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Potential-well characteristics from energy dependence of glory extrema in total elastic scattering cross sections
In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.
Elastic scattering of slow electrons by two-electron ions
Elastic scattering cross section of low energy electrons calculated by continuum Hartree-Fock equations
Elastic scattering cross section for low energy electrons on metastable He atoms, using polarized orbital method
Negative pion proton elastic scattering differential cross sections from 1.71 to 5.53 GeV/c
Utilization of elastically scattered recoil ions to measure solid state track detector registration characteristics and particle trajectory analysis
Horn and Von Oertzen (1967) have shown that tracks in mica are produced by an irradiation with 32-MeV O-16 ions. These tracks were attributed to K and Fe recoils produced by elastic scattering of the incident oxygen beam. In the present work an alternate explanation of their observations is provided. The measured characteristics of the tracks are shown to be compatible with theoretical predictions for production of tracks by inelastic (mostly compound nucleus) reactions with silicon and to be inconsistent with the previously proposed elastic scattering process. The possibility that the tracks are produced by contaminant ions in the beam cannot be ruled out.
At leading order in weak and electromagnetic couplings, cross sections for (anti)neutrino-nucleon elastic scattering are determined by four nucleon form factors that depend on the momentum transfer Q 2 . Including radiative corrections in the Standard Model and potential new physics contributions beyond the Standard Model, eight invariant amplitudes are possible, depending on both Q 2 and the (anti)neutrino energy E ν . We review the definition of these amplitudes and use them to compute both unpolarized and polarized observables including radiative corrections. We show that unpolarized accelerator neutrino cross-section measurements can probe new physics parameter space within the constraints inferred from precision beta decay measurements. Published by the American Physical Society 2024
Semiclassical elastic scattering cross sections for central field potential function
Zero energy positron elastic scattering by helium atoms
Negative pion elastic scattering differential cross section measurements from 1.71 to 5.53 GeV/c, using zero gradient synchrotron beam on liquid hydrogen target
Differential cross sections for 200 MeV protons elastically scattered from C-12 were analyzed utilizing a local, complex, spin-dependent optical potential with a harmonic well radial dependence. Analyses were performed using the WKB and eikonal approximations. For the latter, first-order corrections to he phase shifts were incorporated to account for the spin-orbit contribution. Large disagreement between theory and experiment was observed when the usual Thomas form for the spin-orbit potential was utilized. Substantial improvement was obtained by allowing the parameters in the central and spin-orbit potential terms to vary independently.
We perform a detailed study of neutrino-electron elastic scattering using the monoenergetic Be 7 neutrinos in Borexino, with an emphasis on exploring the differences between the contributions of ν e , ν μ , and ν τ . We find that current data are capable of measuring these components such that the contributions from ν μ and ν τ cannot be zero, although distinguishing between them is challenging—the differences stemming from Standard Model radiative corrections are insufficient without significantly more precise measurements. In studying these components, we compare predicted neutrino-electron scattering event rates within the Standard Model (accounting for neutrino oscillations), as well as going beyond the Standard Model in two ways. We allow for nonunitary evolution to modify neutrino oscillations, and find that with a larger exposure ( ∼ 30 x ), Borexino may provide relevant information for constraining nonunitarity, and that JUNO may be able to accomplish this with its data collection of Be 7 neutrinos. We also consider novel ν μ - and ν τ -electron scattering from a gauged U ( 1 ) L μ − L τ model, showing consistency with previous analyses of Borexino and this scenario, but also demonstrating the impact of uncertainties on Standard Model mixing parameters on these results. Published by the American Physical Society 2024
Differential cross section for elastic scattering of high energy proton beam from He atoms target, discussing momentum transfer role
Elastic scattering cross sections of negative pions by deuterons compared with Glauber model calculations
Absolute differential elastic scattering cross sections measured with the 3-m, high resolution, time-of-flight spectrometer are presented for 54.9eV positrons incident on He. Five point moving average differential cross sections are plotted against average scattering angles which range from 14 to 36 deg. Also the averages of five differential cross sections which have adjacent values of scattering angle are plotted versus the corresponding averages of the scattering angles. The curve fitted to these data is shaped like the theoretical curve but has its minimum and its maximum at scattering angles that are about 4 deg higher and 15 deg lower respectively than predicted by theory.
Three time-dependent wave packet methods for performing elastic scattering calculations from screened Coulomb potentials are compared. The three methods are the time-dependent amplitude density method (TDADM), a Cayley-transform method (CTM), and the Chebyshev propagation method of Tal-Ezer and Kosloff. Both the TDADM and the CTM are based on a time-dependent integral equation for the wave function. In the first, the time-dependent amplitude density is propagated, while in the other two, the wave function is propagated. As a numerical example, phase shifts and cross sections are calculated using a screened Coulomb, Yukawa type potential over the range 200-1000 eV. It is found that, in most cases, all three methods yield comparable accuracy and are about equally efficient computationally. However for l = 0, where the Coulomb well is not screened by the centrifugal potential, the TDADM requires smaller grid spacings to maintain accuracy.