nuclear chart yet. Purpose: The impact of terms corresponding to the tensor at the Hartree level, is studied for infinite nuclear matter as well as deformed nuclei, by developing new density-dependent functionals including these terms. In particular, we study in details the improvement such a term can bring to the description of specific nuclear observables. Methods: The framework of covariant energy density functional is used at the Hartree-Bogoliubov level. The free parameters of covariant functionals are optimized by combining Markov-Chain-Monte-Carlo and simplex algorithms. Results: An improvement of the RMS binding energies, spin-orbit splittings and gaps is obtained over the nuclear chart, including axially deformed ones, when including tensors terms. Small modifications of the potential energy surface and densities are also found. In infinite matter, the Dirac mass is shifted to a larger value, in better agreement with experiments. Conclusions: Taking into account additional terms corresponding to the tensor terms in the vector-isoscalar channel at the Hartree level, improves the description of nuclear properties, both in nuclei and in nuclear matter.

Alpha and cluster decays are analyzed for heavy nuclei located above $^{208}$Pb on the chart of nuclides: $^{216-220}$Rn and $^{220-224}$Ra, that are also candidates for observing the $2 \alpha$ decay mode. A microscopic theoretical approach based on relativistic Energy Density Functionals (EDF), is used to compute axially-symmetric deformation energy surfaces as functions of quadrupole, octupole and hexadecupole collective coordinates. Dynamical least-action paths for specific decay modes are calculated on the corresponding potential energy surfaces. The effective collective inertia is determined using the perturbative cranking approximation, and zero-point and rotational energy corrections are included in the model. The predicted half-lives for $\alpha$-decay are within one order of magnitude of the experimental values. In the case of single $\alpha$ emission, the nuclei considered in the present study exhibit least-action paths that differ significantly up to the scission point. The differences in alpha-decay lifetimes are not only driven by Q values, but also by variances of the least-action paths prior to scission. In contrast, the $2 \alpha$ decay mode presents very similar paths from equilibrium to scission, and the differences in lifetimes are mainly driven by the corresponding Q values. The predicted $^{14}$C cluster decay half-lives are within three orders of magnitudes of the empirical values, and point to a much more complex pattern compared to the alpha-decay mode., Comment: 9 pages, 13 figures

The present paper is the second of a series of publications that aim at investigating relevant directions to turn the nuclear energy density functional (EDF) method as an effective field theory (EFT). The EDF approach has known numerous successes in nuclear theory over the past decades and is currently the only microscopic technique that can be applied to all atomic nuclei. However, the phenomenological character of the EDF method also comes with important limitations, such as the lack of an explicit connection with quantum chromodynamics (QCD). As was argued in the first paper of this series, reformulating the EDF framework as an EFT would enable us to overcome these limitations. In particular, path-integral (PI) techniques are suited to achieve such a purpose as they allow to design numerous non-perturbative approximations and can take Lagrangians possibly derived from EFTs of QCD as inputs. In our previous paper, we have illustrated such technical features for diagrammatic PI techniques in a study of the (0+0)-D $O(N)$-symmetric $\varphi^{4}$-theory. In the present work, we consider another class of PI techniques, i.e. functional renormalization group (FRG) approaches, that we apply on the same toy model. Despite our explicit interest for the nuclear many-body problem, the presented study is also directed towards FRG practitioners from various fields: technical details are provided for FRG techniques based on 1-particle-irreducible (1PI), 2-particle-irreducible (2PI) and 2-particle-point-irreducible (2PPI) effective actions (EAs), coined respectively as 1PI-, 2PI- and 2PPI-FRGs, and the treatment of the $O(N)$ symmetry is also addressed thoroughly. Connections between these various FRG methods are identified as well., Comment: This article is part of a PhD project. The corresponding manuscript can be found at: https://tel.archives-ouvertes.fr/tel-03771188

The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating its reliability. This paper is part of a larger program that aims at formulating the EDF approach as an effective field theory (EFT) in order to overcome these limitations. A relevant framework to achieve this is the path-integral (PI) formulation of quantum field theory (QFT). The latter indeed provides a wide variety of treatments of the many-body problem well suited to deal with non-perturbative interactions and to exploit a Lagrangian resulting from an EFT as a starting point. While developing the formalism in a general setting, we present a comparative study of such techniques applied to a toy model, i.e. the (0+0)-D $O(N)$-symmetric $\varphi^{4}$-theory. More specifically, our focus will be on the following diagrammatic techniques: loop expansion (LE), optimized perturbation theory (OPT) and self-consistent perturbation theory (SCPT). With these methods, we notably address the spontaneous breakdown of the $O(N)$ symmetry with care especially since spontaneous symmetry breakings (SSBs) play a paramount role in current implementations of the EDF approach., Comment: This article is part of a PhD project. The corresponding manuscript can be found at: arXiv:2210.16676

We investigate the localization and clustering features in $^{20}$Ne ($N=Z$) and neutron-rich $^{32}$Ne nuclei at zero and finite temperatures. The finite temperature Hartree-Bogoliubov theory is used with the relativistic density-dependent meson-nucleon coupling functional DD-ME2. It is shown that clustering features gradually weaken with increasing temperature and disappear when the shape phase transition occurs. Considering thermal fluctuations in the density profiles, the clustering features vanish at lower temperatures, compared to the case without thermal fluctuations. The effect of the pairing correlations on the nucleon localization and the formation of cluster structures are also studied at finite temperatures. Due to the inclusion of pairing in the calculations, cluster structures are preserved until the critical temperatures for the shape phase transition are reached. Above the critical temperature of the shape phase transition, the clustering features suddenly disappear, which differs from the results without pairing., 11 pages, 10 figures

Ab initio approaches to the nuclear many-body problem have seen their reach considerably extended over the past decade. However, collective excitations have been scarcely addressed so far due to the prohibitive cost of solving the corresponding equations of motion. Here, a numerically efficient method to compute electromagnetic response functions at zero- and finite-temperature in superfluid and deformed nuclei from an ab initio standpoint is presented and applied to $^{16}$O, $^{28}$Si, $^{46}$Ti and $^{56}$Fe. This work opens the path to systematic ab initio calculations of nuclear responses to electroweak probes across a significant portion of the nuclear chart., Comment: 7 pages, 6 figures

We report on γ -ray spectroscopy of low-lying excited states in the neutron-rich 94, 95, 96Kr isotopes measured as part of the “Shell Evolution And Search for Two-plus energies At RIBF” (SEASTAR) campaign at the RIKEN Radioactive Isotope Beam Factory. Excited yrast and non-yrast states were observed, and half-lives extracted via GEANT4 simulations. In 94, 96Kr candidates for the 3− 1 state were identified. For 95Kr, the prompt SEASTAR data were combined with delayed spectroscopic data measured with the EURICA array to observe transitions on top of the known (7/2)+ isomer at a level energy of 195.5(3) keV. The comparison of the new experimental results with five-dimensional collective Hamiltonian (5DCH) and mapped interacting boson model (IBM) calculations, both using the Gogny D1M interaction, could suggest oblate-prolate shape coexistence already in 96Kr.

Perturbative and non-perturbative expansion methods already constitute a tool of choice to perform ab initio calculations over a significant part of the nuclear chart. In this context, the categories of accessible nuclei directly reflect the class of unperturbed state employed in the formulation of the expansion. The present work generalizes to the nuclear many-body context the versatile method of Ref. \cite{burton20a} by formulating a perturbative expansion on top of a multi-reference unperturbed state mixing deformed non-orthogonal Bogoliubov vacua, i.e. a state obtained from the projected generator coordinate method (PGCM). Particular attention is paid to the part of the mixing taking care of the symmetry restoration, showing that it can be exactly contracted throughout the expansion, thus reducing significantly the dimensionality of the linear problem to be solved to extract perturbative corrections. While the novel expansion method, coined as PGCM-PT, reduces to the PGCM at lowest order, it reduces to single-reference perturbation theories in appropriate limits. Based on a PGCM unperturbed state capturing (strong) static correlations in a versatile and efficient fashion, PGCM-PT is indistinctly applicable to doubly closed-shell, singly open-shell and doubly open-shell nuclei. The remaining (weak) dynamical correlations are brought consistently through perturbative corrections. This symmetry-conserving multi-reference perturbation theory is state-specific and applies to both ground and excited PGCM unperturbed states, thus correcting each state belonging to the low-lying spectrum of the system under study., Comment: The present paper is the first in a series of three and discusses the PGCM-PT formalism in detail. The second paper displays numerical zeroth-order results, i.e. the outcome of PGCM calculations. Second-order, i.e. PGCM-PT(2), calculations performed in both closed- and open-shell nuclei are the object of the third paper