Bulletin of the American Physical Society
2021 Fall Meeting of the APS Division of Nuclear Physics
Volume 66, Number 8
Monday–Thursday, October 11–14, 2021; Virtual; Eastern Daylight Time
Session FM: Nuclear Theory III |
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Chair: Daniel Phillips, Ohio University Room: White Hill |
Tuesday, October 12, 2021 2:00PM - 2:12PM |
FM.00001: Eigenvector Continuation Emulators for Chiral EFT Alberto Garcia, Richard J Furnstahl, Jordan A Melendez, Patrick J Millican, Xilin Zhang, Christian Drischler Full Bayesian analysis for low-energy nuclear calculations are notorious for being computationally expensive. This has motivated the development of emulators to decrease the time needed to perform uncertainty quantification (UQ). Recently, eigenvector continuation (EC) has emerged as an efficient emulator for the prediction of both bound state and scattering observables. EC is a variational technique that uses eigensolutions for several sets of known parameters to form a basis that can be used to accurately interpolate and extrapolate solutions for the same Hamiltonian with different parameters. Here we apply and test EC for the nucleon-nucleon (NN) scattering problem using a variety of chiral effective field theory potentials in momentum space. We also demonstrate an alternative emulator that does not use scattering wave functions. |
Tuesday, October 12, 2021 2:12PM - 2:24PM |
FM.00002: Bayesian analysis of an EFT for fermionic rotational bands Ibrahim K Alnamlah, Eduardo A Coello Perez, Daniel R Phillips We recently developed an Effective Field Theory (EFT) for fermionic rotational bands in odd mass nuclei (arXiv:2011.01083). Here we perform a Bayesian analysis of data on rotational levels of 99Tc, 159Dy, 167, 169Er, 167, 169Tm, 183W, 235U and 239Pu. Our error model accounts for both experimental errors and the theory uncertainty due to the EFT truncation. It also accounts for the difference in the structure of the matrix elements that enter the EFT's Low-Energy Constants (LEC's): we assume that the LECs at even and odd orders in the EFT are drawn from two different distributions. This allows us to simultaneously and reliably extract both the LEC's and the expansion parameter, Q. The LEC's are extracted up to fourth order. Correctly accounting for omitted terms in the error model makes the extraction stable across EFT orders. The analysis is also stable against the addition of data on higher-energy levels. In almost all cases the LEC stablizies before we reach the highest level for which we have data. For all the nuclei listed above there is a clear correlation between the extracted Q and the naive expansion parameter obtained from the rotational, single-particle and vibrational energy scales. But the extracted Q is significantly lower than the naive one. |
Tuesday, October 12, 2021 2:24PM - 2:36PM |
FM.00003: Quantifying Uncertainties In Light-Ion Reactions Konstantinos Kravvaris, Sofia Quaglioni, Petr Navratil, Kevin Quinlan Predictive modeling of astrophysical reactions relies on fundamental understanding of the underlying processes. First-principles calculations have made great strides during the past years in bridging the gap from fundamental nucleon-nucleon and three-nucleon interactions derived from chiral effective field theory to the description of nuclear structure and dynamics. In this talk I will outline the basic principles of the no-core shell model with continuum, an ab initio approach aimed at describing the interface between structure and dynamics in nuclei, and discuss ongoing efforts in quantifying the uncertainties arising from chiral effective field theory, how they affect relevant cross sections, and what the cross sections can in turn reveal about the underlying theory. |
Tuesday, October 12, 2021 2:36PM - 2:48PM |
FM.00004: Uncertainty quantification of spectra and transitions in the nuclear shell-model Jordan M Fox, Calvin W Johnson, Rodrigo Navarro Perez We perform uncertainty quantification (UQ) for transition operators of a high-quality empirical shell-model interaction, USDB, in the sd shell. First, we perform a sensitivity analysis on the Hamiltonian parameters (matrix elements) using principal component analysis. This allows us to compute the statistical uncertainty of energy levels and observables. We also compute the empirical uncertainty on transition coupling constants by Monte Carlo sampling. |
Tuesday, October 12, 2021 2:48PM - 3:00PM |
FM.00005: Interpolating between small- and large-x expansions using Bayesian Model Mixing Alexandra C Semposki, Richard J Furnstahl, Daniel R Phillips Bayesian Model Mixing (BMM) is a statistical technique used to combine models that are valid in different input domains into a composite distribution that has good statistical properties over the entire input space. This is done by weighting each of the models being mixed so that each one contributes to the composite distribution in the regions of the input space where it is valid. In this talk I will present an application of BMM to the problem of mixing two expansions of a function: one that is valid at small values, and the other at large values, of a coupling constant. Interpolation between these limits is often accomplished by choice of a suitable interpolating function, e.g., Padé approximants, but uncertainty quantification (UQ) is difficult in such approaches. One example of such a problem is the partition function of zero-dimensional φ4 theory for which the (asymptotic) expansion at small g and the (convergent) expansion at large g are both known. I will show results from the application of BMM to this problem and discuss the UQ that results from employing BMM and statistical models for the accuracy of the series that describe the two limiting cases. |
Tuesday, October 12, 2021 3:00PM - 3:12PM |
FM.00006: Proton-neutron entanglement entropy in shell model calculations Calvin W Johnson, Oliver C Gorton
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Tuesday, October 12, 2021 3:12PM - 3:24PM |
FM.00007: Comparison of Restricted Boltzmann Machines and Feedforward Neural Networks as Variational Ansätze for Quantum Many-Body Problems Jane M Kim Artificial neural networks have been shown to be powerful ansätze for quantum many-body problems. In this work, Gaussian-binary restricted Boltzmann machines and feedforward neural networks are used as trial wave functions for a variational Monte Carlo calculation. The ground state energy, wave function, and one-particle density are calculated for the Calogero-Sutherland model of bosons in one dimension. This continuous-space model is exactly solvable, allowing for a quantitative comparison between the two networks. These ansätze can be equivalently applied to any continuous-space system with a positive-definite ground state, but in return, they need far more parameters than a typical ansatz which has been tailored for a specific Hamiltonian. The reinforcement learning scheme used to train the networks will be discussed in detail, along with the computational costs. |
Tuesday, October 12, 2021 3:24PM - 3:36PM |
FM.00008: Variational Monte Carlo calculations of atomic nuclei with an artificial neural-network correlator ansatz Alessandro Lovato, Corey Adams, Giuseppe Carleo, Noemi Rocco Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems, even when non-perturbative interactions are prominent. We introduce a neural-network quantum state ansatz suitable for modeling the ground-state wave function of light nuclei and approximately solving the nuclear many-body Schrödinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field. We will present results for the binding energies and point-nucleon densities of light nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parameterizations based on two- and three-body Jastrow functions and virtually-exact Green's function Monte Carlo results. |
Tuesday, October 12, 2021 3:36PM - 3:48PM |
FM.00009: Applying Machine Learning to Many-Body Studies of Infinite Nuclear Matter Julie L Butler, Morten Hjorth-Jensen Neutron stars are extremely cold and dim, making observational astronomy difficult. Therefore, the only way to study them is through many-body studies of their constituent particles using state-of-the-art many-body methods with modern nuclear forces. However, many-body computations of infinite nuclear matter involve a large number of particles and complex potentials. This has a high computational cost, making large studies difficult. Machine learning is emerging as a useful tool in physics that will allow us to tackle problems which are difficult to solve with traditional computational methods. This talk will explore ways in which machine learning can be used to apply many-body methods to infinite nuclear matter to perform faster calculations with physically relevant accuracy. Ridge regression and kernel ridge regression will be applied using a variety of algorithms to find converged correlation energies, extrapolate to the thermodynamic limit, and to find coupled cluster correlation energies using only data from MBPT calculations. Accuracy compared to full calculations and time savings will be presented to justify the use of machine learning as a valid computational method for these calculations. This project is funded by NSF Grants No. PHY-1404159 and PHY-2013047. |
Tuesday, October 12, 2021 3:48PM - 4:00PM |
FM.00010: Coulomb field correction due to virtual e+e− production in heavy ion collisions Thomas Settlemyre, Aldo Bonasera, Hua Zheng The correction to the Coulomb energy due to virtual production of e+e− pairs, which is on the order of one percent of the Coulomb energy at nuclear scales, is discussed. The effects of including a pair-production term in the semi-empirical mass formula and the correction to the Coulomb barrier for a handful of nuclear collisions using the Bass and Coulomb potentials are studied. With an eye toward future work using Constrained Molecular Dynamics (CoMD) model, we also calculate the correction to the Coulomb energy and force between protons after folding with a Gaussian spatial distribution. |
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