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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Numerical challenges for energy conservation in N -body simulations of collapsing self-interacting dark matter halos

Dark matter (DM) halos can be subject to gravothermal collapse if the DM is not collisionless, but engaged in strong self-interactions instead. When the scattering is able to efficiently transfer heat from the centre to the outskirts, the central region of the halo collapses and reaches densities much higher than those for collisionless DM. This phenomenon is potentially observable in studies of strong lensing. Current theoretical efforts are motivated by observations of surprisingly dense substructures. However, a comparison with observations requires accurate predictions. One method to obtain such predictions is to use N-body simulations. Collapsed halos are extreme systems that pose severe challenges when applying state-of-the-art codes to model self-interacting dark matter (SIDM). In this work, we investigate the root of such problems, with a focus on energy non-conservation. Moreover, we discuss possible strategies to avoid them. We ran N-body simulations, both with and without SIDM, of an isolated DM-only halo and we adjusted the numerical parameters to check the accuracy of the simulation. We find that not only the numerical scheme for SIDM can lead to energy non-conservation, but also the modelling of gravitational interaction and the time integration are problematic. The main issues we find are: (a) particles changing their time step in a non-time-reversible manner; (b) the asymmetry in the tree-based gravitational force evaluation; and (c) SIDM velocity kicks breaking the time symmetry. Tuning the parameters of the simulation to achieve a high level of accuracy allows us to conserve energy not only at early stages of the evolution, but also later on. However, the cost of the simulations becomes prohibitively large as a result. Some of the problems that make the simulations of the gravothermal collapse phase inaccurate can be overcome by choosing appropriate numerical schemes. However, other issues still pose a challenge. Our findings motivate further works on addressing the challenges in simulating strong DM self-interactions.

dark matter↗
DOE OSTI2019

Fermi-Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional

Despite the success of density functional approximations (DFAs) in describing the electronic properties of many-electron systems, the most widely used approximations suffer from self-interaction errors (SIE) that limit their predictive power. Herein we describe the effects of removing SIE from the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (GGA) using the Fermi-Lowdin Orbital Self-Interaction Correction (FLOSIC) method. FLOSIC is a size-extensive implementation of the Perdew-Zunger self-interaction correction (PZ-SIC) formalism. We find that FLOSIC-SCAN calculations require careful treatment of numerical details and describe an integration grid that yields reliable accuracy with this approach. We investigate the performance of FLOSIC-SCAN for predicting a wide array of properties and find that it provides better results than FLOSIC-LDA and FLOSIC-PBE in nearly all cases. Furthermore, it gives better predictions than SCAN for orbital energies and dissociation energies where self-interaction effects are known to be important, but total energies and atomization energies are made worse. For these properties, we also investigate the use of the self-consistent FLOSIC-SCAN density in the SCAN functional and find that this DFA@FLOSIC-DFA approach yields improved results compared to pure, self-consistent SCAN calculations. Thus FLOSIC-SCAN provides improved results over the parent SCAN functional in cases where SIEs are dominant, and even when they are not, if the SCAN@FLOSIC-SCAN method is used.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

The effect of self-interaction error on electrostatic dipoles calculated using density functional theory

Spurious electron self-interaction in density functional approximations (DFAs) can lead to inaccurate predictions of charge transfer in heteronuclear molecules that manifest as errors in calculated electrostatic dipoles. Here we show the magnitude of these errors on dipoles computed for a diverse set of 47 molecules taken from the recent benchmark study of Hait and Head-Gordon. We compare results of Perdew-Wang local spin density approximation (PW92), Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and strongly constrained and appropriatedly normed (SCAN) meta-GGA dipole calculations, along with those of their respective self-interaction-corrected (SIC) counterparts, to reference values from accurate wave function-based methods. The SIC calculations were carried out using the Fermi-Löwdin orbital (FLO-SIC) approach. We find that correcting for self-interaction generally increases the degree of charge transfer, thereby increasing the size of calculated dipole moments. The FLO-SIC-PW92 and FLO-SIC-PBE dipoles are in better agreement with reference values than their uncorrected DFA counterparts, particularly for strongly ionic molecules where significant improvement is seen. Applying FLO-SIC to SCAN does not improve dipole values overall. In addition, we show that removing self-interaction improves the description of the dipole for stretched-bond geometries and recovers the physically correct separated atom limit of zero dipole. Finally, we find that the best agreement between the FLO-SIC-DFA and reference dipoles occurs when the molecular geometries are optimized using the FLO-SIC-DFA.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

The Fermi–Löwdin self-interaction correction for ionization energies of organic molecules

(Semi)-local density functional approximations (DFAs) suffer from self-interaction error (SIE). When the first ionization energy (IE) is computed as the negative of the highest occupied orbital (HO) eigenvalue, DFAs notoriously underestimate them compared to quasi-particle calculations. Here, the inaccuracy for the HO is attributed to SIE inherent in DFAs. We assessed the IE based on Perdew-Zunger self-interaction correction on 14 small to moderate-sized organic molecules relevant in organic electronics and polymer donor materials. Though self-interaction corrected DFAs were found to significantly improve the IE relative to the uncorrected DFAs, they overestimate. However, when the self-interaction correction is interiorly scaled using a function of the iso-orbital indicator zs , only the regions where SIE is significant get a correction. We discuss these approaches and show how these methods significantly improve the description of the HO eigenvalue for the organic molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction

The Perdew–Zunger self-interaction correction (PZ-SIC) improves the performance of density functional approximations for the properties that involve significant self-interaction error (SIE), as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by local scaling self-interaction correction (LSIC) of the PZ-SIC to the local spin density approximation (LSDA). Here, we propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of the atomic number Z in the asymptotic expansion of the exchange–correlation (xc) energy for atoms. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator z σ , which distinguishes one-electron regions from many-electron regions. LSIC+ applied to the LSDA works better for many equilibrium properties than LSDA-LSIC and the Perdew, Burke, and Ernzerhof generalized gradient approximation (GGA), and almost close to the strongly constrained and appropriately normed (SCAN) meta-GGA. LSDA-LSIC and LSDA-LSIC+, however, fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bond, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. To make a locally scaled down SIC to functionals beyond the LSDA requires a gauge transformation of the functional’s energy density. Here, the resulting SCAN-sdSIC, evaluated on SCAN-SIC total and localized orbital densities, leads to an acceptable description of many equilibrium properties including the dissociation energies of weak bonds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ~8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation–π and anion–π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion–π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E int ) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent—these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)- based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation–π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E int values, and maximum errors of ±0.2–0.3 kcal/mol (i.e., ~±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A deep potential model with long-range electrostatic interactions

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Preliminary searches for spin-dependent interactions using sidebands of nuclear spin-precession signals

Various theories beyond the Standard Model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A new P-odd and T-odd interaction between polarized and unpolarized nucleons proportional to s⃗⋅r̂ is one such possibility, where r⃗=rr̂ is the spatial vector connecting the nucleons, and s⃗ is the spin of the polarized nucleon. Such an interaction involving a scalar coupling gsN at one vertex and a pseudoscalar coupling gpn at the polarized nucleon vertex can be induced by the exchange of spin-0 pseudoscalar bosons. We describe a new technique to search for interactions of this form and present the first measurements of this type. We show that future improvements to this technique can improve the laboratory upper bound on the product gsNgpn by two orders of magnitude for interaction ranges at the 100 micron scale.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Shock and contact interaction with a simple cubic array of particles

Shock-particle interaction is a fundamental pillar of multiphase compressible flows that has been studied at length for many decades. However, little attention has been paid to the interaction of particles with a contact interface that follows a shock in shock tube experiments and applications relating to blast waves. Presently, the phenomenon is studied at the microscale via particle resolved simulations of shock contact systems interacting with a structured array of particles as well as isolated particles. Simulations are conducted at particle volume fractions of 0%, 5%, 10%, 20%, and 40% at three contact Mach numbers. Additionally, the diaphragm position is varied, which controls the timing of the shock arrival time in relation to the contact arrival time. The modification to the drag on these stationary particles by the contact is analyzed and compared to the compressible Maxey–Riley–Gatignol model, which is adequate for the single particle cases but does not account for fluid mediated particle–particle interactions.

Mechanics↗
DOE OSTI2024

The rise and fall of stretched bond errors: Extending the analysis of Perdew–Zunger self-interaction corrections of reaction barrier heights beyond the LSDA

Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of Jacob’s ladder of approximations. The analysis is based on Fermi–Löwdin Orbital Self-Interaction Correction (FLOSIC) calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange–correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. XC/H = 1.0 implies that an orbital’s self-exchange–correlation energy exactly cancels its self-Hartree energy and that the orbital, therefore, makes no contribution to the SIC in the FLOSIC scheme. For the practical DFAs studied here, XC/H spans a range of values. Here, the largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the strongly constrained and appropriately normed meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew–Zunger SIC approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Multi frame radiography of supersonic water jets interacting with a foil target

Pulsed-power-driven underwater electrical explosion of cylindrical or conical wire arrays produces supersonic water jets that emerge from a bath, propagating through the air above it. Interaction of these jets with solid targets may represent a new platform for attaining materials at high pressure (>1010 Pa) conditions in a university-scale laboratory. However, measurements of the internal structure of such jets and how they interact with targets are difficult optically due to large densities and density contrasts involved. We utilized multi-frame x-ray radiographic imaging capabilities of the ID19 beamline at the European Synchrotron Radiation Facility to explore the water jet and its interaction with a 50 μm thick copper foil placed a few mm from the surface of water. The jet was generated with a ∼130 kA-amplitude current pulse of ∼450 ns rise time applied to a conical wire array. X-ray imaging revealed a droplet-type structure of the jet with an average density of <400 kg/m3 propagating with a velocity of ∼1400 m/s. Measurements of deformation and subsequent perforation of the target by the jet suggested pressures at the jet–target interface of ∼5 × 109 Pa. The results were compared to hydrodynamic simulations for better understanding of the jet parameters and their interaction with the foil target. These results can be used in future research to optimize the platform, and extend it to larger jet velocities in the case of higher driving currents supplied to the wire array.

Physics↗
DOE OSTI2024

Relativistic Douglas–Kroll–Hess calculations of hyperfine interactions within first-principles multireference methods

A relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas–Kroll–Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods, including spin–orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field formalism with restricted active space state interaction for spin–orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativistic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs), such as Tb(III)Pc2 and Tb(II)(CpiPr5)2 without ligand truncation using well-converged basis sets. In particular, for the divalent SMM, which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).

Chemistry↗
DOE OSTI2025

Accurate noncovalent interactions in atomistic systems via quantum Drude oscillators

Accurately modeling polarization and van der Waals (vdW) interactions in atomistic systems typically requires high-level quantum-mechanical methods that are computationally expensive, hence limited in applicability. To address this challenge, efficient yet physically grounded models are needed—ones that not only enable accurate predictions but also provide insight into how noncovalent interactions scale in complex molecular and material systems. This review highlights the quantum Drude oscillator (QDO) model, a physically motivated and computationally efficient framework that captures the essential features of electronic response, including polarization and dispersion forces, across a wide range of chemical and material systems. We discuss how the QDO model quantitatively reproduces the polarization response of many-electron atoms and how key components of noncovalent interactions—exchange-repulsion, polarization, and dispersion—emerge naturally in QDO dimers. Furthermore, the model provides predictive scaling laws that elucidate trends in polarizability and dispersion across the periodic table and in molecular assemblies. By uniting interpretability, accuracy, and efficiency, the QDO model offers a versatile approach for modeling noncovalent interactions in systems ranging from isolated molecules to complex condensed phases and nanostructured materials.

Khabibrakhmanov, Almaz [Univ. of Luxembourg, Luxem↗
DOE OSTI2021

Ion-dependent protein–surface interactions from intrinsic solvent response

Significance Hard–soft interfaces between inorganic surfaces and biomolecules promote self-assembly processes with broad implications in biogeochemistry, energy sciences, nanomedicine, and origins of life. Yet, detailed molecular-scale understanding of inorganic–biomolecule interactions and their dependence on solution conditions is missing. We present a theory for the initial stages of inorganic–biomolecule assembly based on the far-field response of water, using experimentally characterized interactions between muscovite surfaces and mica-binding proteins as model systems. Our work connects molecular details of the solution to assembly outcomes and suggests the initial driving forces for assembly are dominated by long-range, ion-specific interactions. The connections made between interfacial structure and long-range surface–biomolecule interactions provide insights toward a predictive understanding of biomolecular self-assembly on mineral surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Network of epistatic interactions in an enzyme active site revealed by large-scale deep mutational scanning

Cooperative interactions between amino acids are critical for protein function. A genetic reflection of cooperativity is epistasis, which is when a change in the amino acid at one position changes the sequence requirements at another position. To assess epistasis within an enzyme active site, we utilized CTX-M β-lactamase as a model system. CTX-M hydrolyzes β-lactam antibiotics to provide antibiotic resistance, allowing a simple functional selection for rapid sorting of modified enzymes. We created all pairwise mutations across 17 active site positions in the β-lactamase enzyme and quantitated the function of variants against two β-lactam antibiotics using next-generation sequencing. Context-dependent sequence requirements were determined by comparing the antibiotic resistance function of double mutations across the CTX-M active site to their predicted function based on the constituent single mutations, revealing both positive epistasis (synergistic interactions) and negative epistasis (antagonistic interactions) between amino acid substitutions. The resulting trends demonstrate that positive epistasis is present throughout the active site, that epistasis between residues is mediated through substrate interactions, and that residues more tolerant to substitutions serve as generic compensators which are responsible for many cases of positive epistasis. Additionally, we show that a key catalytic residue (Glu166) is amenable to compensatory mutations, and we characterize one such double mutant (E166Y/N170G) that acts by an altered catalytic mechanism. These findings shed light on the unique biochemical factors that drive epistasis within an enzyme active site and will inform enzyme engineering efforts by bridging the gap between amino acid sequence and catalytic function.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Comparison of state-interaction and spinor-representation calculations of spin-orbit coupling within exact two-component coupled-cluster theories

Here a benchmark study of state-interaction and spinor-representation calculations of spin-orbit coupling using the exact two-component Hamiltonians with atomic mean-field integrals (the X2CAMF schemes) at the equation-of-motion coupled-cluster singles and doubles level is reported. We adopt a version of the X2CAMF scheme with spin-orbit integrals correct to first order for the state-interaction calculations and a version correct to infinite order for the spinor-representation calculations. The differences between the state-interaction calculations with minimum active spaces to account for (quasi-)degeneracy and the spinor-representation calculations thus correspond to higher-order spin-orbit contributions. This state-interaction approach with scalar-relativistic effects accurately included in the reference functions and in the spin-orbit integrals is shown to exhibit robust performance for elements across the periodic table. On the other hand, the more rigorous spinor representation shows more rapid convergence with respect to the number of correlated electrons and is the preferred choice for accurate calculations for heavy elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Neutrino(antineutrino)–nucleus interactions in the shallow- and deep-inelastic scattering regions

In $\nu /\bar{\nu }$–nucleon/nucleus interactions shallow inelastic scattering ($\text{SIS}$) is technically defined in terms of the four-momentum transfer to the hadronic system as non-resonant meson production with $Q^2 \lessapprox 1 \text {GeV}^2$. This non-resonant meson production intermixes with resonant meson production in a regime of similar effective hadronic mass W of the interaction. As $Q^2$ grows and surpasses this $ ≈1 \text{GeV}^2$ limit, non-resonant interactions begin to take place with quarks within the nucleon indicating the start of deep inelastic scattering ($\text{DIS}$). To essentially separate this resonant plus non-resonant meson production from $\text{DIS}$ quark-fragmented meson production, a cut of 2 $\text{GeV}$ in W of the interactions is generally introduced. However, since experimentally mesons from resonance decay cannot be separated from non-resonant produced mesons, $\text{SIS}$ for all practical purposes in this review has been defined as inclusive meson production that includes non-resonant plus resonant meson production and the interference between them. Experimentally then for $W \lessapprox 2 \text{GeV}$ inclusive meson production with $W \gtrapprox (M_N + M_π)$ and all $Q^2$ is here defined as $\text{SIS}$, while for $W \gtrapprox 2 \text {GeV}$, the kinematic region with $Q^2 \gtrapprox 1 \text{GeV}^2$ is defined as DIS$\text{DIS}$degrees of attention from the community. While the theoretical/phenomenological study of $\nu$–nucleon and $\nu$–nucleus $\text{DIS}$ scattering is advanced, such studies of a large portion of the $\text{SIS}$ region, particularly the $\text{SIS}$ to $\text{DIS}$ transition region, have hardly begun. Experimentally, the $\text{SIS}$ and the $\text{DIS}$ regions for $\nu$–nucleon scattering have minimal results and only in the experimental study of the $\nu$–nucleus $\text{DIS}$ region are there significant results for some nuclei. Inasmuch as current and future neutrino oscillation experiments have contributions from both higher $W \text{SIS}$ and $\text{DIS}$ kinematic regions and these regions are in need of both considerable theoretical and experimental study, this review will concentrate on these $\text{SIS}$ to $\text{DIS}$ transition and $\text{DIS}$ kinematic regions surveying our knowledge and the current challenges.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Skyrmion–skyrmion interaction in a magnetic film

Interaction of two skyrmions stabilized by the ferromagnetic exchange, Dzyaloshinskii–Moriya interaction (DMI), and external magnetic field has been studied numerically on a 2D lattice of size large compared to the separation, d, between the skyrmions. We show that two skyrmions of the same chirality (determined by the symmetry of the crystal) repel. In accordance with earlier analytical results, their long-range pair interaction falls out with the separation as exp(-d/δ H ), where δ H is the magnetic screening length, independent of the DMI. The prefactor in this expression depends on the DMI that drives the repulsion. The latter results in the spiral motion of the two skyrmions around each other, with the separation between them growing logarithmically with time. When two skyrmions of the total topological charge Q = 2 are pushed close to each other, the discreteness of the atomic lattice makes them collapse into one skyrmion of charge Q = 1 below a critical separation. Experiment is proposed that would allow one to measure the interaction between two skyrmions by holding them in positions with two magnetic tips. Our findings should be of value for designing topologically protected magnetic memory based upon skyrmions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗