arXiv subjects

Vittorio Somà

Publications and source records attributed to Vittorio Somà.

27 records · Page 2Linked to original sources

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.

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arXiv2021

Moving away from singly-magic nuclei with Gorkov Green's function theory

Ab initio calculations of bulk nuclear properties (ground-state energies, root mean square charge radii and charge density distributions) are presented for seven complete isotopic chains around calcium, from argon to chromium. Calculations are performed within the Gorkov self-consistent Green's function approach at second order and make use of two state-of-the-art two- plus three-nucleon Hamiltonians, $NN$+$3N\text{(lnl)}$ and NNLO$_{\text{sat}}$. An overall good agreement with available experimental data is found, in particular for differential energies (charge radii) when the former (latter) interaction is employed. Remarkably, neutron magic numbers $N=28,32,34$ emerge and evolve following experimental trends. In contrast, pairing gaps are systematically underestimated. General features of the isotopic dependence of charge radii are also reproduced, as well as charge density distributions. A deterioration of the theoretical description is observed for certain nuclei and ascribed to the inefficient account of (static) quadrupole correlation in the present many-body truncation scheme. In order to resolve these limitations, we advocate the extension of the formalism towards incorporating breaking of rotational symmetry or, alternatively, performing a stochastic sampling of the self-energy.

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arXiv2021

Importance truncation in non-perturbative many-body techniques

Expansion many-body methods correspond to solving complex tensor networks. The (iterative) solving of the network and the (repeated) storage of the unknown tensors requires a computing power growing polynomially with the size of basis of the one-body Hilbert space one is working with. Thanks to current computer capabilities, ab initio calculations of nuclei up to mass $A\sim100$ delivering a few percent accuracy are routinely feasible today. However, the runtime and memory costs become quickly prohibitive as one attempts (possibly at the same time) (i) to reach out to heavier nuclei, (ii) to employ symmetry-breaking reference states to access open-shell nuclei and (iii) to aim for yet a greater accuracy. The challenge is particularly exacerbated for non-perturbative methods involving the repeated storage of (high-rank) tensors obtained via iterative solutions of non-linear equations. The present work addresses the formal and numerical implementations of so-called importance truncation (IT) techniques within the frame of one particular non-perturbative expansion method, i.e., Gorkov Self-Consistent Green's Function (GSCGF) theory, with the goal to eventually overcome above-mentioned limitations. By a priori truncating irrelevant tensor entries, IT techniques are shown to reduce the storage to less than 1% of its original cost in realistic GSCGF calculations performed at the ADC(2) level while maintaining a 1% accuracy on the correlation energy. The future steps will be to extend the present development to the next, e.g., ADC(3), truncation level and to SCGF calculations applicable to doubly open-shell nuclei.

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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.

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arXiv2021

Accessing the shape of atomic nuclei with relativistic collisions of isobars

Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present in particular different quadrupole deformations. We show that even small differences in these deformations can be probed by relativistic nuclear collisions experiments, where they manifest as deviations from unity in the ratios of elliptic flow coefficients taken between isobaric systems. Collider experiments with isobars represent, thus, a unique means to obtain quantitative information about the geometric shape of atomic nuclei.

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arXiv2020

Bogoliubov many-body perturbation theory under constraint

In order to solve the A-body Schrödinger equation both accurately and efficiently for open-shell nuclei, a novel many-body method coined as Bogoliubov many-body perturbation theory (BMBPT) was recently formalized and applied at low orders. Based on the breaking of U(1) symmetry associated with particle-number conservation, this perturbation theory must operate under the constraint that the average number of particles is self-consistently adjusted at each perturbative order. The corresponding formalism is presently detailed with the goal to characterize the behavior of the associated Taylor series. BMBPT is, thus, investigated numerically up to high orders at the price of restricting oneself to a small, i.e. schematic, portion of Fock space. While low-order results only differ by 2 - 3 % from those obtained via a configuration interaction (CI) diagonalization, the series is shown to eventually diverge. The application of a novel resummation method coined as eigenvector continuation further increase the accuracy when built from low-order BMBPT corrections and quickly converges towards the CI result when applied at higher orders. Furthermore, the numerically-costly self-consistent particle number adjustment procedure is shown to be safely bypassed via the use of a computationally cheap a posteriori correction method. Eventually, the present work validates the fact that low order BMBPT calculations based on an a posteriori (average) particle number correction deliver controlled results and demonstrates that they can be optimally complemented by the eigenvector continuation method to provide results with sub-percent accuracy. This approach is, thus, planned to become a workhorse for realistic ab initio calculations of open-shell nuclei in the near future.

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arXiv2020

Self-consistent Green's function theory for atomic nuclei

Nuclear structure theory has recently gone through a major renewal with the development of ab initio techniques that can be applied to a large number of atomic nuclei, well beyond the light sector that had been traditionally targeted in the past. Self-consistent Green's function theory is one among these techniques. The present work aims to give an overview of the self-consistent Green's function approach for atomic nuclei, including examples of recent applications and a discussion on the perspectives for extending the method to nuclear reactions, doubly open-shell systems and heavy nuclei.

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arXiv2020

Examining the $N$ = 28 shell closure through high-precision mass measurements of $^{46-48}$Ar

The strength of the $N$ = 28 magic number in neutron-rich argon isotopes is examined through high-precision mass measurements of $^{46-48}$Ar, performed with the ISOLTRAP mass spectrometer at ISOLDE/CERN. The new mass values are up to 90 times more precise than previous measurements. While they suggest the persistence of the $N$ = 28 shell closure for argon, we show that this conclusion has to be nuanced in light of the wealth of spectroscopic data and theoretical investigations performed with the \emph{SDPF-U} phenomenological shell model interaction. Our results are also compared with \emph{ab initio} calculations using the Valence Space In-Medium Similarity Renormalization Group and the Self-Consistent Green's Function approaches. Both calculations provide a very good account of mass systematics at and around $Z$ = 18 and, generally, a consistent description of the physics in this region. This combined analysis indicates that $^{46}$Ar is the transition between the closed-shell $^{48}$Ca and collective $^{44}$S.

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arXiv2019

Improved many-body expansions from eigenvector continuation

Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment of microscopic fermionic systems, it is desirable to obtain accurate results through low-order perturbation theory. In atomic nuclei however, effects such as strong short-range repulsion between nucleons can spoil the convergence of the expansion and make the reliability of perturbation theory unclear. Mathematicians have devised an extensive machinery to overcome the problem of divergent expansions by making use of so-called resummation methods. In large-scale many-body applications such schemes are often of limited use since no a priori analytical knowledge of the expansion is available. We present here eigenvector continuation as an alternative resummation tool that is both efficient and reliable because it is based on robust and simple mathematical principles.

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