arXiv subjects

Benjamin Bally

Publications and source records attributed to Benjamin Bally.

At least 19 recordsLinked to original sources

arXiv2026

Ab initio anatomy of quadrupole correlations in $^{16}$O and $^{20}$Ne

Azimuthal hadronic flow measured in ultra-relativistic ion--ion collisions provides a new means of imaging multipole correlations in the ground state of atomic nuclei. Early interpretations largely relied on a classical-rotor picture, in which the measured mean-square elliptic flow is directly related to an intrinsic quadrupole deformation. Atomic nuclei, however, contain additional many-body correlations generated by the Pauli exclusion principle, collective shape fluctuations and non-collective dynamical processes, whose impact on this correspondence has not yet been elucidated. Here, we resolve this issue through an ab initio analysis of $^{16}$O and $^{20}$Ne based on chiral nuclear interactions, combining the in-medium similarity renormalization group with the quantum-number-projected generator coordinate method. By successively isolating antisymmetrization, collective rotational and vibrational, and non-collective dynamical correlations, we determine, for the first time, how each component contributes to the mean-square quadrupole eccentricity. We uncover an unexpected compensation among these distinct correlation mechanisms: despite sizable individual contributions, the squared effective quadrupole deformation inferred from the elliptic flow remains close to the square intrinsic deformation of the nucleus. This result provides a microscopic explanation for the surprising success of the classical-rotor approximation and establishes a quantitative foundation for interpreting $^{16}$O+$^{16}$O and $^{20}$Ne+$^{20}$Ne collision data recently collected at the Large Hadron Collider.

nucl-th↗

arXiv2026

Quantum effects in the quadrupole rotor picture of ultra-relativistic ion-ion collisions

The azimuthal hadronic flow observed in ultra-relativistic ion-ion collisions provides a sensitive probe of many-body ground-state correlations in the colliding nuclei. In particular, collective correlations associated with nuclear "intrinsic deformation" are expected to leave pronounced fingerprints on specific final-state observables. However, such effects are commonly interpreted within a classical rigid-rotor picture, despite the intrinsically quantum nature of nuclei. In this Letter, the validity of this interpretation is assessed systematically across the nuclear chart by comparing the quantum quadrupole rotor with its classical rigid-rotor limit. Quantum contributions associated with the fermionic nature of the nucleons are shown to be largely independent of shell effects, and hence of the intrinsic deformation. While they account for nearly all of the quantum rotor effective quadrupole deformation in light and/or spherical nuclei, they drop below 10% in intrinsically well deformed heavy nuclei. The present letter demonstrates that a quantitative interpretation of nuclear-structure effects in final-state observables requires going beyond the classical rigid-rotor paradigm. Beyond the quantum contributions quantified presently, correlations associated with collective vibrations and with the non-collective nucleonic motion must be further included and characterized.

nucl-th↗

arXiv2026

Imaging two-body correlations in atomic nuclei via low- and high-energy processes

Characterizing the correlated behavior of nucleons inside atomic nuclei constitutes a long-standing challenge, both experimentally and theoretically. It has recently been understood that two-particle correlations in the azimuthal distribution of final hadrons emitted in ultra-relativistic ultra-central ion-ion collisions can be used to quantify ground-state two-body correlations. Performing systematic ab initio nuclear structure calculations of light nuclei, we demonstrate that such an observable does provide a meaningful imaging of nuclear ground states, naturally leading to a robust interpretation of the various categories of two-nucleon correlations at play. This is at variance with the low-energy approach relying on Kumar operators whose traditional interpretation in terms of deformation parameters is shown to be inoperative. A future interesting development will consist of targeting specific three-particle correlations to isolate three-nucleon correlations in which additional nuclear structure information of interest leave their fingerprint.

nucl-th↗

arXiv2026

Mean-field proton-neutron pairing correlations with the Gogny D1S energy density functional

We study proton-neutron pairing correlations within the Hartree-Fock-Bogoliubov (HFB) framework using Gogny-type energy density functionals. By allowing for proton-neutron mixing in the quasi-particle transformation, both isovector ($T=1$) and isoscalar ($T=0$) pairing channels are explicitly included at the mean-field level. The \texttt{TAURUS} code has been extended to treat density-dependent Gogny interactions in this generalized HFB scheme. We examine the numerical behavior of the widely used Gogny D1S functional and compare it with calculations performed using the Hamiltonian-based Brink-Boecker B1 interaction supplemented by a zero-range spin-orbit term. When proton-neutron mixing is included and large single-particle spaces are employed, instabilities are observed for Gogny D1S due to the zero-range density-dependent term contribution to the proton-neutron pairing field, whereas stable solutions are obtained with the B1 interaction. Constrained HFB calculations performed in reduced configuration spaces allow us to explore total energy curves as functions of proton-neutron pairing collective coordinates in selected $sd$-shell nuclei. In all cases studied, the self-consistent minima correspond to vanishing proton-neutron pairing, with energy increasing rapidly as proton-neutron pairing correlations are introduced. These results provide insight into the behavior of Gogny functionals under generalized HFB conditions and offer useful guidance for future developments.

nucl-th↗

arXiv2025

M1 dipole strength from projected generator coordinate method calculations in the sd-shell valence space

The low-energy enhancement observed in the deexcitation $\gamma$-ray strength functions, attributed to magnetic dipole (M1) radiations, has spurred theoretical efforts to improve on its description. Among the most widely used approaches are the quasiparticle random-phase approximation (QRPA) and its extensions. However, these methods often struggle to reproduce the correct behavior of the M1 strength at the lowest $\gamma$ energies. An alternative framework, the projected generator coordinate method (PGCM), offers significant advantages over QRPA by restoring broken symmetries and incorporating both vibrational and rotational dynamics within a unified description. Due to these features, PGCM has been proposed as a promising tool to study the low-energy M1 strength function in atomic nuclei. However, comprehensive investigations employing this method are lacking. The PGCM is presently used within the frame of sd-shell valence space calculations based on the USDB shell-model interaction to benchmark its performance against the solutions obtained via exact diagonalization. The reliability of two different sets of generator coordinates in the PGCM calculations is gauged using ${}^{24}$Mg as a test case. The ability of the PGCM to reproduce results from exact diagonalization in the sd valence space is demonstrated for $1^{+}$ states and M1 transitions. Future work will need to assess whether the proposed method can be applied systematically and extended to large-scale calculations while maintaining a reasonable computational cost.

nucl-th↗

arXiv2025

Nuclear Physics Confronts Relativistic Collisions Of Isobars

High-energy collisions involving the $A=96$ isobars $^{96}$Zr and $^{96}$Ru 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 $^{96}$Zr+$^{96}$Zr and $^{96}$Ru+$^{96}$Ru 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?

nucl-ex↗

arXiv2024

Anisotropic flow in fixed-target $^{208}$Pb+$^{20}$Ne collisions as a probe of quark-gluon plasma

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.

nucl-th↗

arXiv2024

Shell-model study of $^{28}$Si: coexistence of oblate, prolate and superdeformed shapes

We study the shape coexistence in the nucleus $^{28}$Si with the nuclear shell model using numerical diagonalizations complemented with variational calculations based on the projected generator-coordinate method. The theoretical electric quadrupole moments and transitions as well as the collective wavefunctions indicate that the standard USDB interaction in the $sd$ shell describes well the ground-state oblate rotational band, but misses the experimental prolate band. Guided by the quasi-SU(3) model, we show that the prolate band can be reproduced in the $sd$ shell by reducing the energy of the $0d_{3/2}$ orbital. Alternatively, in the extended $sdpf$ configuration space a modification of the SDPF-NR interaction that accommodates cross-shell excitations also reproduces the oblate and prolate bands. Finally, we address the possibility of superdeformation in $^{28}$Si within the $sdpf$ space. Our results indicate that superdeformed structures appear at about $18$-$20$~MeV.

nucl-th↗

arXiv2024

The unexpected uses of a bowling pin: exploiting $^{20}$Ne isotopes for precision characterizations of collectivity in small 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.

nucl-th↗

arXiv2024

Symmetry-projected variational calculations with the numerical suite TAURUS II. Configuration mixing of symmetry-projected reference states

We present the numerical codes TAURUS_pav and TAURUS_mix that, combined, perform the configuration mixing of symmetry-projected real general Bogoliubov quasiparticle states represented in a spherical harmonic oscillator basis. The model space considered is invariant under spatial and isospin rotations but no specific set of orbits is assumed such that the codes can carry out both valence-space and no-core calculations. In addition, no number parity is assumed for the Bogoliubov quasiparticle states such that the codes can be used to describe even-even, odd-even and odd-odd nuclei. To demonstrate the potential of the codes, we perform an example no-core calculation of $^{24}$Mg using a modern microscopic interaction.

nucl-th↗

arXiv2023

The shape of gold

Having a detailed theoretical knowledge of the low-energy structure of the heavy odd-mass nucleus $^{197}$Au is of prime interest as the structure of this isotope represents an important input to theoretical simulations of collider experiments involving gold ions performed worldwide at relativistic energies. In the present article, therefore, we report on new results on the structure of $^{197}$Au obtained from state-of-the-art multi-reference energy density functional (MR-EDF) calculations. Our MR-EDF calculations were realized using the Skyrme-type pseudo-potential SLyMR1, and include beyond mean-field correlations through the mixing, in the spirit of the Generator Coordinate Method (GCM), of particle-number and angular-momentum projected triaxially deformed Bogoliubov quasi-particle states. Comparison with experimental data shows that the model gives a reasonable description of $^{197}$Au with in particular a good agreement for most of the spectroscopic properties of the $3/2_1^+$ ground state. From the collective wave function of the correlated state, we compute an average deformation $\bar{\beta}(3/2_1^+)=0.13$ and $\bar{\gamma}(3/2_1^+)=40^\circ$ for the ground state. We use this result to construct an intrinsic shape of $^{197}$Au representing a microscopically-motivated input for precision simulations of the associated collider processes. We discuss, in particular, how the triaxiality of this nucleus is expected to impact $^{197}$Au+$^{197}$Au collision experiments at ultrarelativistic energy.

nucl-th↗

arXiv2022

Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart

High-energy nuclear collisions encompass three key stages: the structure of the colliding nuclei informed by low-energy nuclear physics, the initial condition (IC) leading to the formation of quark-gluon plasma (QGP), and the hydrodynamic expansion and hadronization of the QGP leading to final-state hadrons observed experimentally. Recent advances in experimental and theoretical methods have ushered in a precision era, enabling an increasingly accurate understanding of these stages. However, most approaches involve simultaneously determining both QGP properties and initial conditions from a single collision system, creating complexity due to the coupled contributions of various stages to the final-state observables. To avoid this, we propose leveraging known knowledge of low-energy nuclear structure and hydrodynamic observables to constrain the IC independently. By conducting comparative studies of collisions involving isobar-like nuclei - species with similar mass numbers but different structures - we disentangle the initial condition's impacts from the QGP properties. This approach not only refines our understanding of the IC but also turns high-energy experiments into a precision tool for imaging nuclear structures, offering insights that complement traditional low-energy approaches. Opportunities for carrying out such comparative experiments at the LHC and other facilities could significantly advance both high-energy and low-energy nuclear physics. Additionally, this approach has implications for the future EIC. While the possibilities are extensive, we focus on selected proposals that could benefit both the high-energy and low-energy nuclear physics communities. Originally prepared as input for the long-range plan of U.S. nuclear physics, this white paper reflects the status as of September 2022, with a brief update on developments since then.

nucl-ex↗

arXiv2022

Structure of $^{128,129,130}$Xe through multi-reference energy density functional calculations

Recently, values for the Kumar quadrupole deformation parameters of the nucleus $^{130}$Xe have been computed from the results of a Coulomb excitation experiment, indicating that this xenon isotope has a prominent triaxial ground state. Within a different context, it was recently argued that the analysis of particle correlations in the final states of ultra-relativistic heavy-ion collisions performed at the Large Hadron Collider (LHC) points to a similar structure for the adjacent isotope, $^{129}$Xe. In the present work, we report on state-of-the-art multi-reference energy density functional calculations that combine projection on proton and neutron number as well as angular momentum with shape mixing for the three isotopes $^{128,129,130}$Xe using the Skyrme-type pseudo-potential SLyMR1. Exploring the triaxial degree of freedom, we demonstrate that the ground states of all three isotopes display a very pronounced triaxial structure. Moreover, comparison with experimental results shows that the calculations reproduce fairly well the low-energy excitation spectrum of the two even-mass isotopes. By contrast, the calculation of $^{129}$Xe reveals some deficiencies of the effective interaction.

nucl-th↗

arXiv2021

Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT

In spite of missing dynamical correlations, the projected generator coordinate method (PGCM) was recently shown to be a suitable method to tackle the low-lying spectroscopy of complex nuclei. Still, describing absolute binding energies and reaching high accuracy eventually requires the inclusion of dynamical correlations on top of the PGCM. In this context, the present work discusses the first realistic results of a novel multi-reference perturbation theory (PGCM-PT) that can do so within a symmetry-conserving scheme for both ground and low-lying excited states. First, proof-of-principle calculations in a small ($e_{\mathrm{max}}=4$) model space demonstrate that exact binding energies of closed- (\nucl{O}{16}) and open-shell (\nucl{O}{18}, \nucl{Ne}{20}) nuclei are reproduced within $0.5-1.5\%$ at second order, i.e. through PGCM-PT(2). Moreover, profiting from the pre-processing of the Hamiltonian via multi-reference in-medium similarity renormalization group transformations, PGCM-PT(2) can reach converged values within smaller model spaces than with an unevolved Hamiltonian. Doing so, dynamical correlations captured by PGCM-PT(2) are shown to bring essential corrections to low-lying excitation energies that become too dilated at leading order, i.e., at the strict PGCM level. The present work is laying the foundations for a better understanding of the optimal way to grasp static and dynamical correlations in a consistent fashion, with the aim of accurately describing ground and excited states of complex nuclei via ab initio many-body methods.

nucl-th↗

arXiv2021

Multi-reference many-body perturbation theory for nuclei II -- Ab initio study of neon isotopes via PGCM and IM-NCSM calculations

The neon isotopic chain displays a rich phenomenology, ranging from clustering in the ground-state of the self-conjugate doubly open-shell stable $^{20}$Ne isotope to the physics of the island of inversion around the neutron-rich $^{30}$Ne isotope. This second (i.e. Paper II) of the present series proposes an extensive ab initio study of neon isotopes based on two complementary many-body methods, i.e. the quasi-exact in-medium no-core shell model (IM-NCSM) and the projected generator coordinate method (PGCM) that is ideally suited to capturing strong static correlations associated with shape deformation and fluctuations. Calculations employ a state-of-the-art generation of chiral effective field theory Hamiltonians and evaluate the associated systematic uncertainties. In spite of missing so-called dynamical correlations, which can be added via the multi-reference perturbation theory proposed in the first paper (i.e. Paper I) of the present series, the PGCM is shown to be a suitable method to tackle the low-lying spectroscopy of complex nuclei. Still, describing the physics of the island of inversion constitutes a challenge that seems to require the inclusion of dynamical correlations. This is addressed in the third paper (i.e. Paper III) of the present series.

nucl-th↗

arXiv2021

Evidence of the triaxial structure of $\boldsymbol{^{129}}$Xe at the Large Hadron Collider

The interpretation of the emergent collective behaviour of atomic nuclei in terms of deformed intrinsic shapes [1] is at the heart of our understanding of the rich phenomenology of their structure, ranging from nuclear energy to astrophysical applications across a vast spectrum of energy scales. A new window onto the deformation of nuclei has been recently opened with the realization that nuclear collision experiments performed at high-energy colliders, such as the CERN Large Hadron Collider (LHC), enable experimenters to identify the relative orientation of the colliding ions in a way that magnifies the manifestations of their intrinsic deformation [2]. Here we apply this technique to LHC data on collisions of $^{129}$Xe nuclei [3-5] to exhibit the first evidence of non-axiality in the ground state of ions collided at high energy. We predict that the low-energy structure of $^{129}$Xe is triaxial (a spheroid with three unequal axes), and show that such deformation can be determined from high-energy data. This result demonstrates the unique capabilities of precision collider machines such as the LHC as new means to perform imaging of the collective structure of atomic nuclei.

nucl-th↗

arXiv2021

Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell

We study the ability of variational approaches based on self-consistent mean-field and beyond-mean-field methods to reproduce exact energies and electromagnetic properties of the nuclei defined within the $sd$-shell valence space using the non-trivial USD Hamiltonian. In particular, Hartree-Fock-Bogoliubov (HFB), variation after particle-number projection (VAPNP) and projected generator coordinate methods (PGCM) are compared to exact solutions {obtained by} the full diagonalization of the Hamiltonian. We analyze the role played by the proton-neutron ($pn$) mixing as well as the quadrupole and pairing degrees of freedom (including both isoscalar and isovector channels) in the description of the spectra of even-even, even-odd and odd-odd nuclei in the whole $sd$-shell.

nucl-th↗

arXiv2021

In-medium $k$-body reduction of $n$-body operators

The computational cost of ab initio nuclear structure calculations is rendered particularly acute by the presence of (at least) three-nucleon interactions. This feature becomes especially critical now that many-body methods aim at extending their reach beyond mid-mass nuclei. Consequently, state-of-the-art ab initio calculations are typically performed while approximating three-nucleon interactions in terms of effective, i.e. system-dependent, zero-, one- and two-nucleon operators. While straightforward in doubly closed-shell nuclei, existing approximation methods based on normal-ordering techniques involve either two- and three-body density matrices or a symmetry-breaking one-body density matrix in open-shell systems. In order to avoid such complications, a simple, flexible, universal and accurate approximation technique involving the convolution of the initial operator with a sole symmetry-invariant one-body matrix is presently formulated and tested numerically. Employed with a low-resolution Hamiltonian, the novel approximation method is shown to induce errors below $2-3\%$ across a large range of nuclei, observables and many-body methods.

nucl-th↗