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In order to relate nanoparticle properties to function, fast and detailed particle characterization, is needed. The ability to characterize nanoparticle samples using optical microscopy techniques has drastically improved over the past few decades; consequently, there are now numerous microscopy methods available for detailed characterization of particles with nanometric size. However, there is currently no ``one size fits all'' solution to the problem of nanoparticle characterization. Instead, since the available techniques have different detection limits and deliver related but different quantitative information, the measurement and analysis approaches need to be selected and adapted for the sample at hand. In this tutorial, we review the optical theory of single particle scattering and how it relates to the differences and similarities in the quantitative particle information obtained from commonly used microscopy techniques, with an emphasis on nanometric (submicron) sized dielectric particles. Particular emphasis is placed on how the optical signal relates to mass, size, structure, and material properties of the detected particles and to its combination with diffusivity-based particle sizing. We also discuss emerging opportunities in the wake of new technology development, with the ambition to guide the choice of measurement strategy based on various challenges related to different types of nanoparticle samples and associated analytical demands.

Traditional single-nanoparticle sizing using optical microscopy techniques assesses size via the diffusion constant, which requires suspended particles in a medium of known viscosity. However, these assumptions are typically not fulfilled in complex natural sample environments. Here, we introduce dual-angle interferometric scattering microscopy (DAISY), enabling optical quantification of both size and polarizability of individual nanoparticles without requiring a priori information regarding the surrounding media or super-resolution imaging. DAISY achieves this by combining the information contained in concurrently measured forward and backward scattering images through twilight off-axis holography and interferometric scattering (iSCAT). Going beyond particle size and polarizability, single-particle morphology can be deduced from the fact that hydrodynamic radius relates to the outer particle radius while the scattering-based size estimate depends on the internal mass distribution of the particles. We demonstrate this by optically differentiating biomolecular fractal aggregates from spherical particles in fetal bovine serum at the single particle level.

The interaction between metallic and biological nanoparticles (NPs) is widely used in various biotechnology and biomedical applications. However, detailed characterization of this type of interaction is challenging due to a lack of high-throughput techniques that can quantify both size and composition of suspended NP complexes. Here, we introduce a technique called ``twilight nanoparticle tracking analysis'' (tNTA) and demonstrate that it provides a quantitative relationship between the measured optical signal and the composition of suspended dielectric-metal NP complexes. We assess the performance of tNTA by analyzing the selective binding of tannic acid-modified gold nanoparticles (TaAuNPs) to herpes simplex viruses (HSV). Our results show that TaAuNPs bind specifically to HSV without causing substantial changes in the size or refractive index of the virus, suggesting that the binding does not cause virus disruption. Instead, the anti-viral properties of TaAuNPs appear to stem from direct particle binding to the virus.

Particle tracking is a fundamental task in digital microscopy. Recently, machine-learning approaches have made great strides in overcoming the limitations of more classical approaches. The training of state-of-the-art machine-learning methods almost universally relies on either vast amounts of labeled experimental data or the ability to numerically simulate realistic datasets. However, the data produced by experiments are often challenging to label and cannot be easily reproduced numerically. Here, we propose a novel deep-learning method, named LodeSTAR (Low-shot deep Symmetric Tracking And Regression), that learns to tracks objects with sub-pixel accuracy from a single unlabeled experimental image. This is made possible by exploiting the inherent roto-translational symmetries of the data. We demonstrate that LodeSTAR outperforms traditional methods in terms of accuracy. Furthermore, we analyze challenging experimental data containing densely packed cells or noisy backgrounds. We also exploit additional symmetries to extend the measurable particle properties to the particle's vertical position by propagating the signal in Fourier space and its polarizability by scaling the signal strength. Thanks to the ability to train deep-learning models with a single unlabeled image, LodeSTAR can accelerate the development of high-quality microscopic analysis pipelines for engineering, biology, and medicine., Comment: 19 pages, 4 figures

The modeling of nuclear reactions and radioactive decays in astrophysical or earth-based conditions requires detailed knowledge of the masses of essentially all nuclei. Microscopic mass models based on nuclear energy density functionals (EDFs) can be descriptive and used to provide this information. The concept of intrinsic symmetry breaking is central to the predictive power of EDF approaches, yet is generally not exploited to the utmost by mass models because of the computational demands of adjusting up to about two dozen parameters to thousands of nuclear masses. We report on a first step to bridge the gap between what is presently feasible for studies of individual nuclei and large-scale models: we present a new Skyrme-EDF-based model that was adjusted using a three-dimensional coordinate-space representation, for the first time allowing for both axial and triaxial deformations during the adjustment process. To compensate for the substantial increase in computational cost brought by the latter, we have employed a committee of multilayer neural networks to model the objective function in parameter space and guide us towards the overall best fit. The resulting mass model BSkG1 is computed with the EDF model independently of the neural network. It yields a root mean square (rms) deviation on the 2457 known masses of 741 keV and an rms deviation on the 884 measured charge radii of 0.024 fm., Comment: 25 pages, 15 figures

The characterisation of the physical properties of nanoparticles in their native environment plays a central role in a wide range of fields, from nanoparticle-enhanced drug delivery to environmental nanopollution assessment. Standard optical approaches require long trajectories of nanoparticles dispersed in a medium with known viscosity to characterise their diffusion constant and, thus, their size. However, often only short trajectories are available, while the medium viscosity is unknown, e.g., in most biomedical applications. In this work, we demonstrate a label-free method to quantify size and refractive index of individual subwavelength particles using two orders of magnitude shorter trajectories than required by standard methods, and without assumptions about the physicochemical properties of the medium. We achieve this by developing a weighted average convolutional neural network to analyse the holographic images of the particles. As a proof of principle, we distinguish and quantify size and refractive index of silica and polystyrene particles without prior knowledge of solute viscosity or refractive index. As an example of an application beyond the state of the art, we demonstrate how this technique can monitor the aggregation of polystyrene nanoparticles, revealing the time-resolved dynamics of the monomer number and fractal dimension of individual subwavelength aggregates. This technique opens new possibilities for nanoparticle characterisation with a broad range of applications from biomedicine to environmental monitoring.

The phenomenon of reflection-asymmetric nuclear shapes is relevant to nuclear stability, nuclear spectroscopy, nuclear decays and fission, and the search for new physics beyond the standard model. Global surveys of ground-state octupole deformation, performed with a limited number of models, suggest that the number of pear-shaped isotopes is fairly limited across the nuclear landscape. We carry out global analysis of ground-state octupole deformations for particle-bound even-even nuclei with $Z \leq 110$ and $N \leq 210$ using nuclear density functional theory (DFT) with several non-relativistic and covariant energy density functionals. In this way, we can identify the best candidates for reflection-asymmetric shapes. The calculations are performed in the frameworks of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory and relativistic Hartree-Bogoliubov theory using DFT solvers employing harmonic oscillator basis expansion. We consider five Skyrme and four covariant energy density functionals. We predict several regions of ground-state octupole deformation. In addition to the "traditional" regions of neutron-deficient actinide nuclei around $^{224}$Ra and neutron-rich lanthanides around $^{146}$Ba, we identified vast regions of reflecion-asymmetric shapes in very neutron-rich nuclei around $^{200}$Gd and $^{288}$Pu, as well as in several nuclei around $^{112}$Ba. Our analysis suggests several promising candidates with stable ground-state octupole deformation, primarily in the neutron-deficient actinide region, that can be reached experimentally. Detailed comparison between Skyrme and covariant models is performed., Comment: 13 pages, 7 figures

The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a variety of applications, including the modeling of stellar nucleosynthesis. We use microscopic nuclear mass models and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines. We apply nuclear density functional theory with several energy density functionals. To account for uncertainties, Bayesian Gaussian processes are trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allows to account for systematic and statistical uncertainties and propagate them to extrapolative predictions. We characterize the drip-line regions where the probability that the nucleus is particle-bound decreases from $1$ to $0$. In these regions, we provide quantified predictions for one- and two-nucleon separation energies. According to our Bayesian model averaging analysis, 7759 nuclei with $Z\leq 119$ have a probability of existence $\geq 0.5$. The extrapolations obtained in this study will be put through stringent tests when new experimental information on exotic nuclei becomes available. In this respect, the quantified landscape of nuclear existence obtained in this study should be viewed as a dynamical prediction that will be fine-tuned when new experimental information and improved global mass models become available.

The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the proton drip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protons from escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of proton emitters poses an appreciable challenge for nuclear theory as it often involves far extrapolations. In addition, significant discrepancies between nuclear models in the proton-rich territory call for quantified predictions. With the help of Bayesian methodology, we mix a family of nuclear mass models corrected with statistical emulators trained on the experimental mass measurements, in the proton-rich region of the nuclear chart. Separation energies were computed within nuclear density functional theory using several Skyrme and Gogny energy density functionals. We also considered mass predictions based on two models used in astrophysical studies. Quantified predictions were obtained for each model using Bayesian Gaussian processes trained on separation-energy residuals and combined via Bayesian model averaging. We obtained a good agreement between averaged predictions of statistically corrected models and experiment. In particular, we quantified model results for one- and two-proton separation energies and derived probabilities of proton emission. This information enabled us to produce a quantified landscape of proton-rich nuclei. The most promising candidates for two-proton decay studies have been identified. The methodology used in this work has broad applications to model-based extrapolations of various nuclear observables. It also provides a reliable uncertainty quantification of theoretical predictions.

Polaritons are compositional light-matter quasiparticles that have recently enabled remarkable breakthroughs in quantum and nonlinear optics, as well as in material science. Despite the enormous progress, however, a direct nanometer-scale visualization of polaritons has remained an open challenge. Here, we demonstrate that plasmon-exciton polaritons, or plexcitons, generated by a hybrid system composed of an individual silver nanoparticle and a few-layer transition metal dichalcogenide can be spectroscopically mapped with nanometer spatial resolution using electron energy loss spectroscopy in a scanning transmission electron microscope. Our experiments reveal important insights about the coupling process, which have not been reported so far. These include nanoscale variation of Rabi splitting and plasmon-exciton detuning, as well as absorption-dominated extinction signals, which in turn provide the ultimate evidence for the plasmon-exciton hybridization in the strong coupling regime. These findings pioneer new possibilities for in-depth studies of polariton-related phenomena with nanometer spatial resolution.

The region of heavy calcium isotopes forms the frontier of experimental and theoretical nuclear structure research where the basic concepts of nuclear physics are put to stringent test. The recent discovery of the extremely neutron-rich nuclei around $^{60}$Ca [Tarasov, 2018] and the experimental determination of masses for $^{55-57}$Ca (Michimasa, 2018] provide unique information about the binding energy surface in this region. To assess the impact of these experimental discoveries on the nuclear landscape's extent, we use global mass models and statistical machine learning to make predictions, with quantified levels of certainty, for bound nuclides between Si and Ti. Using a Bayesian model averaging analysis based on Gaussian-process-based extrapolations we introduce the posterior probability $p_{ex}$ for each nucleus to be bound to neutron emission. We find that extrapolations for drip-line locations, at which the nuclear binding ends, are consistent across the global mass models used, in spite of significant variations between their raw predictions. In particular, considering the current experimental information and current global mass models, we predict that $^{68}$Ca has an average posterior probability ${p_{ex}\approx76}$% to be bound to two-neutron emission while the nucleus $^{61}$Ca is likely to decay by emitting a neutron (${p_{ex}\approx 46}$ %)., Comment: Supplementary Material available upon request

New superheavy nuclei are often identified through their characteristic $\alpha$-decay energies, which requires accurate calculations of $Q_{\alpha}$ values. While many $Q_{\alpha}$ predictions are available, little is known about their uncertainties, and this makes it difficult to carry out extrapolations to yet-unknown systems. This work aims to analyze several models, compare their predictions to available experimental data, and study their performance for the unobserved $\alpha$-decay chains of $^{296}$120 and $^{298}$120, which are of current experimental interest. Our quantified results will also serve as a benchmark for future, more sophisticated statistical studies. We use nuclear superfluid Density Functional Theory (DFT) with several Skyrme energy density functionals (EDFs). To estimate systematic model uncertainties we employ uniform model averaging. We evaluated the $Q_{\alpha}$ values for even-even nuclei from Fm to $Z=120$. For well deformed nuclei between Fm and Ds, we find excellent consistency between different model predictions, and a good agreement with experiment. For transitional nuclei beyond Ds, inter-model differences grow, resulting in an appreciable systematic error. In particular, our models underestimate $Q_{\alpha}$ for the heaviest nucleus $^{294}$Og. The robustness of DFT predictions for well deformed superheavy nuclei supports the idea of using experimental $Q_{\alpha}$ values, together with theoretical predictions, as reasonable $(Z,A)$ indicators. Unfortunately, this identification method is not expected to work well in the region of deformed-to-spherical shape transition as one approaches $N=184$. The use of $Q_{\alpha}$ values in the identification of new superheavy nuclei will benefit greatly from both progress in developing new spectroscopic-quality EDFs and more sophisticated statistical techniques of uncertainty quantification., Comment: 7 pages, 6 figures

Nuclear masses play a fundamental role in understanding how the heaviest elements in the Universe are created in the $r$-process. We predict $r$-process nucleosynthesis yields using neutron capture and photodissociation rates that are based on nuclear density functional theory. Using six Skyrme energy density functionals based on different optimization protocols, we determine for the first time systematic uncertainty bands -- related to mass modeling -- for $r$-process abundances in realistic astrophysical scenarios. We find that features of the underlying microphysics make an imprint on abundances especially in the vicinity of neutron shell closures: abundance peaks and troughs are reflected in trends of neutron separation energy. Further advances in nuclear theory and experiments, when linked to observations, will help in the understanding of astrophysical conditions in extreme $r$-process sites., Comment: 7 pages, 3 figures

The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or EDF. But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy FAM based on the QRPA. To compute sum rules, we carry out contour integration of the response function in the complex-energy plane. We benchmark our results against the conventional matrix formulation of the QRPA theory, the Thouless theorem for the energy-weighted sum rule, and the dielectric theorem for the inverse energy-weighted sum rule. We demonstrate that calculated sum-rule values agree with those obtained from the matrix formulation of the QRPA. We also discuss the applicability of both the Thouless theorem about the energy-weighted sum rule and the dielectric theorem for the inverse energy-weighted sum rule to nuclear density functional theory in cases when the EDF is not based on a Hamiltonian. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. The FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used., Comment: 11 pages, 2 figures, submitted to Phys. Rev. C