Global Sensitivity Analysis of Bulk Properties of an Atomic Nucleus

Electromagnetic properties of nuclei from first principles: a case for synergies between experiment and theory

One of the overarching goals in nuclear science is to understand how the nuclear chart emerges from the underlying fundamental interactions. The description of the structure of nuclei from first principles, using ab initio methods for the solution of the many-nucleon problem with inputs from chiral effective field theory, has advanced dramatically over the past two decades. We present an overview over the available ab initio tools with a specific emphasis on electromagnetic observables, such as multipole moments and transition strengths. These observables still pose a challenge for ab initio theory and are one of the most exciting domains to exploit synergies with modern experiments. Precise experimental data are vital for the validation of the theory predictions and the refinement of ab initio methods. We discuss some of the past and future experimental efforts highlighting these synergies. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Floating Block Method for Quantum Monte Carlo Simulations

Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. These new applications require something that is missing from the published literature, an efficient quantum Monte Carlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of ^{4}He, ^{8}Be, ^{12}C, and ^{16}O nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

First observation of 28O

Subjecting a physical system to extreme conditions is one of the means often used to obtain a better understanding and deeper insight into its organization and structure. In the case of the atomic nucleus, one such approach is to investigate isotopes that have very different neutron-to-proton (N/Z) ratios than in stable nuclei. Light, neutron-rich isotopes exhibit the most asymmetric N/Z ratios and those lying beyond the limits of binding, which undergo spontaneous neutron emission and exist only as very short-lived resonances (about 10-21 s), provide the most stringent tests of modern nuclear-structure theories. Here we report on the first observation of 28O and 27O through their decay into 24O and four and three neutrons, respectively. The 28O nucleus is of particular interest as, with the Z = 8 and N = 20 magic numbers1,2, it is expected in the standard shell-model picture of nuclear structure to be one of a relatively small number of so-called 'doubly magic' nuclei. Both 27O and 28O were found to exist as narrow, low-lying resonances and their decay energies are compared here to the results of sophisticated theoretical modelling, including a large-scale shell-model calculation and a newly developed statistical approach. In both cases, the underlying nuclear interactions were derived from effective field theories of quantum chromodynamics. Finally, it is shown that the cross-section for the production of 28O from a 29F beam is consistent with it not exhibiting a closed N = 20 shell structure.

Reduced basis surrogates for quantum spin systems based on tensor networks

Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on matrix-product-state calculations. Once the reduced basis has been obtained, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

Accelerated coupled cluster calculations with Procrustes orbital interpolation

The coupled cluster method is considered a gold standard in quantum chemistry, reliably giving energies that are exact within chemical accuracy (1.6 mhartree). However, even in the coupled cluster single-double (CCSD) approximation, where the cluster operator is truncated to include only single and double excitations, the method scales as O(N⁶) in the number of electrons, and the cluster operator needs to be solved for iteratively, increasing the computation time. Inspired by eigenvector continuation, we present here an algorithm making use of the Gaussian processes that provides an improved initial guess for the coupled cluster amplitudes. The cluster operator is written as a linear combination of sample cluster operators that are obtained at particular sample geometries. By reusing the cluster operators from previous calculations in that way, it is possible to obtain a start guess for the amplitudes that surpasses both MP2 guesses and "previous geometry"-guesses in terms of the number of necessary iterations. As this improved guess is very close to the exact cluster operator, it can be used directly to calculate the CCSD energy to chemical accuracy, giving approximate CCSD energies scaling as O(N⁵).

A clustering method for small scRNA-seq data based on subspace and weighted distance

Background

Identifying the cell types using unsupervised methods is essential for scRNA-seq research. However, conventional similarity measures introduce challenges to single-cell data clustering because of the high dimensional, high noise, and high dropout.

Methods

We proposed a clustering method for small ScRNA-seq data based on Subspace and Weighted Distance (SSWD), which follows the assumption that the sets of gene subspace composed of similar density-distributing genes can better distinguish cell groups. To accurately capture the intrinsic relationship among cells or genes, a new distance metric that combines Euclidean and Pearson distance through a weighting strategy was proposed. The relative Calinski-Harabasz (CH) index was used to estimate the cluster numbers instead of the CH index because it is comparable across degrees of freedom.

Results

We compared SSWD with seven prevailing methods on eight publicly scRNA-seq datasets. The experimental results show that the SSWD has better clustering accuracy and the partitioning ability of cell groups. SSWD can be downloaded at https://github.com/ningzilan/SSWD.

Ab initio predictions link the neutron skin of 208Pb to nuclear forces

Heavy atomic nuclei have an excess of neutrons over protons, which leads to the formation of a neutron skin whose thickness is sensitive to details of the nuclear force. This links atomic nuclei to properties of neutron stars, thereby relating objects that differ in size by orders of magnitude. The nucleus 208Pb is of particular interest because it exhibits a simple structure and is experimentally accessible. However, computing such a heavy nucleus has been out of reach for ab initio theory. By combining advances in quantum many-body methods, statistical tools and emulator technology, we make quantitative predictions for the properties of 208Pb starting from nuclear forces that are consistent with symmetries of low-energy quantum chromodynamics. We explore 109 different nuclear force parameterizations via history matching, confront them with data in select light nuclei and arrive at an importance-weighted ensemble of interactions. We accurately reproduce bulk properties of 208Pb and determine the neutron skin thickness, which is smaller and more precise than a recent extraction from parity-violating electron scattering but in agreement with other experimental probes. This work demonstrates how realistic two- and three-nucleon forces act in a heavy nucleus and allows us to make quantitative predictions across the nuclear landscape.

Spectral density reconstruction with Chebyshev polynomials

Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and semiexclusive scattering cross sections in atomic nuclei and transport properties of nuclear and neutron star matter. Integral transform techniques play an important role in accessing the spectral density in a variety of nuclear systems. However, their accuracy is in practice limited by the need to perform a numerical inversion which is often ill-conditioned. In the present work we extend a recently proposed quantum algorithm which circumvents this problem. We show how to perform controllable reconstructions of the spectral density over a finite energy resolution with rigorous error estimates. An appropriate expansion in Chebyshev polynomials allows for efficient simulations also on classical computers. We apply our idea to obtain the local density of states for graphene in a magnetic field as a proof of principle. This paves the way for future applications in nuclear and condensed matter physics.

Entropy subspace separation-based clustering for noise reduction (ENCORE) of scRNA-seq data

Single-cell RNA sequencing enables us to characterize the cellular heterogeneity in single cell resolution with the help of cell type identification algorithms. However, the noise inherent in single-cell RNA-sequencing data severely disturbs the accuracy of cell clustering, marker identification and visualization. We propose that clustering based on feature density profiles can distinguish informative features from noise. We named such strategy as 'entropy subspace' separation and designed a cell clustering algorithm called ENtropy subspace separation-based Clustering for nOise REduction (ENCORE) by integrating the 'entropy subspace' separation strategy with a consensus clustering method. We demonstrate that ENCORE performs superiorly on cell clustering and generates high-resolution visualization across 12 standard datasets. More importantly, ENCORE enables identification of group markers with biological significance from a hard-to-separate dataset. With the advantages of effective feature selection, improved clustering, accurate marker identification and high-resolution visualization, we present ENCORE to the community as an important tool for scRNA-seq data analysis to study cellular heterogeneity and discover group markers.

Convergence of Eigenvector Continuation

Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to selected training values of the control parameters. The method has proven to be very efficient and accurate for interpolating and extrapolating eigenvectors. However, almost nothing is known about how the method converges, and its rapid convergence properties have remained mysterious. In this Letter, we present the first study of the convergence of eigenvector continuation. In order to perform the mathematical analysis, we introduce a new variant of eigenvector continuation that we call vector continuation. We first prove that eigenvector continuation and vector continuation have identical convergence properties and then analyze the convergence of vector continuation. Our analysis shows that, in general, eigenvector continuation converges more rapidly than perturbation theory. The faster convergence is achieved by eliminating a phenomenon that we call differential folding, the interference between nonorthogonal vectors appearing at different orders in perturbation theory. From our analysis we can predict how eigenvector continuation converges both inside and outside the radius of convergence of perturbation theory. While eigenvector continuation is a nonperturbative method, we show that its rate of convergence can be deduced from power series expansions of the eigenvectors. Our results also yield new insights into the nature of divergences in perturbation theory.

Ab Initio Computation of Charge Densities for Sn and Xe Isotopes

We present the first ab initio calculations for open-shell nuclei past the tin isotopic line, focusing on Xe isotopes as well as doubly magic Sn isotopes. We show that, even for moderately hard interactions, it is possible to obtain meaningful predictions and that the NNLO_{sat} chiral interaction predicts radii and charge density distributions close to the experiment. We then make a new prediction for ^{100}Sn. This paves the way for ab initio studies of exotic charge density distributions at the limit of the present ab initio mass domain, where experimental data is becoming available. The present study closes the gap between the largest isotopes reachable by ab initio methods and the smallest exotic nuclei accessible to electron scattering experiments.

Laser spectroscopy of indium Rydberg atom bunches by electric field ionization

This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over previous non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions in the indium atom from the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2\text {5d}\,^2\text {D}_{5/2}$$\end{document}5s25d2D5/2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2\text {5d}\,^2\text {D}_{3/2}$$\end{document}5s25d2D3/2 states to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2n$$\end{document}5s2np \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}2P and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2n\text {f}\,^2$$\end{document}5s2nf2F Rydberg states, up to a principal quantum number of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=72$$\end{document}n=72. The extracted Rydberg level energies were used to re-evaluate the ionization potential of the indium atom to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$46,670.107(4)\,\hbox {cm}^{-1}$$\end{document}46,670.107(4)cm-1. The nuclear magnetic dipole and nuclear electric quadrupole hyperfine structure constants and level isotope shifts of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2\text {5d}\,^2\text {D}_{5/2}$$\end{document}5s25d2D5/2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2\text {5d}\,^2\text {D}_{3/2}$$\end{document}5s25d2D3/2 states were determined for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{113,115}$$\end{document}113,115In. The results are compared to calculations using relativistic coupled-cluster theory. A good agreement is found with the ionization potential and isotope shifts, while disagreement of hyperfine structure constants indicates an increased importance of electron correlations in these excited atomic states. With the aim of further increasing the detection sensitivity for measurements on exotic isotopes, a systematic study of the field-ionization arrangement implemented in the work was performed at the same time and an improved design was simulated and is presented. The improved design offers increased background suppression independent of the distance from field ionization to ion detection.