The rich phenomenology of quantum many-body systems such as atomic nuclei is complex to interpret. Often, the behaviour (e.g. evolution with the number of constituents) of measurable/observable ...quantities such as binding or excitation energies can be best understood based on a simplified picture involving auxiliary quantities that are not observable, i.e. whose values vary with parameters that are internal to the theoretical construction (contrarily to measurable/observable quantities). While being useful, the simplified interpretation is thus theoretical-scheme dependent. This applies, in particular, to the so-called single-nucleon shell structure based on auxiliary effective single-particle energies (ESPEs). In this context, the present work aims at (i) recalling the way to compute ESPEs out of solutions of many-body Schrödinger's equation, (ii) illustrating the use of ESPEs within the frame of state-of-the-art ab initio calculations to interpret the outcome of a recent nuclear experiment, and (iii) demonstrating the impact of several alterations on the computation of ESPEs. While the chosen alterations constitute approximations within the ab initio scheme, they are built-in when employing other theoretical constructs at play in nuclear physics. The present considerations are thus meant to empirically illustrate variations that can be expected between ESPEs computed within different (equally valid) theoretical schemes. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.The rich phenomenology of quantum many-body systems such as atomic nuclei is complex to interpret. Often, the behaviour (e.g. evolution with the number of constituents) of measurable/observable quantities such as binding or excitation energies can be best understood based on a simplified picture involving auxiliary quantities that are not observable, i.e. whose values vary with parameters that are internal to the theoretical construction (contrarily to measurable/observable quantities). While being useful, the simplified interpretation is thus theoretical-scheme dependent. This applies, in particular, to the so-called single-nucleon shell structure based on auxiliary effective single-particle energies (ESPEs). In this context, the present work aims at (i) recalling the way to compute ESPEs out of solutions of many-body Schrödinger's equation, (ii) illustrating the use of ESPEs within the frame of state-of-the-art ab initio calculations to interpret the outcome of a recent nuclear experiment, and (iii) demonstrating the impact of several alterations on the computation of ESPEs. While the chosen alterations constitute approximations within the ab initio scheme, they are built-in when employing other theoretical constructs at play in nuclear physics. The present considerations are thus meant to empirically illustrate variations that can be expected between ESPEs computed within different (equally valid) theoretical schemes. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.
We present a systematic study of both nuclear radii and binding energies in (even) oxygen isotopes from the valley of stability to the neutron drip line. Both charge and matter radii are compared to ...state-of-the-art ab initio calculations along with binding energy systematics. Experimental matter radii are obtained through a complete evaluation of the available elastic proton scattering data of oxygen isotopes. We show that, in spite of a good reproduction of binding energies, ab initio calculations with conventional nuclear interactions derived within chiral effective field theory fail to provide a realistic description of charge and matter radii. A novel version of two- and three-nucleon forces leads to considerable improvement of the simultaneous description of the three observables for stable isotopes but shows deficiencies for the most neutron-rich systems. Thus, crucial challenges related to the development of nuclear interactions remain.
A Rayleigh–Schrödinger many-body perturbation theory (MBPT) approach is introduced by making use of a particle-number-breaking Bogoliubov reference state to tackle (near-)degenerate open-shell ...fermionic systems. By choosing a reference state that solves the Hartree–Fock–Bogoliubov variational problem, the approach reduces to the well-tested Møller–Plesset, i.e., Hartree–Fock based, MBPT when applied to closed-shell systems. Due to its algorithmic simplicity, the newly developed framework provides a computationally simple yet accurate alternative to state-of-the-art non-perturbative many-body approaches. At the price of working in the quasi-particle basis associated with a single-particle basis of sufficient size, the computational scaling of the method is independent of the particle number. This paper presents the first realistic applications of the method ranging from the oxygen to the nickel isotopic chains on the basis of a modern nuclear Hamiltonian derived from chiral effective field theory.
Background: The possibility that an unconventional depletion (referred to as a “bubble”) happens in the middle of the charge density distribution of certain nuclei due to a purely quantum mechanical ...effect has attracted theoretical and experimental attention in recent years. Based on a mean-field rationale, a correlation between the occurrence of such a semibubble and an anomalously weak splitting between low angular-momentum spin-orbit partners has been further conjectured. Energy density functional and valence-space shell model calculations have been performed to identify and characterize the best candidates, among which Si 34 appears as a particularly interesting case. While the experimental determination of the charge density distribution of the unstable Si 34 is currently out of reach, ($d, p$) experiments on this nucleus have been performed recently to test the correlation between the presence of a bubble and an anomalously weak 1/2––3/2– splitting in the spectrum of Si 35as compared to S 37. Purpose: We study the potential bubble structure of Si 34 on the basis of the state-of-the-art ab initio self-consistent Green's function many-body method. Methods: We perform the first ab initio calculations of Si 34 and S 36. In addition to binding energies, the first observables of interest are the charge density distribution and the charge root-mean-square radius for which experimental data exist in S 36. The next observable of interest is the low-lying spectroscopy of Si 35 and S 37 obtained from ($d, p$) experiments along with the spectroscopy of Al 33 and P 35 obtained from knock-out experiments. The interpretation in terms of the evolution of the underlying shell structure is also provided. The study is repeated using several chiral effective field theory Hamiltonians as a way to test the robustness of the results with respect to input internucleon interactions. The convergence of the results with respect to the truncation of the many-body expansion, i.e., with respect to the many-body correlations included in the calculation, is studied in detail. We eventually compare our predictions to state-of-the-art multireference energy density functional and shell model calculations. Results: The prediction regarding the (non)existence of the bubble structure in Si 34 varies significantly with the nuclear Hamiltonian used. Yet, demanding that the experimental charge density distribution and the root-mean-square radius of S 36 be well reproduced, along with Si 34 and S 36 binding energies, only leaves the NNLO sat Hamiltonian as a serious candidate to perform this prediction. In this context, a bubble structure, whose fingerprint should be visible in an electron scattering experiment of Si 34, is predicted. Furthermore, a clear correlation is established between the occurrence of the bubble structure and the weakening of the 1/2––3/2– splitting in the spectrum of Si 35 as compared to S 37. Conclusions: The occurrence of a bubble structure in the charge distribution of Si 34 is convincingly established on the basis of state-of-the-art ab initio calculations. This prediction will have to be reexamined in the future when improved chiral nuclear Hamiltonians are constructed. On the experimental side, present results act as a strong motivation to measure the charge density distribution of Si 34 in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform one-neutron removal on Si 34 and S 36 in order to further test our theoretical spectral strength distributions over a wide energy range.
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
+
3
N
(lnl)
and NNLO
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 correlations 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.
A precision mass investigation of the neutron-rich titanium isotopes ^{51-55}Ti was performed at TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). The range of the measurements covers the ...N=32 shell closure, and the overall uncertainties of the ^{52-55}Ti mass values were significantly reduced. Our results conclusively establish the existence of the weak shell effect at N=32, narrowing down the abrupt onset of this shell closure. Our data were compared with state-of-the-art ab initio shell model calculations which, despite very successfully describing where the N=32 shell gap is strong, overpredict its strength and extent in titanium and heavier isotones. These measurements also represent the first scientific results of TITAN using the newly commissioned multiple-reflection time-of-flight mass spectrometer, substantiated by independent measurements from TITAN's Penning trap mass spectrometer.
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 behaviour 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 increases 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.
•Low-order BMBPT is validated as a cheap workhorse for singly open-shell nuclei.•Eigenvector continuation presents great potential to achieve high-accuracy results.•Particle-number constraint can be bypassed by low-cost a posteriori correction.
Current models of inter-nucleon interactions are built within the frame of Effective Field Theories (EFTs). Contrary to traditional nuclear potentials, EFT interactions require a renormalization of ...their parameters in order to derive meaningful estimations of the observables. In this paper, a renormalization procedure is designed in connection with many-body approximations applicable to large-
A
systems and formulated within the frame of many-body perturbation theory. The procedure is shown to generate counterterms that are independent of the targeted
A
-body sector. As an example, the procedure is applied to the random phase approximation. This work constitutes one step towards the design of a practical EFT for many-body systems.
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