Background: Besides its intrinsic value as a fundamental nuclear-structure observable, the weak-charge density of 208 Pb-a quantity that is closely related to its neutron distribution-is of fundamental importance in constraining the equation of state of neutron-rich matter.Purpose: To assess the impact that a second electroweak measurement of the weak-charge form factor of 208 Pb may have on the determination of its overall weak-charge density.Methods: Using the two putative experimental values of the form factor, together with a simple implementation of Bayes' theorem, we calibrate a theoretically sound-yet surprisingly little known-symmetrized Fermi function, that is characterized by a density and form factor that are both known exactly in closed form.Results: Using the charge form factor of 208 Pb as a proxy for its weak-charge form factor, we demonstrate that using only two experimental points to calibrate the symmetrized Fermi function is sufficient to accurately reproduce the experimental charge form factor over a significant range of momentum transfers. Conclusions:It is demonstrated that a second measurement of the weak-charge form factor of 208 Pb supplemented by a robust theoretical input in the form of the symmetrized Fermi function, would place significant constraints on the neutron distribution of 208 Pb. In turn, such constraints will become vital in the interpretation of hadronic experiments that will probe the neutron-rich skin of exotic nuclei at future radioactive beam facilities.

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We develop a complete framework for modeling general electromechanical systems in the quasi-electrostatic regime. The equations are applicable to a broad range of electrostatic problems and offer the advantage of being theoretically tractable for scaling arguments. Additionally, we show how the formalism can be used together with finite element simulations to obtain estimates for non-stationary effects such as charge accumulation in insulators. As a demonstration, we combined the formalism with measurements from Advanced LIGO to give an updated estimate for the Johnson noise coupling to the gravitational-wave channel. The induced signal was determined to be 10 times lower than the instrument’s design sensitivity in the detection band and scaling as f −2.

Background: The neutron distribution of neutron-rich nuclei provides critical information on the structure of finite nuclei and neutron stars. Parity violating experiments -such as PREX and CREX -provide a clean and largely model-independent determination of neutron densities. Such experiments, however, are challenging and expensive which is why sound statistical arguments are required to maximize the information gained.Purpose: To introduce a new framework, "the transfer function formalism", aimed at uncertainty quantification, model selection, and experimental design in the context of neutron densities.Methods: The transfer functions (TFs) are built analytically by expressing the linear response of the objective function (e.g., χ 2 ) to small perturbations of the data. Using the TF formalism, we are able to analyze the expected overall uncertainty -quantified in terms of bias and varianceof the mean square radius and interior density of 48 Ca and 208 Pb.Results: Using relativistic mean field models as a proxy for the weak-charge density -and assuming that a total of five measurements could be performed on the weak form factor of 48 Ca and 208 Pb -we identify the optimal models and experimental locations that minimize the uncertainty in the extraction of the radius and interior density. We also explore the use of the TF formalism to understand the influence of prior distributions for the model parameters, as well as the optimization of model hyperparameters not constrained by the data.Conclusions: We establish how the choice of experimental locations and the model that is used can have a significant impact on the final uncertainties of the extracted quantities of interest. For challenging experiments such as CREX and PREX, a proper quantification of such uncertainties is critical. We have demonstrated how the TF formalism provides several advantages for this type of analysis.

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Measurements of elastic electron scattering data within the past decade have highlighted twophoton exchange contributions as a necessary ingredient in theoretical calculations to precisely evaluate hydrogen elastic scattering cross sections. This correction can modify the cross section at the few percent level. In contrast, dispersive effects can cause significantly larger changes from the Born approximation. The purpose of this experiment is to extract the carbon-12 elastic cross section around the first diffraction minimum, where the Born term contributions to the cross section are small to maximize the sensitivity to dispersive effects. The analysis uses the LEDEX data from the high resolution Jefferson Lab Hall A spectrometers to extract the cross sections near the first diffraction minimum of 12 C at beam energies of 362 MeV and 685 MeV. The results are in very good agreement with previous world data, although with less precision. The average deviation from a static nuclear charge distribution expected from linear and quadratic fits indicate a 30.6% contribution of dispersive effects to the cross section at 1 GeV. The magnitude of the dispersive effects near the first diffraction minimum of 12 C has been confirmed to be large with a strong energy dependence and could account for a large fraction of the magnitude for the observed quenching of the longitudinal nuclear response. These effects could also be important for nuclei radii extracted from parity-violating asymmetries measured near a diffraction minimum.