Nuclear Structure Observables Research Articles

Ab initio symmetry-adapted emulator for studying emergent collectivity and clustering in nuclei

We discuss emulators from the ab initio symmetry-adapted no-core shell-model framework for studying the formation of alpha clustering and collective properties without effective charges. We present a new type of an emulator, one that utilizes the eigenvector continuation technique but is based on the use of symplectic symmetry considerations. This is achieved by using physically relevant degrees of freedom, namely, the symmetry-adapted basis, which exploits the almost perfect symplectic symmetry in nuclei. Specifically, we study excitation energies, point-proton root-mean-square radii, along with electric quadrupole moments and transitions for 6Li and 12C. We show that the set of parameterizations of the chiral potential used to train the emulators has no significant effect on predictions of dominant nuclear features, such as shape and the associated symplectic symmetry, along with cluster formation, but slightly varies details that affect collective quadrupole moments, asymptotic normalization coefficients, and alpha partial widths up to a factor of two. This makes these types of emulators important for further constraining the nuclear force for high-precision nuclear structure and reaction observables.

A Brief Account of Steven Weinberg’s Legacy in ab initio Many-Body Theory

In this contribution to the special issue "Celebrating 30 years of Steven Weinberg's papers on Nuclear Forces from Chiral Lagrangians," we emphasize the important role chiral effective field theory has played in leading nuclear physics into a precision era. To this end, we share our perspective on a few of the recent advances made in ab initio calculations of nuclear structure and nuclear matter observables, as well as Bayesian uncertainty quantification of effective field theory truncation errors.

From Halo Effective Field Theory to the study of breakup and transfer reactions: reliably probing the halo structure of 11Be and 15C

In this work we study one-neutron halo nuclei, and in particular 11Be and 15C, which can be seen as an inert core of 10Be or 14C plus a loosely bound neutron. During the last decades several transfer and breakup reactions involving these systems have been measured on different targets and energies. We study these processes using one single structure model for each nucleus applying the halo effective field theory (Halo EFT) at next-to-leading order NLO. The main parameters of this EFT are adjusted on nuclear-structure data and/or ab initio predictions. We model the transfer reaction within the Adiabatic Distorted Wave Approximation (ADWA) and the breakup process applying an eikonal model with a consistent treatment of nuclear and Coulomb interactions at all orders. At high energy, our model includes a proper treatment of special relativity Our theoretical calculations are in good agreement with experiment for a variety of reaction observables, thus assessing the robustness of the structure model provided for these nuclei. This new idea enables us also to reliably estimate the nuclear-structure observables that actually affect the reaction process, and hence that can be inferred from such measurements.

Extrapolation of nuclear structure observables with artificial neural networks

Calculations of nuclei are often carried out in finite model spaces. Thus, finite-size corrections enter, and it is necessary to extrapolate the computed observables to infinite model spaces. In this work, we employ extrapolation methods based on artificial neural networks for observables such as the ground-state energy and the point-proton radius. We extrapolate results from no-core shell model and coupled-cluster calculations to very large model spaces and estimate uncertainties. Training the network on different data typically yields extrapolation results that cluster around distinct values. We show that a preprocessing of input data, and the inclusion of correlations among the input data, reduces the problem of multiple solutions and yields more stable extrapolated results and consistent uncertainty estimates. We perform extrapolations for ground-state energies and radii in $^{4}$He, $^{6}$Li, and $^{16}$O, and compare the predictions from neural networks with results from infrared extrapolations.

C15 : From halo effective field theory structure to the study of transfer, breakup, and radiative-capture reactions

Aside from being a one-neutron halo nucleus, $^{15}$C is interesting because it is involved in reactions of relevance for several nucleosynthesis scenarios. The aim of this work is to analyze various reactions involving $^{15}$C, using a single structure model based on Halo EFT. To develop a Halo-EFT model of $^{15}$C at NLO, we first extract the ANC of its ground state by analyzing $^{14}$C(d,p)$^{15}$C transfer data at low energy. Using this Halo-EFT description, we study the $^{15}$C Coulomb breakup at high (605AMeV) and intermediate (68AMeV) energies using eikonal models with a consistent treatment of nuclear and Coulomb interactions at all orders, and proper relativistic corrections. Finally, we study the $^{14}$C(n,$\gamma$)$^{15}$C radiative capture. Our theoretical cross sections are in good agreement with experimental data for all reactions, thereby assessing the robustness of the $^{15}$C Halo-EFT model. Since a simple NLO description is enough to reproduce all data, the only nuclear-structure observables that matter are the binding energy and its ANC, showing that all the reactions considered are purely peripheral. In particular, it confirms the ANC value obtained for the $^{15}$C ground state: 1.59$\pm$0.06fm$^{-1}$. Our model provides also a new estimate of the radiative-capture cross section at astrophysical energy (23.3keV): 4.66$\pm$0.14$\mu$b. Including a Halo-EFT description of $^{15}$C within precise models of reactions is confirmed to be an excellent way to relate the nucleus reaction cross sections and structure. Its systematic expansion enables us to deduce which nuclear-structure observables are actually probed in the collision. From this, we can infer valuable information on both the structure of $^{15}$C and its synthesis through the $^{14}$C(n,$\gamma$)$^{15}$C radiative capture at astrophysical energies.

Sensitivities and correlations of nuclear structure observables emerging from chiral interactions

Starting from a set of different two- and three-nucleon interactions from chiral effective field theory, we use the importance-truncated no-core shell model for ab initio calculations of excitation energies as well as electric quadrupole (E2) and magnetic dipole (M1) moments and transition strengths for selected p-shell nuclei. We explore the sensitivity of the excitation energies to the chiral interactions as a first step towards and systematic uncertainty propagation from chiral inputs to nuclear structure observables. The uncertainty band spanned by the different chiral interactions is typically in agreement with experimental excitation energies, but we also identify observables with notable discrepancies beyond the theoretical uncertainty that reveal insufficiencies in the chiral interactions. For electromagnetic observables we identify correlations among pairs of E2 or M1 observables based on the ab initio calculations for the different interactions. We find extremely robust correlations for E2 observables and illustrate how these correlations can be used to predict one observable based on an experimental datum for the second observable. In this way we circumvent convergence issues and arrive at far more accurate results than any direct ab initio calculation. A prime example for this approach is the quadrupole moment of the first 2^+ state in C-12, which is predicted with an drastically improved accuracy.

Overview of jet physics with ALICE at the LHC

In these proceedings, a selection of recent results on jet physics from ALICE experiment is presented, including jet spectra, nuclear modification factors, jet structure and fragmentation observables, obtained in different collision systems (pp, p–Pb and Pb–Pb).

Interweaving of elementary modes of excitation in superfluid nuclei through particle-vibration coupling: Quantitative account of the variety of nuclear structure observables

A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In this way it is possible to probe the single-particle and collective components of the nuclear many-body wavefunction resulting from their mutual coupling and diagonalising the low-energy Hamiltonian. We address the question of how accurately such a description can account for experimental observations. It is concluded that renormalizing empirically and on equal footing bare single-particle and collective motion in terms of self-energy (mass) and vertex corrections (screening), as well as particle-hole and pairing interactions through particle-vibration coupling allows theory to provide an overall, quantitative account of the data.

In-beam spectroscopy of heavy elements

Traditionally the experimental study of heavy and superheavy elements has belonged to the realm of decay spectroscopy and nuclear reactions. Only in the past twenty years or so has it become feasible to study nuclei with Z=96 and beyond with in-beam spectroscopic techniques. Since the pioneering studies in the late 1990s, development of both instrumentation and experimental techniques has resulted in a significant lowering of the spectroscopic limit for in-beam measurements. Such measurements give access to a wide range of nuclear structure observables which in general are beyond the reach of other techniques. The current review aims to present the most recent developments and results in the field, building upon previous reviews with a similar theme.

Constraining the density slope of nuclear symmetry energy at subsaturation densities using electric dipole polarizability inPb208

Nuclear structure observables usually most effectively probe the properties of nuclear matter at subsaturation densities rather than at saturation density. We demonstrate that the electric dipole polarizibility $\alpha _ {\text{D}}$ in $^{208}$Pb is sensitive to both the magnitude $E_{\text{sym}}(\rho_{\text{c}})$ and density slope $L(\rho_{\text{c}})$ of the symmetry energy at a subsaturation cross density $\rho_{\text{c}} = 0.11$ fm$^{-3}$. Using the experimental data of $\alpha _ {\text{D}}$ in $^{208}$Pb from RCNP and the recent accurate constraint of $E_{\text{sym}}(\rho_{\text{c}})$ from the binding energy difference of heavy isotope pairs, we extract a value of $L(\rho_{\text{c}}) = 47.3 \pm 7.8$ MeV. The implication of the present constraint of $L(\rho_{\text{c}})$ to the symmetry energy at saturation density, the neutron skin thickness of $^{208}$Pb and the core-crust transition density in neutron stars is discussed.

New Horizons in Ab Initio Nuclear Structure Theory

Nuclear interactions derived within chiral effective field theory enable nuclear structure and reaction calculations solidly rooted in QCD. Using chiral two- and three-body interactions in ab initio studies of a variety of nuclear observables is, both, promising and challenging. Particularly the inclusion of chiral 3N interactions into exact and approximate many-body calculations is demanding and computationally expensive. We present recent key developments that facilitate ab initio calculations of ground and low-lying excited states of p- and sd-shell nuclei with full 3N interactions in the Importance-Truncated No-Core Shell Model using consistent Similarity Renormalization Group transformations of the NN+3N Hamiltonian. The treatment of 3N interactions without approximations allows for first studies of the dependence of nuclear-structure observables on the details of chiral interactions. Moreover, we present results for heavy nuclei obtained in Coupled Cluster calculations using a normal-ordered two-body approximation of the 3N interaction.

Constraining the 0ν2β matrix elements by nuclear structure observables

The discovery that neutrinos have finite rest mass has led to renewed interest in neutrinoless double beta decay. The development of large-scale experiments to search for neutrinoless double beta decay has increased the probability of a credible observation of the process in the near future. The reliability of calculations of the associated nuclear matrix elements is likely soon to become a critical issue. In this paper experimental techniques that access properties of the ground-state wave functions of double-beta-decay candidates, the occupancies of valence single-particle orbitals and pairing correlations, are summarized and the experimental data for candidate nuclei are reviewed. The results are discussed in relation to questions concerning which aspects of nuclear structure may play an important role in determining the nuclear matrix elements for neutrinoless double beta decay.

Nuclear Structure in the UCOM Framework: From Realistic Interactions to Collective Excitations

The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant short-range central and tensor correlations are described explicitly by a unitary transformation. The application of UCOM in the context of the no-core shell model provides insight into the interplay between dominant short-range and residual long-range correlations in the nuclear many-body problem. The use of the correlated interaction within Hartree-Fock, many-body perturbation theory, and Random Phase Approximation gives access to various nuclear structure observables throughout the nuclear chart.

Breakup and Electromagnetic Response of Light Weakly-Bound Dicluster Systems

This study is focused on the break-up and electromagnetic response of light weakly-bound dicluster nuclei. The cluster picture in the case of $ ^7$Li is shown to be a very good approximation and in this framework we calculate nuclear structure observables. We solve the Schr\"odinger equation for the relative motion both for discrete and continuum states and this automatically takes into a proper account the role of resonances. A concentration of strength in the low energy continuum, solely due to the weakly-bound nature of the bound states is seen and explained as a favourable matching between the wavelengths of the initial and final states. Finally preliminary results on form factors are briefly outlined and their microscopic derivation as well as utilization in reaction studies is discussed.

The structure of nuclear systems derived from low momentum nucleon–nucleon potentials

Various nuclear structure observables are evaluated employing low-momentum nucleon–nucleon (NN) potentials V low- k derived from the CD-Bonn and Nijmegen NN interactions V NN. By construction, the high momentum modes of the original V NN are integrated out in V low- k , with the requirement that the deuteron binding energy and low energy phase shifts of V NN are exactly reproduced. Using this interaction, we evaluate the bulk properties (binding energy and saturation density) of nuclear matter and finite nuclei, in particular their dependence on the cut-off parameter. We also study the pairing gap and the residual interaction in nuclear matter in terms of the Landau parametrization. At low and medium densities, the HF and BHF binding energies for nuclear matter calculated with the V low- k 's derived from the CD-Bonn and Nijmegen potentials are nearly identical. The pairing gaps and Landau parameters derived from V low- k are remarkably close to those given by the full-space V NN. The V low- k interactions, however, fail to reproduce the saturation property of nuclear matter at higher densities if the cut-off for the high momentum modes is assumed density independent.

Atomic Force Microscopy of the Cell Nucleus

In mammals and plants, the cell nucleus is organized in dynamic macromolecular domains involved in DNA and RNA metabolism. These domains can be visualized by light and electron microscopy and their composition analyzed by using several cytochemical approaches. They are composed of chromatin or ribonucleoprotein structures as interchromatin and perichromatin fibers and granules, coiled bodies, and nuclear bodies. In plants, DNA arrangement defines chromocentric and reticulated nuclei. We used atomic force microscopy to study the in situ structure of the plant cell nucleus. Samples of the plants Lacandonia schismatica and Ginkgo biloba were prepared as for electron microscopy and unstained semithin sections were mounted on glass slides. For comparison, we also examined entire normal rat kidney cells using the same approach. Samples were scanned with an atomic force microscope working in contact mode. Recognizable images of the nuclear envelope, pores, chromatin, and nucleolus were observed. Reticulated chromatin was observed in L. schismatica. Different textures in the nucleolus of G. biloba were also observed, suggesting the presence of nucleolar subcompartments. The observation of nuclear structure in situ with the atomic force microscope offers a new approach for the analysis of this organelle at high resolution.

Two-body correlations in nuclear systems

Correlations in the nuclear wave-function beyond the mean-field or Hartree-Fock approximation are very important to describe basic properties of nuclear structure. Various approaches to account for such correlations are described and compared to each other. This includes the holeline expansion, the coupled cluster or “exponential S” approach, the self-consistent evaluation of Greens functions, variational approaches using correlated basis functions and recent developments employing quantum Monte-Carlo techniques. Details of these correlations are explored and their sensitivity to the underlying nucleon-nucleon interaction. Special attention is paid to the attempts to investigate these correlations in exclusive nucleon knock-out experiments induced by electron scattering. Another important issue of nuclear structure physics is the role of relativistic effects as contained in phenomenological mean field models. The sensitivity of various nuclear structure observables on these relativistic features are investigated. The report includes the discussion of nuclear matter as well as finite nuclei.

Observation and analysis of rotational and nuclear hyperfine structure in bands of the red system of copper dichloride

Part of the electronic spectrum of copper dichloride, CuCl2, between 590 and 600 nm, has been recorded in the gas phase using a sample prepared at low temperatures (ca. 10 K) in a free jet expansion. Under these conditions it is possible to resolve vibrational, rotational and even hyperfine structure. Nine bands in this region have been analysed in detail. Six involve the dominant isotopomer, Cu35Cl2 and the other three the mixed form, Cu35Cl37Cl (it is not possible at this stage to identify the copper isotope). All the bands show parallel rotational structure of a linear molecule, consistent with an electronic assignment to a 2Πu–2Πg transition suggested by ab initio calculations. Seven of the bands are assigned as 2Π3/2–2Π3/2, one as 2Π1/2–2Π1/2 and the other as 2Δ5/2–2Δ5/2. The majority of the bands are thought to involve the molecule in its ground vibrational state but the last of these presumably involves excited vibrational levels in the bending vibration ν2. The Cu—Cl bond length determined from the lower-state rotational constant for Cu35Cl2 is r″0= 0.203 614(26) nm. The greater occurrence of transitions which involve the 2Π3/2 spin component suggests that this spin component is lower in energy than the 2Π1/2 component, contrary to theoretical expectations. The vibrational structure of the spectrum in the wave-length region studied is very complicated and no detailed vibrational assignments have been made. It is thought that the (0–0) band of the electronic transition lies at significantly longer wavelengths than those covered in this study.

Observation of nuclear spin-spin structure in zero and low external static magnetic fields

Observation of nuclear spin-spin structure in zero and low external static magnetic fields

Observation of nuclear quadrupole hyperfine structure in the infrared spectrum of hydrogen iodide using a tunable-diode laser

Nuclear quadrupole hyperfine structure has been observed in the 1-0 vibration-rotation band of hydrogen iodide with a tunable-diode laser. The measured splittings agree well with microwave measurements of the HI molecule. Evidence for a slight change in the iodine nuclear quadrupole coupling constant from the ground to first excited vibrational state in hydrogen iodide was found.