We perform a Bayesian analysis of a relativistic mean-field approach, which is an implementation of the chiral confining model with both chiral symmetry breaking and confinement effects, and which was recently proven to reproduce well the ground state properties of finite nuclei. We additionally explore the impact of couplings between ρ and ω mesons as well as a non-linear ω coupling. Our models are simultaneously constrained by nuclear matter properties near saturation density, multi-messenger neutron star astrophysical observations, and/or lattice QCD predictions of the nucleon mass. It exhibits tension in simultaneously reproducing the ∼ 2M_⊙ massive NS and the tidal deformability inferred from GW170817. We show that an additional ωρ coupling, favored by Bayes factor analysis, substantially alleviates this tension, while adding a non-linear ω self-interaction is not necessary for the RMF-CC model. Owing to the strong constraints on the scalar sector imposed by chiral dynamics and the softening of the equation of state at high densities induced by our treatment of confinement, the RMF-CC approach favors stiff equations of state. Since we do not consider phase transition in the core of neutron stars, this stiffening is obtained with large values of the incompressibility modulus of about ∼300 MeV. We finally compare the well-known RMF model with RMF-CC models with the same constraints, and we obtain a preference for the RMF model in the absence of a phase transition in the core of neutron stars.

Mass measurements of ^31-33Na and ^31-35Mg using the TITAN MR-TOF-MS at TRIUMF's ISAC facility are presented, with the uncertainty of the ^33Na mass reduced by over two orders of magnitude. The excellent performance of the MR-TOF-MS has also allowed the discovery of a millisecond isomer in ^32Na. The precision obtained shows that the binding energy of the normally closed N = 20 neutron shell reaches a minimum for ^32Mg but increases significantly for ^31Na, hinting at the possibility of enhanced shell strength toward the unbound ^28O. We compare the results with new ab initio predictions that raise intriguing questions of nuclear structure beyond the dripline.

Whether or not femto-scale droplets of quark-gluon plasma (QGP) are formed in so-called small systems at high-energy colliders is a pressing question in the phenomenology of the strong interaction. For proton-proton or proton-nucleus collisions the answer is inconclusive due to the large theoretical uncertainties plaguing the description of these processes. While upcoming data on collisions of 16O nuclei may mitigate these uncertainties in the near future, here we demonstrate the unique possibilities offered by complementing 16O + 16O data with collisions of 20Ne ions. We couple both nuclear lattice effective field theory (NLEFT) and projected generator coordinate method (PGCM) ab initio descriptions of the structure of 20Ne and 16O to hydrodynamic simulations of 16O + 16O and 20Ne + 20Ne collisions at high energy. We isolate the imprints of the bowling-pin shape of 20Ne on the collective flow of hadrons, which can be used to perform quantitative tests of the hydrodynamic QGP paradigm. In particular, we predict that the elliptic flow of 20Ne + 20Ne collisions is enhanced by as much as 1.174(8)stat(31)syst for NLEFT and 1.139(6)stat(39)syst for PGCM relative to 16O + 16O collisions for the 1% most central events. At the same time, theoretical uncertainties largely cancel when studying relative variations of observables between two systems. This demonstrates a method based on experiments with two light-ion species for precision characterizations of the collective dynamics and its emergence in a small system.

The System for Measuring Overlap with Gas (SMOG2) at the LHCb detector enables the study of fixed-target ion-ion collisions at relativistic energies (sqrt[s_{NN}]∼100  GeV in the center of mass). With input from ab initio calculations of the structure of ^{16}O and ^{20}Ne, we compute 3+1D hydrodynamic predictions for the anisotropic flow of Pb+Ne and Pb+O collisions to be tested with upcoming LHCb data. This will allow the detailed study of quark-gluon plasma formation as well as experimental tests of the predicted nuclear shapes. Elliptic flow (v_{2}) in Pb+Ne collisions is greatly enhanced compared to the Pb+O baseline due to the shape of ^{20}Ne, which is deformed in a bowling-pin geometry. Owing to the large ^{208}Pb radius, this effect is seen in a broad centrality range, a unique feature of this collision configuration. Larger elliptic flow further enhances the quadrangular flow (v_{4}) of Pb+Ne collisions via nonlinear coupling, and impacts the sign of the kurtosis of the elliptic flow vector distribution (c_{2}{4}). Exploiting the shape of ^{20}Ne proves thus an ideal method to investigate the formation of quark-gluon plasma in fixed-target experiments at LHCb, and demonstrates the power of System for Measuring Overlap with Gas as a tool to image nuclear ground states.

The behavior of spin doublets is known to play a major role in nuclear structure and shell effects. Pseudo-spin doublets are also known to impact the single-particle spectrum. The covariant framework, having these two effects encoded in its approach, is an excellent tool to understand the main mechanism driving theses spin and pseudo-spin symmetries and their breaking. A perturbative expansion of the degeneracy raising related to spin and pseudo-spin effects is proposed, up to second order. It allows to understand the main behavior of spin and pseudo-spin energy doublets, such as their A dependence, as well as their common footing and differences. In the case of the spin symmetry, only the lower component of the Dirac bi-spinor is involved, whereas in the case of the pseudo-spin one, both the upper and lower components are involved. Their interplay with the covariant potentials is also analyzed.

High-energy collisions involving the A=96 isobars ^96Zr and ^96Ru have been performed in 2018 at Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC) as a means to search for the chiral magnetic effect in QCD. This would manifest itself as specific deviations from unity in the ratio of observables taken between ^96Zr+^96Zr and ^96Ru+^96Ru collisions. Measurements of such ratios (released at the end of 2021) indeed reveal deviations from unity, but these are primarily caused by the two collided isobars having different radial profiles and intrinsic deformations. To make progress in understanding RHIC data, nuclear physicists across the energy spectrum gathered in Heidelberg in 2022 as part of an EMMI Rapid Reaction Task Force (RRTF) to address the following question. Does the combined effort of low-energy nuclear structure physics and high-energy heavy-ion physics enable us to understand the observations made in isobar collisions at RHIC?

A simple pattern of organisation, the nuclear shell structure, emerges from the complex interactions between nucleons in nuclei and determines, to some significant degree, nuclear structure properties. Recent experimental investigations of exotic nuclei revealed a shortfall in our current understanding of nuclear shell evolution and nuclear magicity. We introduce a novel perspective where the Dirac mass kinetic term, which stems from the singular participation of a spin-0 boson in the nuclear strong force, plays a pivotal role in generating the nuclear shell structure. Namely, the combination of the Dirac mass kinetic Term with the spin-orbit term redefines magic numbers both in stable and exotic nuclei. The identification of this mechanism allows to provide a broad understanding of the origin and evolution of nuclear magic numbers.

The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental length scale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudospin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.

Whether or not femto-scale droplets of quark-gluon plasma (QGP) are formed in so-called small systems at high-energy colliders is a pressing question in the phenomenology of the strong interaction. For proton-proton or proton-nucleus collisions the answer is inconclusive due to the large theoretical uncertainties plaguing the description of these processes. While upcoming data on collisions of $^{16}$O nuclei may mitigate these uncertainties in the near future, here we demonstrate the unique possibilities offered by complementing $^{16}$O$^{16}$O data with collisions of $^{20}$Ne ions. We couple both NLEFT and PGCM ab initio descriptions of the structure of $^{20}$Ne and $^{16}$O to hydrodynamic simulations of $^{16}$O$^{16}$O and $^{20}$Ne$^{20}$Ne collisions at high energy. We isolate the imprints of the bowling-pin shape of $^{20}$Ne on the collective flow of hadrons, which can be used to perform quantitative tests of the hydrodynamic QGP paradigm. In particular, we predict that the elliptic flow of $^{20}$Ne$^{20}$Ne collisions is enhanced by as much as 1.170(8)$_{\rm stat.}$(30)$_{\rm syst.}$ for NLEFT and 1.139(6)$_{\rm stat.}$(39)$_{\rm syst.}$ for PGCM relative to $^{16}$O$^{16}$O collisions for the 1% most central events. At the same time, theoretical uncertainties largely cancel when studying relative variations of observables between two systems. This demonstrates a method based on experiments with two light-ion species for precision characterizations of the collective dynamics and its emergence in a small system.

Giant resonances (GRs) are a striking manifestation of collective motions in atomic nuclei. The present paper is the second in a series of four dedicated to the use of the projected generator coordinate method (PGCM) for the ab initio determination of the isoscalar giant monopole resonance (GMR) in closed- and open-shell mid-mass nuclei. While the first paper was dedicated to quantifying various uncertainty sources, the present paper focuses on the first applications to three doubly-open shell nuclei, namely $^{46}$Ti, $^{28}$Si and $^{24}$Mg. In particular, the goal is to investigate from an ab initio standpoint (i) the coupling of the GMR with the giant quadrupole resonance (GQR) in intrinsically-deformed nuclei, (ii) the possible impact of shape coexistence and shape mixing on the GMR, (iii) the GMR based on shape isomers and (iv) the impact of anharmonic effects on the monopole response. The latter is studied by comparing PGCM results to those obtained via the quasi-particle random phase approximation (QRPA), the traditional many-body approach to giant resonances, performed in a consistent setting. Eventually, PGCM results for sd-shell nuclei are in excellent agreement with experimental data, which is attributed to the capacity of the PGCM to capture the important fragmentation of the monopole response in light, intrinsically-deformed systems. Still, the comparison to data in $^{28}$Si and $^{24}$Mg illustrates the challenge (and the potential benefit) of extracting unambiguous experimental information.

Giant Resonances are, with nuclear rotations, the most evident expression of collectivity in finite nuclei. These two categories of excitations, however, are traditionally described within different formal schemes, such that vibrational and rotational degrees of freedom are separately treated and coupling effects between those are often neglected. The present work puts forward an approach aiming at a consitent treatment of vibrations and rotations. Specifically, this paper is the last in a series of four dedicated to the investigation of the giant monopole resonance in doubly open-shell nuclei via the ab initio Projected Generator Coordinate Method (PGCM). The present focus is on the treatment and impact of angular momentum restoration within such calculations. The PGCM being based on the use of deformed mean-field states, the angular-momentum restoration is performed when solving the secular equation to extract vibrational excitations. In this context, it is shown that performing the angular momentum restoration only after solving the secular equation contaminates the monopole response with an unphysical coupling to the rotational motion, as was also shown recently for (quasi-particle) random phase approximation calculations based on a deformed reference state. Eventually, the present work based on the PGCM confirms that an a priori angular momentum restoration is necessary to handle consistently both collective motions at the same time. This further pleads in favor of implementing the full-fledged projected (quasi-particle) random phase approximation in the future.

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 [1] 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 [2], 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 us to design numerous non-perturbative approximations and can take Lagrangians possibly derived from EFTs of QCD as inputs. In our previous paper [2], we have illustrated such technical features for diagrammatic PI techniques in a study of the (0+0)-D O(N)-symmetric φ ^4 -theory. In the present work, we consider another class of PI techniques, i.e. functional renormalization group (FRG) approaches, that we apply to 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, 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.

Giant resonances (GRs) are a striking manifestation of collective motions in mesoscopic systems such as atomic nuclei. Until recently, theoretical investigations have essentially relied on the (quasiparticle) random phase approximation ((Q)RPA), and extensions of it, based on phenomenological energy density functionals (EDFs). As part of a current effort to describe GRs within an ab initio theoretical scheme, the present work promotes the use of the projected generator coordinate method (PGCM). This method, which can handle anharmonic effects while satisfying symmetries of the nuclear Hamiltonian, displays a favorable (i.e. mean-field-like) scaling with system's size. Presently focusing on the isoscalar giant monopole resonance (GMR) of light- and medium-mass nuclei, PGCM's potential to deliver wide-range ab initio studies of GRs in closed- and open-shell nuclei encompassing pairing, deformation, and shape coexistence effects is demonstrated. The comparison with consistent QRPA calculations highlights PGCM's unique attributes and sheds light on the intricate interplay of nuclear collective excitations. The present paper is the first in a series of four and focuses on technical aspects and uncertainty quantification of ab initio PGCM calculations of GMR using the doubly open-shell $^{46}$Ti as an illustrative example. The second paper displays results for a set of nuclei of physical interest and proceeds to the comparison with consistent (deformed) ab initio QRPA calculations. While the third paper analyzes useful moments of the monopolar strength function and different ways to access them within PGCM calculations, the fourth paper focuses on the effect of the symmetry restoration on the monopole strength function.

Nuclear clustering has been studied with covariant Energy Density Functional approaches for more than a decade. It recently allowed to bridge microscopically the description of cluster states in light nuclei with the one of cluster and alpha decays in heavy ones. The proper use of theoretical tools, such as the density and the nucleonic localization function, allows to shed light on the mechanisms of formation and identification of clusters in nuclei. Finally, a global analysis of nuclear clustering is discussed, in order to identify control parameters for a nuclear cluster phase.

One of the main methods used to microscopically describe collective states in atomic nuclei is the quasiparticle random-phase approximation (QRPA). However, due to its high computational cost, systematic studies covering the full nuclear chart are rare. In this work we show the first results of our systematic large-scale QRPA calculations. We do this by means of the quasiparticle finite-amplitude method (QFAM), which significantly reduces computation times. We use two kinds of interactions, the covariant DD-PC1 and a novel chiral interaction.

The spectroscopic quadrupole moment of the first excited state, Q__S(2^+_1), at 1.634 MeV in ^20Ne was determined from sensitive reorientation-effect Coulomb-excitation measurements using a heavy target and safe energies well below the Coulomb barrier. Particle-γ coincidence measurements were collected at iThemba LABS with a digital data-acquisition system using the AFRODITE array coupled to an annular, doubled-sided silicon detector. A precise value of Q__S(2^+_1)=-0.22(2) eb was determined at backward angles in agreement with the only safe-energy measurement prior to this work, Q__S(2^+_1)=-0.23(8) eb. This result adopts 1ħω shell-model calculations of the nuclear dipole polarizability of the 2^+_1 state that contributes to the effective quadrupole interaction and determination of Q__S(2^+_1). It disagrees, however, with the ideal rotor model for axially-symmetric nuclei by almost 3σ. Larger discrepancies are computed by modern state-of-the-art calculations performed in this and prior work, including ab initio shell model with chiral effective interactions and the multi-reference relativistic energy density functional (MR-EDF) model. The intrinsic nucleon density of the 2^+_1 state in ^20Ne calculated with the MR-EDF model illustrates the presence of α clustering, which explains the largest discrepancy with the rotor model found in the nuclear chart and motivates the explicit inclusion of α clustering for full convergence of E2 collective properties.

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 [1] 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 [2], 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 us to design numerous non-perturbative approximations and can take Lagrangians possibly derived from EFTs of QCD as inputs. In our previous paper [2], we have illustrated such technical features for diagrammatic PI techniques in a study of the (0+0)-D O(N)-symmetric phi( 4) -theory. In the present work, we consider another class of PI techniques, i.e. functional renormalization group (FRG) approaches, that we apply to 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.

The System for Measuring Overlap with Gas (SMOG2) at the LHCb detector enables the study of fixed-target ion-ion collisions at relativistic energies ($\sqrt{s_{\rm NN}}\sim100$ GeV in the centre-of-mass). With input from \textit{ab initio} calculations of the structure of $^{16}$O and $^{20}$Ne, we compute 3+1D hydrodynamic predictions for the anisotropic flow of Pb+Ne and Pb+O collisions, to be tested with upcoming LHCb data. This will allow the detailed study of quark-gluon plasma (QGP) formation as well as experimental tests of the predicted nuclear shapes. Elliptic flow ($v_2$) in Pb+Ne collisions is greatly enhanced compared to the Pb+O baseline due to the shape of $^{20}$Ne, which is deformed in a bowling-pin geometry. Owing to the large $^{208}$Pb radius, this effect is seen in a broad centrality range, a unique feature of this collision configuration. Larger elliptic flow further enhances the quadrangular flow ($v_4$) of Pb+Ne collisions via non-linear coupling, and impacts the sign of the kurtosis of the elliptic flow vector distribution ($c_2\{4\}$). Exploiting the shape of $^{20}$Ne proves thus an ideal method to investigate the formation of QGP in fixed-target experiments at LHCb, and demonstrates the power of SMOG2 as a tool to image nuclear ground states.

Giant resonances (GRs) are a striking manifestation of collective motions in atomic nuclei. The present paper is the second in a series of four dedicated to the use of the projected generator coordinate method (PGCM) for the ab initio determination of the isoscalar giant monopole resonance (GMR) in closed- and open-shell mid-mass nuclei. While the first paper was dedicated to quantifying various uncertainty sources, the present paper focuses on the first applications to three doubly-open shell nuclei, namely ^46Ti, ^28Si and ^24Mg. In particular, the goal is to investigate from an ab initio standpoint (i) the coupling of the GMR with the giant quadrupole resonance (GQR) in intrinsically-deformed nuclei, (ii) the possible impact of shape coexistence and shape mixing on the GMR, (iii) the GMR based on shape isomers and (iv) the impact of anharmonic effects on the monopole response. The latter is studied by comparing PGCM results to those obtained via the quasi-particle random phase approximation (QRPA), the traditional many-body approach to giant resonances, performed in a consistent setting. Eventually, PGCM results for sd-shell nuclei are in excellent agreement with experimental data, which is attributed to the capacity of the PGCM to capture the important fragmentation of the monopole response in light, intrinsically-deformed systems. Still, the comparison to data in ^28Si and ^24Mg illustrates the challenge (and the potential benefit) of extracting unambiguous experimental information.