Efficient computation of the N-th rank QED polarization tensor: Universal worldline structure of form factors
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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Probing the Electronic Structure of a Thorium Nitride Complex by Solid-State 15N NMR Spectroscopy
The solid-state 15N NMR powder spectra of the thorium nitride complex, [K(18-crown-6)(THF)2][(R2N)3Th(m-15N)(Th(NR2)3] ([K][1-15N], R = SiMe3), and the thorium amide complex, [Th(NR2)3(15NH2)] (2-15N) were recorded. The spectrum for [K][1-15N] represents the first reported solid-state 15N NMR data for an actinide nitride complex. The experimentally measured tensor spans are 847 ppm for [K][1-15N] and 237 ppm for 2-15N. Both shielding tensors exhibit a near-zero asymmetry parameter, which for [K][1-15N] is consistent with a local rotational symmetry of its 15N-labelled nitride ligand. For 2-15N, the lack of asymmetry can be rationalized by a quasi-free Th-NH2 bond rotation in the solid-state. DFT calculations overestimate the tensor span somewhat for [K][1-15N], but provide isotropic shifts in good agreement with both the solid-state and solution values for both complexes. Natural localized molecular orbital (NLMO) analyses of the nuclear shielding reveal that the larger tensor span in [K][1-15N] vs. 2-15N is primarily a consequence of more pronounced covalency of the N-Th bonds, and large spin-orbit coupling due to significant Th 5f orbital contribution to those bonds, impacting the principal components of the shielding tensor perpendicular to the Th-N-Th axis. Overall, our analysis confirms the involvement of the 5f orbitals in Th-N multiple bonds, and further demonstrates the value of solid-state NMR spectroscopy for interrogating actinide-ligand bonding.
actinides, covalent bonding, Nuclear Magnetic Reso↗
Color halo scenario of charmonium-like hybrids
The internal structures of J PC =1 -- ,(o,1,2) -+ charmonium-like hybrids are investigated under lattice QCD in the quenched approximation. We define the Bethe-Salpeter wave function (Φn(r)) in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator ($\bar{c}cg$) between the vacuum and n-th state for J PC , with r being the spatial separation between a localized $\bar{c}c$ component and the chromomagnetic strength tensor. These wave functions exhibit some similarities for states with the aforementioned different quantum numbers, and their r-behaviors (no node for the ground states and one node for the first excited states) imply that r can be a meaningful dynamical variable for these states. Additionally, the mass splittings of the ground states and first excited states of charmonium-like hybrids in these channels are obtained for the first time to be approximately 1.2-1.4 GeV. These results do not support the flux-tube description of heavy-quarkonium-like hybrids in the Born-Oppenheimer approximation. In contrast, a charmonium-like hybrid can be viewed as a "color halo" charmonium for which a relatively localized color octet $\bar{c}c$ is surrounded by gluonic degrees of freedom, which can readily decay into a charmonium state along with one or more light hadrons. The color halo picture is compatible with the decay properties of Y (42600) and suggests LHCb and BelleII to search for (0,1,2) -+ charmonium-like hybrids in Xc0,1,2N and J/ψω(φ) final states.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Timely Reporting of Heavy Hitters Using External Memory
Given an input stream S of size N, a Φ-heavy hitter is an item that occurs at least ΦN times in S. The problem of finding heavy-hitters is extensively studied in the database literature. In this work, we study a real-time heavy-hitters variant in which an element must be reported shortly after we see its T = Φ N-th occurrence (and hence it becomes a heavy hitter). We call this the Timely Event Detection (TED) Problem. The TED problem models the needs of many real-world monitoring systems, which demand accurate (i.e., no false negatives) and timely reporting of all events from large, high-speed streams with a low reporting threshold (high sensitivity). Like the classic heavy-hitters problem, solving the TED problem without false-positives requires large space (Ω (N) words). Thus in-RAM heavy-hitters algorithms typically sacrifice accuracy (i.e., allow false positives), sensitivity, or timeliness (i.e., use multiple passes). We show how to adapt heavy-hitters algorithms to external memory to solve the TED problem on large high-speed streams while guaranteeing accuracy, sensitivity, and timeliness. Our data structures are limited only by I/O-bandwidth (not latency) and support a tunable tradeoff between reporting delay and I/O overhead. With a small bounded reporting delay, our algorithms incur only a logarithmic I/O overhead. We implement and validate our data structures empirically using the Firehose streaming benchmark. Multi-threaded versions of our structures can scale to process 11M observations per second before becoming CPU bound. In comparison, a naive adaptation of the standard heavy-hitters algorithm to external memory would be limited by the storage device’s random I/O throughput, i.e., ≈100K observations per second.
97 MATHEMATICS AND COMPUTING↗
Statistical Hauser-Feshbach model calculation for (α, n) reaction cross section and discrete level population
We calculate the α-particle induced reactions on 17,18 O, 19 F, and 23 Na, in the energy range 0 ≤ E α ≤ 10 MeV, with a particular attention to the branching ratios of populated discrete levels in the (α,n) channels. Since there are too many open channels to employ the R-matrix theory, we apply the statistical Hauser-Feshbach model to calculate these reaction cross sections and branching ratios. The branching ratio is defined as b n = $\frac{σ_n}{Σ_iσ_i + σ_c}$ , where σ n is the n-th level production cross section after the neutron emission, and σ c is the production of the continuum state. In the cases of our target nuclei and the energy range of interest, the residual nuclei of the neutron emission channel are always in their discrete states, so that σ c can be negligible.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Position Operators in Terms of Converging Finite-Dimensional Matrices and Their Intertwining with Geometry, Transport, and Gauge
The position operator 𝑟̂ appears as 𝑖∂ 𝑝 in wave mechanics, while its matrix form (e.g., under a Bloch basis) is well known diverging in diagonals, causing difficulties in basis transformation, observable yielding, etc. We aim to find a convergent r-matrix (CRM) to improve the existing divergent r-matrix (DRM), and investigate its influence at both the conceptual and the application levels. A key modification is increasing the familiar substitution of 𝑟̂ by 𝑖∂ 𝑝 to 𝑖∑ 𝑗 ∂ 𝑘 𝑗 , namely the N-th Weyl algebra. Resolving the divergence makes r-matrix rigorously defined, and we are able to show r-matrix is distinct from a spin matrix in terms of its defining principles, transformation behavior, and the observable it yields. Conceptually, the CRM fills the logical gap between the r-matrix and the Berry connection (this unremarked vagueness has caused the diagonal divergence). In application, we focus on transport, and discover that the Hermitian matrix is not identical with the associative Hermitian operator, i.e., 𝑟 𝑚,𝑛 = 𝑟$^∗_{𝑛,𝑚}$ ⇎ 𝑟̂ = 𝑟̂ † , which subtly affects the celebrated Berry curvature formula for adiabatic current. We also discuss how such a non-representation CRM can contribute to building a unified transport theory.
Weyl algebras↗
Implementation of fuel management multi-cycle optimization capabilities in RAVEN optimization framework
Optimization in nuclear fuel-management assists the core reload engineer with finding optimal out-of-core and in-core strategies. RAVEN is INL’s open source software that is equipped with fuel-management optimization capabilities including single-cycle, single- and multi-objective optimization of pressurized water reactors (PWRs) loading patterns (LP) of a fresh core using genetic algorithm (GA) and non-dominated sorting genetic algorithm (NSGA-II). In practice, however, medium and long term planning of fuel-management needs a multi-cycle approach, where the history and availability of fuel assemblies is considered in the optimization process. In this paper, we present a description of an initial expansion of RAVEN fuel-management optimization capabilities for a multi-cycle optimization framework. N-th cycle optimization capabilities that account for the unique history of recycled fuel assembly in the core were added. The multi-cycle optimization approach taken is formulated as a cycle-wise optimization problem where out-of-core decisions are used to onset each cycle optimization. Out-of-core decisions are managed externally to the in-core optimization by a fuel inventory management module. A proof-of-concept optimization problem is also presented.
42 - ENGINEERING↗
Materials Data on Th2N3 by Materials Project
Th2N3 crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. Th4+ is bonded in a 7-coordinate geometry to seven N+2.67- atoms. There are a spread of Th–N bond distances ranging from 2.36–2.73 Å. There are two inequivalent N+2.67- sites. In the first N+2.67- site, N+2.67- is bonded to six equivalent Th4+ atoms to form NTh6 octahedra that share corners with twelve equivalent NTh4 tetrahedra, edges with six equivalent NTh6 octahedra, and edges with six equivalent NTh4 tetrahedra. In the second N+2.67- site, N+2.67- is bonded to four equivalent Th4+ atoms to form NTh4 tetrahedra that share corners with six equivalent NTh6 octahedra, corners with six equivalent NTh4 tetrahedra, edges with three equivalent NTh6 octahedra, and edges with three equivalent NTh4 tetrahedra. The corner-sharing octahedra tilt angles range from 17–56°.
36 MATERIALS SCIENCE↗
Materials Data on Th3N4 by Materials Project
Th3N4 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Th4+ sites. In the first Th4+ site, Th4+ is bonded to six equivalent N3- atoms to form edge-sharing ThN6 octahedra. All Th–N bond lengths are 2.54 Å. In the second Th4+ site, Th4+ is bonded in a 7-coordinate geometry to seven N3- atoms. There are a spread of Th–N bond distances ranging from 2.32–2.91 Å. There are two inequivalent N3- sites. In the first N3- site, N3- is bonded to six Th4+ atoms to form distorted NTh6 octahedra that share corners with three equivalent NTh6 octahedra, corners with six equivalent NTh4 tetrahedra, edges with nine equivalent NTh6 octahedra, and edges with three equivalent NTh4 tetrahedra. The corner-sharing octahedral tilt angles are 0°. In the second N3- site, N3- is bonded to four equivalent Th4+ atoms to form NTh4 tetrahedra that share corners with six equivalent NTh6 octahedra, corners with six equivalent NTh4 tetrahedra, edges with three equivalent NTh6 octahedra, and edges with three equivalent NTh4 tetrahedra. The corner-sharing octahedra tilt angles range from 25–50°.
36 MATERIALS SCIENCE↗
Materials Data on ThN by Materials Project
ThN is Halite, Rock Salt structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Th is bonded to six equivalent N atoms to form a mixture of edge and corner-sharing ThN6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Th–N bond lengths are 2.59 Å. N is bonded to six equivalent Th atoms to form a mixture of edge and corner-sharing NTh6 octahedra. The corner-sharing octahedral tilt angles are 0°.
36 MATERIALS SCIENCE↗