Bulletin of the American Physical Society
APS April Meeting 2018
Volume 63, Number 4
Saturday–Tuesday, April 14–17, 2018; Columbus, Ohio
Session G12: Hadrons and Light Ions; Bayesian Methods |
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Sponsoring Units: DNP Chair: Roxanne Springer, Duke University Room: A222-223 |
Sunday, April 15, 2018 8:30AM - 8:42AM |
G12.00001: The power law for mass-dependent nuclear reactions Roy Peterson Many authors have parameterized the nuclear mass dependence of their intermediate and high energy hadron-nucleus data as a power law proportional to A\textasciicircum $\alpha $. A derivation of this law will be presented in this talk, with a simple expression for the exponent $\alpha $ in terms of the hadron-nucleon total cross section SGT and a nuclear radius r0A\textasciicircum 1/3 fm. These exponents have been compiled for many examples of intermediate and high energy hadron-nucleus total, total reaction, and inclusive quasifree cross sections for masses from A$=$12 through 238. These fitted exponents, plotted against SGT, form smooth trends. The exponents for total and total reaction cross sections are similar to the derived expression for r0$=$1.6 fm, while those for quasifree cross sections are similar to the expression for r0$=$1.2 fm. Computations in the Glauber model follow these same trends. [Preview Abstract] |
Sunday, April 15, 2018 8:42AM - 8:54AM |
G12.00002: A study of Lambda-nucleon scattering using the CLAS detector Joseph Rowley, Kenneth Hicks, John W. Price Previous data for the elastic scattering of Lambda hyperons from the nucleon dates back to the bubble chamber era of the 1970s. Data for $\Lambda N$ scattering is very limited in comparison with other elastic scattering processes, such as NN or $\pi N$. Using the high luminosity photon beam incident on a long (40 cm) liquid hydrogen target at Hall B of Jefferson Lab, the CLAS detector was used to identify a final state with a proton in coincidence with a scattered Lambda baryon. The $\Lambda$, before elastic scattering, was produced via the $\gamma p \to K^+ \Lambda$ reaction, for which the cross section is well known. This allows us to determine the flux of $\Lambda$ particles, with which we can then measure the $\Lambda p$ elastic scattering cross section in the momentum range between 0.5 and 1.0 GeV/c. Preliminary results from the analysis of this reaction will be presented. Future directions of related possibilities for measuring hyperon-nucleon scattering at CLAS will be discussed. [Preview Abstract] |
Sunday, April 15, 2018 8:54AM - 9:06AM |
G12.00003: Large Longitudinal Spin Alignment Generated in Inelastic Nuclear Reactions Daniel Hoff E/A=24 MeV $^7$Li projectiles, inelastically excited by collisions with Be, C, and Al targets, are found to have large longitudinal spin alignment when the targets remain in their ground state. The observed alignment is consistent with an alignment mechanism stemming from an angular-momentum-excitation-energy mismatch. The longitudinal spin alignment of $^7$Li* [4.63 MeV] is well described by a DWBA cluster-model ($\alpha+t$). The longitudinal spin alignment of several other systems is also well described by DWBA calculations, including one where a cluster model is inappropriate, demonstrating the proposed alignment mechanism is a general phenomenon. Predictions of spin alignment have been made for the inelastic excitation of $^{12}$C at both low and high beam energies where the mismatching condition is inactive and active, respectively. [Preview Abstract] |
Sunday, April 15, 2018 9:06AM - 9:18AM |
G12.00004: Direct capture potential models in light of halo EFT, and vice versa Kenneth Nollett, Xilin Zhang, Daniel Phillips Use of measured nuclear cross sections in astrophysics requires extrapolating and interpolating models. For the direct captures $^7\mathrm{Be}(p,\gamma)^8\mathrm{B}$ and $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$, two-body potential models have served this role usefully for decades, using wave functions generated at all radii from a single potential well. Halo effective field theory (halo EFT) provides a newer way to encode many-body physics in a two-body formalism; like potential models, halo EFT is dominated by large-distance contributions to the matrix elements. Our halo EFT implementations of these reactions describe long-range contributions in terms of the effective range expansion and asymptotic normalizations, while encoding short-range contributions in contact interactions similar to $R$-matrix radiative widths. We have established the correspondence between the two formalisms by constructing representations of specific potential models within halo EFT, and we have used potential models to examine EFT power counting and truncation error. We will present insights into both types of model that resulted, in particular regarding the nature of short-distance effects and the role of model selection in astrophysical uncertainty quantification. [Preview Abstract] |
Sunday, April 15, 2018 9:18AM - 9:30AM |
G12.00005: A Linear equation for the Phase Amplitude description of a wave function George Rawitscher Milne's 1932 non-linear equation for the amplitude of a wave function has now been superseded by a third order linear equation for the square of the amplitude. The advantage of the new equation is that it can be solved non-iteratively by a superposition of Chebyshev polynomials, accurate out to large distances. This method is much simpler to implement than the iterative solution of Milne's equation. It is economical and accurate, and could serve as a starting point for the solution of coupled equations in coordinate space. However, the solution becomes unstable in the vicinity of turning points. Numerical examples for various types of potentials will be presented. [Preview Abstract] |
Sunday, April 15, 2018 9:30AM - 9:42AM |
G12.00006: Bayesian Gaussian Process Models for Effective Field Theory Truncation Errors Jordan Melendez, Dick Furnstahl, Daniel Phillips, Matthew Pratola, Sarah Wesolowski Effective field theories (EFTs) have truncation errors which are continuous functions of kinematic variables. This work extends a point-wise analysis of truncation errors in an EFT of nucleon-nucleon scattering to a curve-wise analysis via Gaussian processes that account for correlations in the truncation errors in both angle and energy. The Gaussian process is a Bayesian model of random curves, and this talk will explain how to construct and test such a model from scratch, including the incorporation of physics knowledge into hierarchical models, the application of priors, and model validation techniques explored via toy data. The use of modern statistics packages make it easy to code and visualize models that can be efficiently sampled with the No-U-Turn Sampler (NUTS). We show that statistical analyses using Gaussian processes can be a powerful tool for validating or questioning the construction of effective field theories. [Preview Abstract] |
Sunday, April 15, 2018 9:42AM - 9:54AM |
G12.00007: Applying Bayesian Truncation Error Models to Chiral Effective Field Theory R.J. Furnstahl, J.A. Melendez, D. Phillips, M.t. Pratola, S. Wesolowski Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. We apply a Bayesian truncation error model to various chiral EFTs, including the new Entem-Machleidt-Nosyk and Reinert-Krebs-Epelbaum potentials, to analyze their construction and fits. Our results show good agreement for some potentials but untamed convergence patterns for others, which may point to problems in fitting or the power-counting model (e.g., from regulator artifacts). This shows that our statistical model can be used as a diagnostic tool for chiral EFT fitting issues that may be obscured otherwise. We also discuss extending the statistical model to other EFTs, including pionless EFT. [Preview Abstract] |
Sunday, April 15, 2018 9:54AM - 10:06AM |
G12.00008: Estimating parameters and making predictions for nucleon-nucleon scattering: the role of EFT truncation errors Daniel Phillips, Sarah Wesolowski, Richard Furnstahl Determination of low-energy constants (LECs) and their uncertainties is essential for the robust application of chiral effective field theory ($\chi$EFT). In this and the subsequent talk we take the first steps in applying our recently-developed Bayesian parameter-estimation framework to NN potentials derived from $\chi$EFT. Our Bayesian machinery consistently incorporates uncertainties from the EFT truncation in the estimation of the LECs that appear in the $\chi$EFT NN potential. Combining the resulting LEC posteriors with truncation uncertainties for observables yields rigorous, statistically meaningful error bars for $\chi$EFT predictions. The interplay of these two different sources of uncertainty as the order of the EFT calculation is increased will also be discussed. [Preview Abstract] |
Sunday, April 15, 2018 10:06AM - 10:18AM |
G12.00009: Two case studies in a Bayesian approach to estimating the parameters of nucleon-nucleon interactions in chiral effective field theory Sarah Wesolowski, Richard Furnstahl, Daniel Phillips We apply our previously developed Bayesian framework for effective field theory (EFT) parameter estimation to the semi-local nucleon-nucleon (NN) interactions of Epelbaum, Krebs, and Meißner (EKM) as a test case. The main output of Bayesian parameter estimation is a posterior probability distribution function (pdf) for those parameters, the so-called low-energy constants (LECs), and this pdf contains all the necessary correlation and uncertainty information needed for propagation of LEC uncertainty to observable calculations. We discuss two case studies where information about the physics of the interaction can be gleaned from the behavior of the posterior: first, an operator redundancy is detected in the s-waves at fourth order in the interactions; and second, we assess the impact of including truncation uncertainties consistently on the extracted parameters as a function of the amount of high-energy data included. [Preview Abstract] |
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