Search NASA⌕ Search

SEARCH · Search NASA

Results for “R MATRIX”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

R-matrix evaluation of the 15 N Compound System for Criticality Safety Analyses [Abstract]

The evaluation of the 15 N compound system was selected by the Nuclear Criticality Safety Program (NCSP) due to the importance of nitrogen in criticality benchmarks and in actinide chemistry encountered during fuel reprocessing. For improved accuracy in transport calculations, it is recommended to obtain and distribute resonance parameters to describe n + 14 N reactions.

AZURE↗
DOE OSTI2016

PAMOP Project: Petaflop Computations in Support of Experiments.

Our computation effort is primarily concentrated in support of current and future measurements being carried out at various synchrotron radiation facilities around the globe and for charge transfer experiments. In our work we solve the Schrödinger or Dirac equation for the appropriate collision problem using the R-matrix or R-matrix with pseudo-states approach from first principles. The time dependent lattice (TDL) method is also used in our work on charge exchange. A brief summary of the methodology and ongoing developments implemented in the R-matrix suite of Breit-Pauli and Dirac-Atomic R-matrix codes (DARC) is presented. We illustrate vividly the sophistication level of large scale petaflop computations necessary to model accurately the spectra currently being measured at various synchrotron radiation facilities. The new Cray XC40 architecture installed at HLRS is playing a vital role in our computational effort.

Advance Light Source↗
DOE OSTI2014

Petascale Computations for Large-Scale Atomic and Molecular Collisions. In: Sustained Simulations Performance.

Petaflop architectures are currently being utilized efficiently to perform large scale computations in Atomic, Molecular and Optical Collisions. We solve the Schrödinger or Dirac equation for the appropriate collision problem using the R-matrix or R-matrix with pseudo-states approach. We briefly outline the parallel methodology used and implemented for the current suite of Breit-Pauli and DARC codes. Various examples are shown of our theoretical results compared with those obtained from Synchrotron Radiation facilities and from Satellite observations. We also indicate future directions and implementation of the R-matrix codes on emerging GPU architectures.

Accurate Cross Section↗
DOE OSTI2016

Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices

In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and non-dynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov, and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise R-matrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder’s elliptic R-matrix are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Atomic data and spectral model for Fe II

We present extensive calculations of radiative transition rates and electron impact collision strengths for Fe ii. The data sets involve 52 levels from the 3d{sup 7}, 3d{sup 6}4s, and 3d{sup 5}4s{sup 2} configurations. Computations of A-values are carried out with a combination of state-of-the-art multiconfiguration approaches, namely the relativistic Hartree–Fock, Thomas–Fermi–Dirac potential, and Dirac–Fock methods, while the R-matrix plus intermediate coupling frame transformation, Breit–Pauli R-matrix, and Dirac R-matrix packages are used to obtain collision strengths. We examine the advantages and shortcomings of each of these methods, and estimate rate uncertainties from the resulting data dispersion. We proceed to construct excitation balance spectral models, and compare the predictions from each data set with observed spectra from various astronomical objects. We are thus able to establish benchmarks in the spectral modeling of [Fe ii] emission in the IR and optical regions as well as in the UV Fe ii absorption spectra. Finally, we provide diagnostic line ratios and line emissivities for emission spectroscopy as well as column densities for absorption spectroscopy. All atomic data and models are available online and through the AtomPy atomic data curation environment.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

ATOMIC DATA AND SPECTRAL MODEL FOR Fe III

We present new atomic data (radiative transitions rates and collision strengths) from large-scale calculations and a non-LTE spectral model for Fe III. This model is in very good agreement with observed astronomical emission spectra, in contrast with previous models that yield large discrepancies in observations. The present atomic computations employ a combination of atomic physics methods, e.g., relativistic Hartree-Fock, the Thomas-Fermi-Dirac potential, and Dirac-Fock computation of A-values and the R-matrix with intermediate coupling frame transformation and the Dirac R-matrix. We study advantages and shortcomings of each method. It is found that the Dirac R-matrix collision strengths yield excellent agreement with observations, much improved over previously available models. By contrast, the transformation of the LS-coupling R-matrix fails to yield accurate effective collision strengths at around 10{sup 4} K, despite using very large configuration expansions, due to the limited treatment of spin-orbit effects in the near-threshold resonances of the collision strengths. The present work demonstrates that accurate atomic data for low-ionization iron-peak species are now within reach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Investigation of the triple-α reaction in a full three-body approach

Here, the triple-alpha reaction is the key to our understanding about the nucleosynthesis and the observed abundance of 12 C in stars. The theory of this process is well established at high temperatures but rather ambiguous in the low temperature regime where measurements are impossible. Develop a new three-body method, which tackles properly the scattering boundary condition for three charged particles and takes into account both the resonant and the non-resonant reaction mechanisms on the same footing, to compute the triple-alpha reaction rate at low temperatures. Methods: We combine the R-matrix expansion, the R-matrix propagation method, and the screening technique in the hyperspherical harmonics basis. Both the 2 + 1 bound state and the 0 + 2 resonant state in 12 C are well reproduced. We also study the cluster structure of these states. We calculate the triple-alpha reaction rate for T = 0.01 - 0.1 GK. In conclusion, we obtain the same rate as NACRE for temperatures above 0.07 GK, but the new rate is largely enhanced at lower temperatures (≈ 10 12 at 0.02 GK). The differences are caused by the direct capture contribution to the reaction when three alpha particles can not reach the resonant energies.

12C hyperspherical harmonics↗
DOE OSTI2026

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↗
DOE OSTI2022

Performing Bayesian Analyses With AZURE2 Using BRICK: An Application to the 7 Be System

Phenomenological R-matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist (χ 2 -based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, emcee, has been implemented for the R-matrix code AZURE2, creating the Bayesian R-matrix Inference Code Kit (BRICK). Bayesian uncertainty estimation has then been carried out for a simultaneous R-matrix fit of the 3 He (α,γ) 7 Be and 3 He (α,α) 3 He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state α-particle asymptotic normalization coefficients in 7 Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗