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MTUQ: a framework for estimating moment tensors, point forces, and their uncertainties

SUMMARY We introduce MTUQ, an open-source Python package for seismic source estimation and uncertainty quantification, emphasizing flexibility and operational scalability. MTUQ provides MPI-parallelized grid search and global optimization capabilities, compatibility with 1-D and 3-D Green’s function database formats, customizable data processing, C-accelerated waveform and first-motion polarity misfit functions, and utilities for plotting seismic waveforms and visualizing misfit and likelihood surfaces. Applicability to a range of full- and constrained-moment tensor, point force, and centroid inversion problems is possible via a documented application programming interface, accompanied by example scripts and integration tests. We demonstrate the software using three different types of seismic events: (1) a 2009 intraslab earthquake near Anchorage, Alaska; (2) an episode of the 2021 Barry Arm landslide in Alaska; and (3) the 2017 Democratic People’s Republic of Korea underground nuclear test. With these events, we illustrate the well-known complementary character of body waves, surface waves, and polarities for constraining source parameters. We also convey the distinct misfit patterns that arise from each individual data type, the importance of uncertainty quantification for detecting multimodal or otherwise poorly constrained solutions, and the software’s flexible, modular design.

58 GEOSCIENCES↗

Mean-Field and RPA Approaches to Stable and Unstable Nuclei with Semi-Realistic NN Interaction

A M3Y-type semi-realistic NN interaction has been applied to the mean-field and the RPA calculations. Explicitly including the tensor force and the central part of the one-pion exchange potential, the semi-realistic interaction is useful in studying the Z or N dependence of the nuclear shell structure. The magicity of N = 32, 40 and 58 in the neutron-rich Ca and Ni nuclei has been investigated, and the Z = 28 magicity in {sup 78}Ni has been argued. Significance of the tensor force in magnetic transitions is demonstrated by the M1 excitation of {sup 208}Pb.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Imprints of high-momentum nucleons in nuclei on hard photons from heavy-ion collisions near the Fermi energy

The short-range correlation (SRC) induced by the tensor force in the isosinglet neutron-proton interaction channel leads to a high-momentum tail (HMT) in the single-nucleon momentum distributions n(k) in nuclei. Owing to the remaining uncertainties about the tensor force, the shape of the nucleon HMT may be significantly different from the dilute interacting Fermi gas model prediction n(k) ~ 1/k 4 similar to the HMT in cold atoms near the unitary limit. Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck transport model incorporating approximately the nucleon HMT, we investigate hard photon emissions in 14 N + 12 C and 48 Ca + 124 Sn reactions at beam energies around the Fermi energy. Imprints of different shapes of the HMT on the energy spectrum, angular distribution and transverse momentum spectrum of hard photons are studied. Furthermore, while the angular distribution does not carry any information about the shape of the nucleon HMT, the energy spectra and especially the mid-rapidity transverse momentum spectra of hard photons are found to bare strong imprints of the shapes of nucleon HMTs in the two colliding nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

New Studies of Short-Range Correlations and Their Effects on Nuclei

Over the last decade, data gathered on short range correlations (SRC) and the EMC effect have stimulated tremendous progress in our understanding of the nuclear force. In particular, the tensor force was found to be the major factor in the formation of N-N short range correlations. More recently a connection between the N-N SRC probabilities and EMC effect amplitudes was first observed. However, the real origin and characteristics of this connection have not been convincingly determined experimentally or theoretically. The project consists of several approved experiments scheduled to run at Jefferson Lab in Newport News, VA. These inclusive scattering measurements will provide a detailed map of the nature of short range correlations and its role in the in-medium modification of the nucleons. The isospin dependence in 2 N- and 3 N-SRCs will be accessed through the use of two light mirror nuclei 3 He and 3 H. An extensive A-dependence study of 2 N and 3 N-SRCs will be performed as well as a measurement of the quark distribution in short range correlations, i.e. the EMC eect in SRCs. A measurement of the deuteron tensor structure function in the deep inelastic scattering regime will verify the possible contribution of hidden color components in the deuteron wave function. This project aims to help answer the fundamental question on the nature of the short range interactions and their implications at the nucleonic and partonic levels.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Few-body models for nuclear astrophysics

We present applications of microscopic models to nuclear reactions of astrophysical interest, and we essentially focus on few-body systems. The calculation of radiative-capture and transfer cross sections is outlined, and we discuss the corresponding reaction rates. Microscopic theories are briefly presented, and we emphasize on the matrix elements of four-body systems. The microscopic extension of the R-matrix theory to nuclear reactions is described. Applications to the {sup 2}H(d, γ){sup 4}He, {sup 2}H(d, p){sup 3}H and {sup 2}H(d, n){sup 3}He reactions are presented. We show the importance of the tensor force to reproduce the low-energy behaviour of the cross sections.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Finite Volume Corrections to the Nucleon Axial Charge

By considering the pion-mediated tensor force between nucleons on a finite lattice, we seek to explain the volume dependence of the nucleon axial charge g{sub A}. We observe that the wave function renormalization associated with this pion-exchange force significantly reduces g{sub A} in a finite volume.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Systematic study of tensor effects in shell evolution

In the framework of the Hartree-Fock-Bogoliubov approach with the Skyrme interactions SLy5, SLy5+T, SLy5+T{sub w}, and several sets of the TIJ parametrizations (Skyrme effective interaction parametrizations including the tensor terms), the effect of the tensor force on the shell evolution at Z,N=8, 20, and 28 is investigated. It is shown that the evolution of the gap (defined as the energy difference between the last occupied and first unoccupied single-particle orbits) with SLy5+T is similar to that with SLy5+T{sub w}, and the gap values with SLy5+T are smaller than those with SLy5+T{sub w} in the cases of Z,N=8, 20. At Z, N = 28, the gap values with SLy5 are smaller than those with SLy5+T and larger than those with SLy5+T{sub w}. To understand these features, we analyze the spin-orbit potentials with and without the tensor contributions and the radial wave functions of relevant orbits. Meanwhile, we find that the deviation of the calculated gaps with SLy5+T{sub w} from the experimental ones is larger than that with SLy5+T. This indicates that SLy5+T{sub w} is not suitable for investigating the properties of the ground-state gap evolution. Finally, it is seen that the gap evolutions with different sets of the TIJ parametrizations are similar to each other except for the ones with T22, and there is almost no difference between the tensor effect in gap evolution with the perturbative method and the one with the complete fitting method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Possible molecular bound state of two charmed baryons

One-boson-exchange approach is widely used in the study of baryon-baryon interactions. Because of the higher masses, charmed baryons are likely to form molecular bound states. We here investigate this possibility in the {Lambda}{sub c{Lambda}c}(J{sup P} = 0{sup +}, I = 0) system, which may be the lowest mass state composed of two charmed baryons. Since the long-range interactions must play an important role for the formation of possible molecular bound states, we consider the one-pion-exchange potential explicitly and embed the short-range effects into a phenomenological cutoff parameter. As single pion exchange does not occur between two {Lambda}{sub c}'s, couplings to the nearby {Sigma}{sub c{Sigma}c}, {Sigma}{sub c{Sigma}c}* and {Sigma}{sub c}*{Sigma}{sub c}{sup *} channels may be crucial in binding two {Lambda}{sub c}'s. We find that it is possible to have a molecular bound state of two {Lambda}{sub c}'s, where the tensor force plays a crucial role, although the predicted binding energies are sensitive to the cutoff parameter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Neutrino-nucleus reactions based on recent structure studies

Neutrino-nucleus reactions are studied with the use of new shell model Hamiltonians, which have proper tensor components in the interactions and prove to be successful in the description of Gamow-Teller (GT) strengths in nuclei. The new Hamiltonians are applied to obtain new neutrino-nucleus reaction cross sections in {sup 12}C, {sup 13}C, {sup 56}Fe and {sup 56}Ni induced by solar and supernova neutrinos. The element synthesis by neutrino processes in supernova explosions is discussed with the new cross sections. The enhancement of the production yields of {sup 7}Li, {sup 11}B and {sup 55}Mn is obtained while fragmented GT strength in {sup 56}Ni with two-peak structure is found to result in smaller e-capture rates at stellar environments. The monopole-based universal interaction with tensor force of π+ρ meson exchanges is used to evaluate GT strength in {sup 40}Ar and ν-induced reactions on {sup 40}Ar. It is found to reproduce well the experimental GT strength in {sup 40}Ar.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Short-range correlations in nuclei

Atomic nuclei are held together by the strong nuclear force acting between protons and neutrons (nucleons). While the long range, averaged part of this force is well described by the nuclear shell model, the short-range and tensor components create a fascinating substructure: pairs of nucleons that momentarily approach each other very closely, acquiring large relative momenta. These short-range correlated (SRC) pairs account for roughly 20% of all nucleons in any nucleus and almost all of the high momentum nucleons. This chapter provides an introduction to SRC pairs: their origin in the nucleon-nucleon tensor force, the experimental methods used to study them, principally deep inelastic and quasielastic electron and proton scattering, and the comprehensive picture that has emerged over the past three decades.

FOS: Physical sciences↗

Coarse graining the Bethe–Goldstone equation: Nucleon–nucleon high-momentum components

The $δ$-shell representation of the nuclear force allows a simplified treatment of nuclear correlations. We show how this applies to the Bethe–Goldstone equation as an integral equation in coordinate space with a few mesh points, which is solved by inversion of a five-dimensional square matrix in the single channel cases and a 10 × 10 matrix for the tensor-coupled channels. This allows us to readily obtain the high-momentum distribution, for all partial waves, of a back-to-back correlated nucleon pair in nuclear matter. We find that the probability of finding a high-momentum correlated neutron–proton pair is about 18 times that of a proton–proton one, as a result of the strong tensor force, thus confirming in an independent way previous results and measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Repulsive nature of optical potentials for high-energy heavy-ion scattering

The recent works by the present authors predicted that the real part of heavy-ion optical potentials changes its character from attraction to repulsion around the incident energy per nucleon E/A=200-300 MeV on the basis of the complex G-matrix interaction and the double-folding model (DFM) and revealed that the three-body force plays an important role there. In the present paper, we have precisely analyzed the energy dependence of the calculated DFM potentials and its relation to the elastic-scattering angular distributions in detail in the case of the {sup 12}C+{sup 12}C system in the energy range of E/A=100-400 MeV. The tensor force contributes substantially to the energy dependence of the real part of the DFM potentials and plays an important role to lower the attractive-to-repulsive transition energy. The nearside and farside (N/F) decompositions of the elastic-scattering amplitudes clarify the close relation between the attractive-to-repulsive transition of the potentials and the characteristic evolution of the calculated angular distributions with the increase of the incident energy. Based on the present analysis, we propose experimental measurements for the predicted strong diffraction phenomena of the elastic-scattering angular distribution caused by the N/F interference around the attractive-to-repulsive transition energy together with the reduced diffractions below and above the transition energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Probing the core of the strong nuclear interaction

The strong nuclear interaction between nucleons (protons and neutrons) is the effective force that holds the atomic nucleus together. This force stems from fundamental interactions between quarks and gluons (the constituents of nucleons) that are described by the equations of quantum chromodynamics. However, as these equations cannot be solved directly, nuclear interactions are described using simplified models, which are well constrained at typical inter-nucleon distances but not at shorter distances. This limits our ability to describe high-density nuclear matter such as that in the cores of neutron stars. Here we use high-energy electron scattering measurements that isolate nucleon pairs in short-distance, high-momentum configurations, accessing a kinematical regime that has not been previously explored by experiments, corresponding to relative momenta between the pair above 400 mega electron volts per c (c, speed of light in vacuum). As the relative momentum between two nucleons increases and their separation thereby decreases, we observe a transition from a spin-dependent tensor force to a predominantly spin-independent scalar force. These results demonstrate the usefulness of using such measurements to study the nuclear interaction at short distances and also support the use of point-like nucleon models with two- and three-body effective interactions to describe nuclear systems up to densities several times higher than the central density of the nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of the Vector and Tensor Asymmetries at Large Missing Momentum in Quasielastic ( e → , e ' p ) Electron Scattering from Deuterium

Here, we report the measurement of the beam-vector and tensor asymmetries A e d V and A d T in quasielastic ( e → , e ' p ) electrodisintegration of the deuteron at the MIT-Bates Linear Accelerator Center up to missing momentum of 500 MeV / c . Data were collected simultaneously over a momentum transfer range 0.1 < Q 2 < 0.5 ( GeV / c ) 2 with the Bates Large Acceptance Spectrometer Toroid using an internal deuterium gas target polarized sequentially in both vector and tensor states. The data are compared with calculations. The beam-vector asymmetry A e d V is found to be directly sensitive to the D -wave component of the deuteron and has a zero crossing at a missing momentum of about 320 MeV / c , as predicted. The tensor asymmetry A d T at large missing momentum is found to be dominated by the influence of the tensor force in the neutron-proton final-state interaction. The new data offer a strong constraint on theoretical models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗

On computing stress in polymer systems involving multi-body potentials from molecular dynamics simulation

Hardy stress definition has been restricted to pair potentials and embedded-atom method potentials due to the basic assumptions in the derivation of a symmetric microscopic stress tensor. Force decomposition required in the Hardy stress expression becomes obscure for multi-body potentials. In this work, we demonstrate the invariance of the Hardy stress expression for a polymer system modeled with multi-body interatomic potentials including up to four atoms interaction, by applying central force decomposition of the atomic force. The balance of momentum has been demonstrated to be valid theoretically and tested under various numerical simulation conditions. The validity of momentum conservation justifies the extension of Hardy stress expression to multi-body potential systems. Computed Hardy stress has been observed to converge to the virial stress of the system with increasing spatial averaging volume. This work provides a feasible and reliable linkage between the atomistic and continuum scales for multi-body potential systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Changes of deformed shell gaps at N ~ 100 in light rare-earth, neutron-rich nuclei

There have been compelling evidences indicating that deformed single-particle states in neutron- rich regions are different from those in the stable region. It was pointed out that for the light rare- earth (60Nd, 62Sm, and 64Gd), neutron-rich (N = 98-102) nuclei, the Woods-Saxon potential, the Nilsson modified oscillator potential with "universal" parameters, and the folded Yukawa potential all failed to describe the correct ordering of neutron single-particle states. The location and size of deformed shell gaps in this mass region are under current debate. We propose a modification for the "standard" Nilsson parameters of Bengtsson and Ragnarsson introduced in 1985. The proposed N-dependent spin-orbit interaction brings an effect of the tensor force for the deformed potential, which causes dynamic changes in deformed shell gaps with neutron number and deformation. By applying the modified Nilsson parameters to generate deformed bases for the Projected Shell Model, we demonstrate that the calculation can explain consistently the current experimental data, including the ground state configuration in odd-neutron nuclei, upbending of the yrast moment of inertia at higher spins and the energies of 2-quasineutron 6- and 4- isomers in even-even nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗