Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix elements”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Effective field theories for collective excitations of atomic nuclei

Collective modes emerge as the relevant degrees of freedom that govern low-energy excitations of atomic nuclei. These modes—rotations, pairing rotations, and vibrations—are separated in energy from non-collective excitations, making it possible to describe them in the framework of effective field theory. Rotations and pairing rotations are the remnants of Nambu–Goldstone modes from the emergent breaking of rotational symmetry and phase symmetries in finite deformed and finite superfluid nuclei, respectively. The symmetry breaking severely constrains the structure of low-energy Lagrangians and thereby clarifies what is essential and simplifies the description. The approach via effective field theories exposes the essence of nuclear collective excitations and is defined with a breakdown scale in mind. This permits one to make systematic improvements and to estimate and quantify uncertainties. Effective field theories of collective excitations have been used to compute spectra, transition rates, and other matrix elements of interest. In particular, predictions of the nuclear matrix element for neutrinoless double beta decay then come with quantified uncertainties. This review summarizes these results and also compares the approach via effective field theories to well-known models and ab initio computations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Coulomb excitation of 80,82 Kr and a change in structure approaching N = Z = 40

Nuclei approaching N = Z = 40 are known to exhibit strongly deformed structures and are thought to be candidates for shape coexistence. In the krypton isotopes, 80,82 Kr are poorly characterized, preventing an understanding of evolving deformation approaching N = 40. The present work aims to determine electric quadrupole transition strengths and quadrupole moments of 80,82 Kr in order to better characterize their deformation. Sub-barrier Coulomb excitation was employed, impinging the isotopes of krypton on 196 Pt and 208 Pb targets. Utilizing a semiclassical description of the safe Coulomb-excitation process E 2 matrix elements could then be determined. Eleven new or improved matrix elements are determined in 80 Kr and seven in 82 Kr . The new B(E2;0$^+_1$ → 2$^+_1$ ) value in 82 Kr disagrees with the evaluated value by 3σ , which can be explained in terms of deficiencies in a previous Coulomb-excitation analysis. Conclusions: Comparison of measured Q s ( 2$^+_1$ ) and B(E2; 0$^+_1$ → 2$^+_1$ ) values indicates that neutron-deficient ( N ≤ 42 ) isotopes of krypton are closer to axial deformation than other isotopic chains in the mass region. A continuation of this trend to higher Z may result in Sr and Zr isotopes exhibiting near-axial prolate deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Evidence for triaxial shape coexistence in 74 Ge

The deformation properties of the low-lying states in 74 Ge have been investigated using multistep Coulomb excitation. The measurements were carried out with the advanced 𝛾-ray tracking array, GRETINA, and the CHICO2 particle detector. A comprehensive set of 𝐸⁢2 transition and diagonal matrix elements was deduced following an analysis with the semiclassical coupled-channels code GOSIA. The data were compared with results of calculations carried out within the framework of the generalized triaxial rotor model as well as with the configuration interaction shell model and the symmetric rotor model. Results from calculations with covariant density functional theory were used to construct a five-dimensional collective Hamiltonian for further comparisons with the data. Collectively, the calculations provide an accurate reproduction of the experimental matrix elements and further support an understanding in terms of the coexistence of two axially asymmetric shapes. In conclusion, this leads to an overall interpretation of the underlying structure of 74 Ge requiring triaxiality, as is also the case in the neighboring even-mass Ge isotopes.

59 ≤ A ≤ 89↗
DOE OSTI2026

Inverse problem in the large momentum effective theory framework

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed nonperturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using nonperturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the exact asymptotic behavior is minimal for values of 𝑥 where the framework is currently applicable. We show that the crux of the inverse problem lies in harmonics of the order of 𝜆 = 𝑧⁢𝑃 𝑧 ∼ 5–15, where the signal in the lattice data is often barely existent in current studies, and the asymptotic behavior is not firmly established. We stress the need for more sophisticated techniques to account for this inverse problem, whether in the LaMET or related frameworks like the short-distance factorization. We also address a misconception that, with available lattice methods, the LaMET framework allows a “direct” computation of the 𝑥-dependence, whereas the alternative short-distance factorization only gives access to moments or fits of the 𝑥-dependence.

Dutrieux, Hervé [Aix-Marseille Université, Marseil↗
DOE OSTI2025

Half-Life and Precision Shape Measurement of the 2⁢𝜈⁢𝛽⁢𝛽 Decay of 130 Te

Here, we present a new measurement of the 2⁢𝜈⁢𝛽⁢𝛽 half-life of 130 Te (𝑇$^{2⁢𝜈}_{1/2}$) using the first complete model of the CUORE data, based on 1038 kg yr of collected exposure. Thanks to optimized data selection, we achieve a factor of two improvement in precision, obtaining 𝑇$^{2⁢𝜈}_{1/2}$ = (9.32⁢$^{+0.05}_{−0.04}$⁢stat⁢ $^{+0.07}_{−0.07}$⁢syst)×10 20 yr. The signal-to-background ratio is increased by 70% compared to our previous results, enabling the first application of the improved 2⁢𝜈⁢𝛽⁢𝛽 formalism to 130 Te . Within this framework, we determine a credibility interval for the effective axial coupling in the nuclear medium as a function of nuclear matrix elements. We also extract values for the higher-order nuclear matrix element ratios: second-to-first and third-to-first. The second-to-first ratio agrees with nuclear model predictions, while the third-to-first ratio deviates from theoretical expectations. These findings provide essential tests of nuclear models and key inputs for future 0⁢𝜈⁢𝛽⁢𝛽 searches.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Pion and Kaon decays from lattice QCD and |Vud|, |Vus|

We review lattice calculations of the form factors for Kaon semileptonic decays and the leptonic decay constants of Kaons and Pions. We discuss the determinations of the CKM matrix elements $|V_{ud}|$ and $|V_{us}|$ using the form factors and experimental results. We use the CKM matrix elements to test first-row unitarity of the CKM matrix.

Simone, J. N. [Fermilab] (ORCID:0000000185153337)↗
DOE OSTI2020

Tailoring grain growth and solid solution strengthening of single-phase CrCoNi medium-entropy alloys by solute selection

In the present study, we selected solutes to be added to the CrCoNi medium-entropy alloy (MEA) based on the mismatch of self-diffusion activation energy (SDQ) between the alloying elements and constituent elements of the matrix, and then investigated their grain growth behavior and mechanical properties. Mo and Al were selected as the solutes for investigation primarily because they have higher and lower SDQ, respectively, than those of the matrix elements; a secondary factor was their higher and lower shear modulus. Their concentrations were fixed at 3 at.% each because previous work had shown these compositions to be single-phase solid solutions with the face-centered cubic structure. Three alloys were produced by arc melting, casting, homogenizing, cold rolling and annealing at various temperatures and times to produce samples with different grain sizes. They were (a) the base alloy CrCoNi, (b) the base alloy plus 3 at.% Mo, and (c) the base alloy plus 3 at.% Al. The activation energies for grain growth of the CrCoNi, CrCoNi-3Mo and CrCoNi-3Al MEAs were found to be ~251, ~368 and ~219 kJ/mol, respectively, consistent with the notion that elements with higher SDQ (in this study Mo) retard grain growth (likely by a solute-drag effect), whereas those with lower values (Al) accelerate grain growth. The room-temperature tensile properties show that Mo increases the yield strength by ~40% but Al addition has a smaller strengthening effect consistent with their relative shear moduli. The yield strength as a function of grain size for the three singlephase MEAs follows the classical Hall-Petch relationship with much higher slopes (> 600 MPa μm -0.5 ) than traditional solid solutions. Furthermore, this work shows that the grain growth kinetics and solid solution strengthening of the CrCoNi MEA can be tuned by selecting solute elements that have appropriate diffusion and physical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Chiral effective field theory calculations of weak transitions in light nuclei

In this work, we report quantum Monte Carlo calculations of weak transitions in A≤10 nuclei, based on the Norfolk two- and three-nucleon chiral interactions, and associated one- and two-body axial currents. Furthermore, we find that the contribution from two-body currents is at the 2–3% level, with the exception of matrix elements entering the rates of 8Li, 8B, and 8He β decay. These matrix elements are suppressed in impulse approximation based on the (leading order) Gamow Teller transition operator alone; two-body currents provide a 20–30% correction, which is, however, insufficient to bring theory in agreement with experimental data. For the other transitions, the agreement with the data is satisfactory, and the results exhibit a negligible to mild model dependence when different combinations of Norfolk interactions are utilized to construct the nuclear wave functions. We report a complete study of two-body weak transition densities which reveals the expected universal behavior of two-body currents at short distances throughout the range of A=3 to A=10 systems considered here.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Position-space renormalization schemes for four-quark operators in HQET

Abstract X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge-invariant operators to be equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between theX-space scheme and$$ \overline{\textrm{MS}} $$ MS ¯ in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to$$ \overline{\textrm{MS}} $$ MS ¯ -renormalized matrix elements. UsingX-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power-divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents theO(α S ) matching coefficients betweenX-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such asB−$$ \overline{B} $$ B ¯ mixing.

Physics↗
DOE OSTI2021

Thermal fluctuations and carrier localization induced by dynamic disorder in MAPbI 3 described by first-principles based tight-binding model

Halide perovskites are strongly influenced by large amplitude anharmonic lattice fluctuations at room temperature. We develop a tight binding model for dynamically disordered MAPbI$_3$ based on density functional theory (DFT) calculations to calculate electronic structure for finite temperature crystal structures at the length scale of thermal disorder and carrier localization. The model predicts individual Hamiltonian matrix elements and band structures with high accuracy, owing to the inclusion of additional matrix elements and descriptors for non-Coulombic interactions. We apply this model to electronic structure at length and time scales inaccessible to first principles methods, finding an increase in band gap, carrier mass, and the sub-picosecond fluctuations in these quantities with increasing temperature as well as the onset of carrier localization in large supercells induced by thermal disorder at 300 K. Finally, we identify the length scale $L^*= 5$ nm as the onset of localization in the electronic structure, associated with associated with decreasing band edge fluctuations, increasing carrier mass, and Rashba splitting approaching zero.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bridging hadronic and vacuum structure by heavy quarkonia

We discuss the central and, mostly, spin-dependent potentials in heavy quarkonia $\overline{b}$$b$,$\overline{c}$$c$, with two goals in mind. The first is phenomenological: using the splitting between the 1S and 2S pairs, as well as the 1P and 2P quartet masses, we obtain pertinent matrix elements of all these potentials. The second is theoretical: using standard wave functions, we compute these matrix elements, quantifying the perturbative, nonperturbative and “string” contributions. The model for nonperturbative effects is a “dense instanton liquid model,” in which the QCD vacuum is made mostly of (strongly color correlated) instanton-anti-instanton pairs or “molecules.” Their contributions are calculated via standard Wilson lines, with or without extra powers of gauge fields. We find a reasonable description of all central, spin-spin, and spin-orbit forces at distances 𝑟 = 0–0.7 fm, relevant for $\overline{b}$$b$ and $\overline{c}$$c$ quarkonia.

Bound states↗
DOE OSTI2025

Mechanical form factors and densities of nonrelativistic fermions

The hadron physics community has been actively debating the interpretation of so-called mechanical properties of hadrons. Nonrelativistic quantum-mechanical systems like the hydrogen atom have been appealed to in these debates as analogies. Since such appeals are likely to continue, it is important to have Galilei-covariant expressions for matrix elements of the energy-momentum tensor. In this work, I obtain Galilei-covariant breakdowns of such matrix elements into mechanical form factors, with a special focus on spin-half states. I additionally study the spatial densities associated with these form factors, using the pilot wave interpretation to guide their breakdown into contributions from internal structure and from quantum-mechanical effects such as wave packet dispersion. For completeness, I also obtain nonrelativistic Breit frame densities.

form factors↗
DOE OSTI2025

2 νββ spectrum in chiral effective field theory

We investigate two-neutrino double beta decay (2νββ) in chiral effective field theory. We find contributions from weak magnetism and double-weak pion-exchange at next-to-leading-order in the chiral power counting. We discuss the impact of the chiral corrections on the electron spectra and find that they should be included in analyses of 2νββ decay that aim to uncover new physics signatures in the electron spectrum. We illustrate this point by revisiting the effect of sterile neutrinos and non-standard charged interactions. We also find that the pion-exchange contributions involve nuclear matrix elements that are related to those appearing in neutrinoless double beta decay (0νββ). We investigate whether the 0νββ nuclear matrix elements can be obtained from detailed measurements of the energy spectrum of the outgoing electrons in 2νββ transitions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Polarized gluon pseudodistributions at short distances

We formulate the basic points of the pseudo-PDF approach to the lattice calculation of polarized gluon PDFs. We present the results of our calculations of the one-loop corrections for the bilocal G μα (z)G~ λβ (0) correlator of gluonic fields. Expressions are given for a general situation when all four indices are arbitrary, and also for specific combinations of indices corresponding to three matrix elements that contain the twist-2 invariant amplitude related to the polarized PDF. We study the evolution properties of these matrix elements, and derive matching relations between Euclidean and light-cone Ioffe-time distributions. These relations are necessary for extraction of the polarized gluon distributions from the lattice data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Application of an efficient generator-coordinate subspace-selection algorithm to neutrinoless double- β decay

The generator coordinate method begins with the variational construction of a set of nonorthogonal mean-field states that span a subspace of the full many-body Hilbert space. These states are then often projected onto states with good quantum numbers to restore symmetries, leading to a set with members that can be similar to one another, and it is sometimes possible to reduce this set without greatly affecting results. Here, we propose a greedy algorithm that we call the energy-transition-orthogonality procedure (ENTROP) to select subsets of important states. As applied here, the approach selects on the basis of diagonal energy, orthogonality, and contribution to the matrix element that governs neutrinoless double-β decay. We present both shell-model and preliminary ab initio calculations of this matrix element for the decay of 76Ge, with quadrupole deformation parameters and the isoscalar pairing strength as generator coordinates. ENTROP converges quickly, reducing significantly the number of basis states needed for an accurate calculation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Sterile neutrinos and neutrinoless double beta decay in effective field theory

We investigate neutrinoless double beta decay (0νββ) in the presence of sterile neutrinos with Majorana mass terms. These gauge-singlet fields are allowed to interact with Standard-Model (SM) fields via renormalizable Yukawa couplings as well as higher-dimensional gauge-invariant operators up to dimension seven in the Standard Model Effective Field Theory extended with sterile neutrinos. At the GeV scale, we use Chiral effective field theory involving sterile neutrinos to connect the operators at the level of quarks and gluons to hadronic interactions involving pions and nucleons. This allows us to derive an expression for 0νββ rates for various isotopes in terms of phase-space factors, hadronic low-energy constants, nuclear matrix elements, the neutrino masses, and the Wilson coefficients of higher-dimensional operators. The required hadronic low-energy constants and nuclear matrix elements depend on the neutrino masses, for which we obtain interpolation formulae grounded in QCD and chiral perturbation theory that improve existing formulae that are only valid in a small regime of neutrino masses. The resulting framework can be used directly to assess the impact of 0νββ experiments on scenarios with light sterile neutrinos and should prove useful in global analyses of sterile-neutrino searches. We per- form several phenomenological studies of 0νββ in the presence of sterile neutrinos with and without higher-dimensional operators. We find that non-standard interactions involving sterile neutrinos have a dramatic impact on 0νββ phenomenology, and next-generation experiments can probe such interactions up to scales of $\mathcal O$ (100) TeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Deep Minima in the Triply Differential Cross Section for Ionization of Atomic Hydrogen by Electron and Positron Impact

We investigate ionization of atomic hydrogen by electron- and positron-impact. We apply the Coulomb–Born (CB1) approximation, various modified CB1 approximations, the three body distorted wave (3DW) approximation, and the time-dependent close-coupling (TDCC) method to electron-impact ionization of hydrogen. For electron-impact ionization of hydrogen for an incident energy of approximately 76.45 eV, we obtain a deep minimum in the CB1 triply differential cross section (TDCS). However, the TDCC for 74.45 eV and the 3DW for 74.46 eV gave a dip in the TDCS. For positron-hydrogen ionization (breakup) we apply the CB1 approximation and a modified CB1 approximation. We obtain a deep minimum in the TDCS and a zero in the CB1 transition matrix element for an incident energy of 100 eV with a gun angle of 56.13 °. Corresponding to a zero in the CB1 transition matrix element, there is a vortex in the velocity field associated with this element. For both electron- and positron-impact ionization of hydrogen the velocity field rotates in the same direction, which is anticlockwise. All calculations are performed for a doubly symmetric geometry; the electron-impact ionization is in-plane and the positron-impact ionization is out-of-plane.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

One-loop matching for quark dipole operators in a gradient-flow scheme

The quark chromoelectric dipole (qCEDM) operator is a CP-violating operator describing, at hadronic energies, beyond-the-standard-model contributions to the electric dipole moment of particles with nonzero spin. In this paper we define renormalized dipole operators in a regularization-independent scheme using the gradient flow, and we perform the matching at one loop in perturbation theory to renormalized operators of the same and lower dimension in the more familiar MS scheme. We also determine the matching coefficients for the quark chromo-magnetic dipole operator (qCMDM), which contributes for example to matrix elements relevant to CP-violating and CP-conserving kaon decays. The calculation provides a basis for future lattice QCD computations of hadronic matrix elements of the qCEDM and qCMDM operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗