Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “sum rules”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Impact of dynamical chiral symmetry breaking and dynamical diquark correlations on proton generalized parton distributions

We calculate the leading-twist, helicity-independent generalized parton distributions (GPDs) of the proton, at finite skewness, in the Nambu–Jona-Lasinio (NJL) model of quantum chomodynamics (QCD). The NJL model reproduces low-energy characteristics of QCD, including dynamical chiral symmetry breaking (DCSB). The proton bound-state amplitude is solved for using the Faddeev equation in a quark-diquark approximation, including both dynamical scalar and axial vector diquarks. GPDs are calculated using a dressed non-local correlator, consistent with DCSB, which is obtained by solving a Bethe-Salpeter equation. The model and approximations used observe Lorentz covariance, and as a consequence the GPDs obey polynomiality sum rules. Extractions of electromagnetic and gravitational form factors are performed. We find a D-term of -1.08 when the non-local correlator is properly dressed, and 0.85 when the bare correlator is used instead, suggesting that within this framework proton stability requires the constituent quarks to be dressed consistently with DCSB. In conclusion, we also find that the anomalous gravitomagnetic moment vanishes, as required by Poincare symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Reexamination of isoscalar giant resonances in 12 C and 93 Nb through 6 Li scattering

Inelastic Li 6 scattering at 100 MeV/u on C 12 and Nb 93 has been measured with the high-resolution magnetic spectrometer Grand Raiden. The magnetic-rigidity settings of the spectrometer covered excitation energies from 10 to 40 MeV and scattering angles in the range 0 ° < θ lab. < 2 ° . The isoscalar giant monopole resonance was selectively excited in the present data. Measurements free of instrumental background and the very favorable resonance-to-continuum ratio of Li 6 scattering allowed for precise determination of the E 0 strengths in C 12 and Nb 93 . Additionally, it was found that the monopole strength in C 12 exhausts 52 ± 3 (stat.) ± 8 (sys.) % of the energy-weighted sum rule (EWSR), which is considerably higher than results from previous α -scattering experiments. The monopole strength in Nb 93 exhausts 92 ± 4 (stat.) ± 10 (sys.) % of the EWSR, and it is consistent with measurements of nuclei with mass number of A ≈ 90 . Such comparison indicates that the isoscalar giant monopole resonance distributions in these nuclei are very similar, and no influence due to nuclear structure was observed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

The convergence of quadrupole rotational invariants from the nuclear shell model

Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of convergence is addressed. Shell-model calculations performed in the sd- and pf-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states using the first 40 states of the relevant spins. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined. It is found that, on average, the inclusion of four intermediate states results in the leading-order invariant, $\langle\hat{Q^2}\rangle$, converging to within 10% of its true value and the triaxiality term, cos (3δ), converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly. The convergence of quadrupole rotationally invariant sum rules was quantified in the sd- and pf-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Finally, larger spaces, such as the rare-earth region, potentially offer faster convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Testing the impact of electromagnetic fields on the directed flow of constituent quarks in heavy-ion collisions

It has been proposed that strong electromagnetic fields produced in the early stages of heavy-ion collisions can lead to splitting of the rapidity-odd directed flow of positive and negative hadrons. For light hadrons, the interpretation of such measurements is complicated by the low magnitude of directed flow as well as by ambiguities arising from transported quarks. To overcome these complications, we propose measurements using only hadrons carrying produced quarks (u¯, d¯, s s¯ ). Here, we discuss how to identify the kinematics where such hadrons are produced via the coalescence mechanism and therefore their flow is the sum of the flow of their constituent quarks. With this sum rule verified for certain combinations of hadrons, the expected systematic violation of this rule with increasing electric charge can be measured, which could be a consequence of the electromagnetic fields produced in the collisions. Our approach can be tested with the high statistics data from Phase II of the Beam Energy Scan program at the Relativistic Heavy Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Ab initio coupled-cluster calculations of ground and dipole excited states in He 8

We perform coupled-cluster calculations of ground- and dipole excited-state properties of the 8 He halo nucleus with nucleon-nucleon and three-nucleon interactions from chiral effective field theory, both with and without explicit delta degrees of freedom. By increasing the precision in our coupled-cluster calculations via the inclusion of leading-order three-particle three-hole excitations in the cluster operator, we obtain a ground-state energy and a charge radius that are consistent with experiment, albeit with a slight underbinding. We also investigate the excited states induced by the electric dipole operator and present a discussion on the Thomas-Reiche-Kuhn and cluster sum rules. Lastly, we compute the electric dipole polarizability, providing a theoretical benchmark for future experimental determinations that will study this exotic nucleus.

6 ≤ A ≤ 19↗
DOE OSTI2023

Final-state interactions and spin structure in E 1 breakup of Li 11 in halo effective field theory

In this work, we calculate the E1 breakup of the 2n halo nucleus 11 Li in halo effective field theory (Halo EFT) at leading order. In Halo EFT, 11 Li is treated as a three-body system of a 9 Li core and two neutrons. We present a detailed investigation of final-state interactions (FSIs) in the neutron-neutron (nn) and neutron-core (nc) channels. We employ Møller operators to formulate an expansion scheme that satisfies the non-energy-weighted cluster sum rule and successively includes higher-order terms in the multiple-scattering series for the FSI. Computing the E1 strength up to third order in this scheme, we observe apparent convergence and good agreement with experiment. The neutron-neutron FSI is by far the most important contribution and largely determines the maximum value of the E1 distribution. However, inclusion of nc FSI does shift the peak position to slightly lower energies. Moreover, we investigate the sensitivity of the E1 response to the spin structure of the neutron- 9 Li interaction. We contrast results for an interaction that is the same in the spin-1 and spin-2 channels with one that is only operative in the spin-2 channel, and find that good agreement with experimental data is only obtained if the interaction is present in both spin channels. The latter case is shown to be equivalent to a calculation in which the spin of 9 Li is neglected.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

g 9/2 neutron strength in the N = 29 isotones and the 52 Cr(d,p)⁢ 53 Cr reaction

We performed a measurement of the 52 Cr(d,p)⁢⁢ 53 Cr reaction at 16 MeV using the Florida State University Super-Enge Split-Pole Spectrograph (SE-SPS) and observed 26 states. While all of the states observed here had been seen in previous (d,p) experiments, we changed five L assignments from those reported previously and determined L values for nine states that had not had such assignments made previously. The g 9/2 neutron strength observed in 53 Cr in the present work and in the N = 29 isotones 49 Ca, 51 Ti, and 55 Fe via (d,p) reactions is much smaller than the sum rule for this strength. Most of the observed L = 4 strength in these nuclei is located in states near 4 MeV excitation energy. The remaining g 9/2 strength may be located in the continuum or may be fragmented among many bound states. A covariant density-functional theory calculation provides support for the hypothesis that the g 9/2 neutron orbit is unbound in 53 Cr. The (α, 3 He) reaction may provide a more sensitive probe for the missing g 9/2 neutron strength. Additionally, particle-γ coincidence experiments may help resolve some remaining questions in this nucleus.

39 ≤ A ≤ 58↗
DOE OSTI2024

Multiparticle integral and differential correlation functions

This paper formalizes the use of integral and differential cumulants for measurements of multiparticle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net-charge fluctuations. This enables the introduction of multiparticle balance functions, defined based on differential correlation functions (factorial cumulants), that suppress two- and three-prong resonance decays effects and enable measurements of underlying long-range correlations obeying quantum number conservation constraints. These multiparticle balance functions satisfy simple sum rules determined by quantum number conservation. It is additionally shown that these multiparticle balance functions arise as an intrinsic component of high-order net-charge cumulants. This implies that the magnitude of these cumulants, measured in a specific experimental acceptance, is strictly constrained by charge conservation and primarily determined by the rapidity and momentum width of these balance functions. The paper also presents techniques to reduce the computation time of differential correlation functions up to order n = 10 based on the methods of moments. Published by the American Physical Society 2024

Physics↗
DOE OSTI2024

Mixed-species charge and baryon balance functions studies with PYTHIA

Mixed species charge and baryon balance functions are computed based on proton-proton ( p p ) collisions simulated with the PYTHIA8 model. Simulations are performed with selected values of the collision energy s and the Monash tune and the ropes and shoving modes of PYTHIA8 to explore whether such measurements provide useful new information and constraints on mechanisms of particle production in p p collisions. Charge balance functions are studied based on mixed pairs of pions, kaons, and protons, whereas baryon balance functions are computed for mixed low mass strange and nonstrange baryons. Both charge and baryon balance functions of mixed particle pairs feature shapes and amplitudes that sensitively depend on the particle considered owing largely to the particle production mechanisms implemented in PYTHIA. The evolution of balance functions integrals with the longitudinal width of the acceptance are presented and one finds that sums of such integrals for a given reference particle obey expected sum rules for both charge and baryon balance functions. Additionally, both types of balance functions are found to evolve in shape and amplitude with increasing collision energy s and the PYTHIA tunes considered. Published by the American Physical Society 2024

Physics↗
DOE OSTI2024

Electromagnetic observables of open-shell nuclei from coupled-cluster theory

Here we develop a new method to describe electromagnetic observables of open-shell nuclei with two nucleons outside a closed shell. This approach combines the equation-of-motion coupled-cluster method for such systems and the Lorentz integral transform technique, expanding the applicability of coupled-cluster theory for electromagnetic observables beyond closed-(sub)shell nuclei. To validate this new approach, we compute the non-energy-weighted dipole sum rule and the dipole polarizability of 16,24 ⁢O in both the closed-(sub)shell and the new equation-of-motion coupled-cluster frameworks, finding agreement within error bars. We then analyze the evolution of the dipole polarizability along the oxygen and calcium isotopic chains. Our predictions agree well with available experimental data and other available theoretical calculations for the closed-(sub)shell 16,22 ⁢O and the open-shell 18 O. In the calcium isotopes, we observe that our dipole polarizability predictions for open-shell nuclei are lower than those of closed-(sub)shell nuclei. We expect that our predictions for 24 O and 54,56 ⁢Ca will motivate future experimental studies at the drip line.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Measurement of the nucleon spin structure functions for 0.01 < 𝑄 2 < 1 GeV 2 using CLAS

The spin structure functions of the proton and the deuteron were measured during the EG4 experiment at Jefferson Lab in 2006. Data were collected for longitudinally polarized electron scattering off longitudinally polarized NH 3 and ND 3 targets, for 𝑄 2 values as small as 0.012 and 0.02 GeV 2 , respectively, using the CEBAF Large Acceptance Spectrometer. This is the archival paper of the EG4 experiment that summarizes the previously reported results of the polarized structure functions 𝑔 1 , 𝐴 1 ⁢𝐹 1 , and their moments $\bar{Γ}$ 1 , $\bar{𝛾}$ 0 , and $\bar{𝐼}$ TT , for both the proton and the deuteron. In addition, we report on new results on the neutron 𝑔 1 extracted by combining proton and deuteron data and correcting for Fermi smearing, and on the neutron moments $\bar{Γ}$ 1 , $\bar{𝛾}$ 0 , and $\bar{𝐼}$ TT formed directly from those of the proton and the deuteron. Our data are in good agreement with the Gerasimov-Drell-Hearn sum rule for the proton, deuteron, and neutron. Furthermore, the isovector combination was formed for 𝑔 1 and the Bjorken integral $\bar{Γ}^{𝑝−𝑛}_1$, and it was compared to available theoretical predictions. All of our results, to the best of our knowledge, provide for the first time extensive tests of spin observable predictions from chiral effective field theory (𝜒⁢EFT) in a 𝑄 2 range commensurate with the pion mass. Finally, they motivate further improvement in 𝜒⁢EFT calculations from other approaches such as the lattice gauge method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Moments of the neutron g₂ structure function at intermediate Q²

We present new experimental results of the ³He spin structure function g₂ in the resonance region at Q² values between 1.2 and 3.0 (GeV/c)². Spin dependent moments of the neutron were then extracted.Our main result, the inelastic contribution to the neutron d₂ matrix element, was found to be small (Q²) = 2.4 (GeV/c)² and in agreement with the Lattice QCD calculation. The Burkhardt-Cottingham sum rule for ³He neutron was tested with the measured data and using the Wandzura-Wilczek relation for the low x unmeasured region.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Statistical properties of Pu 243 , and Pu 242 ( n , γ ) cross section calculation

The level density and γ-ray strength function (γSF) of 243 Pu have been measured in the quasicontinuum using the Oslo method. Excited states in 243 Pu were populated using the 242 Pu(d,p) reaction. The level density closely follows the constant-temperature level density formula for excitation energies above the pairing gap. The γSF displays a double-humped resonance at low energy as also seen in previous investigations of actinide isotopes. The structure is interpreted as the scissors resonance and has a centroid of ω SR = 2.42(5) MeV and a total strength of B SR = 10.1(15) μ 2 N , which is in excellent agreement with sum-rule estimates. Lastly, the measured level density and γSF were used to calculate the 242 Pu(n,γ) cross section in a neutron energy range for which there were previously no measured data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Light-front spin-dependent spectral function and nucleon momentum distributions for a three-body system

Poincare covariant definitions for the spin-dependent spectral function and for the momentum distributions within the light-front Hamiltonian dynamics are proposed for a three-fermion bound system, starting from the light-front wave function of the system. The adopted approach is based on the Bakamjian–Thomas construction of the Poincaré generators, which allows one to easily import the familiar and wide knowledge on the nuclear interaction into a light-front framework. The proposed formalism can find useful applications in refined nuclear calculations, such as those needed for evaluating the European Muon Collaboration effect or the semi-inclusive deep inelastic cross sections with polarized nuclear targets, since remarkably the light-front unpolarized momentum distribution by definition fulfills both normalization and momentum sum rules. As a result, also shown is a straightforward generalization of the definition of the light-front spectral function to an A -nucleon system.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

From bare to renormalized order parameter in gauge space: Structure and reactions

The physical reason why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of pairing rotational bands, making use of simple BCS (constant matrix elements) or of many-body (Nambu-Gorkov (NG), nuclear field theory (NFT)) spectroscopic amplitudes, is not immediately obvious. Restoration of spontaneous symmetry breaking and associated emergent generalised rigidity in gauge space provides the answer, and points to a new emergence: a physical sum rule resulting from the intertwining of structure and reaction processes and closely connected with the central role induced pairing interaction plays in structure together with the fact that successive transfer dominates Cooper pair tunneling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Transverse-momentum-dependent quark distribution functions of spin-one targets: Formalism and covariant calculations

In this paper, we present a covariant formulation and model calculations of the leading-twist time-reversal even transverse-momentum-dependent quark distribution functions (TMDs) for a spin-one target. Emphasis is placed on a description of these three-dimensional distribution functions which is independent of any constraints on the spin quantization axis. We apply our covariant spin description to all nine leading-twist time-reversal even ρ meson TMDs in the framework provided by the Nambu–Jona-Lasinio model, incorporating important aspects of quark confinement via the infrared cutoff in the proper-time regularization scheme. In particular, the behaviors of the three-dimensional TMDs in a tensor polarized spin-one hadron are illustrated. Sum rules and positivity constraints are discussed in detail. Our results do not exhibit the familiar Gaussian behavior in the transverse momentum, and other results of interest include the finding that the tensor polarized TMDs—associated with spin-one hadrons—are very sensitive to quark orbital angular momentum, and that the TMDs associated with the quark operator γ + γ T γ 5 would vanish were it not for dynamical chiral symmetry breaking. In addition, we find that 44% of the ρ meson's spin is carried by the orbital angular momentum of the quarks, and that the magnitude of the tensor polarized quark distribution function is about 30% of the unpolarized quark distribution. Finally, a qualitative comparison between our results for the tensor structure of a quark-antiquark bound state is made to existing experimental and theoretical results for the two-nucleon (deuteron) bound state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Minimal nuclear energy density functional

In this paper, we present a minimal nuclear energy density functional (NEDF) called “SeaLL1” that has the smallest number of possible phenomenological parameters to date. SeaLL1 is defined by seven significant phenomenological parameters, each related to a specific nuclear property. It describes the nuclear masses of even-even nuclei with a mean energy error of 0.97 MeV and a standard deviation of 1.46 MeV , two-neutron and two-proton separation energies with rms errors of 0.69 MeV and 0.59 MeV respectively, and the charge radii of 345 even-even nuclei with a mean error ε r = 0.022 fm and a standard deviation σ r = 0.025 fm . SeaLL1 incorporates constraints on the equation of state (EoS) of pure neutron matter from quantum Monte Carlo calculations with chiral effective field theory two-body ( NN ) interactions at the next-to-next-to-next-to leading order (N3LO) level and three-body ( NNN ) interactions at the next-to-next-to leading order (N2LO) level. Two of the seven parameters are related to the saturation density and the energy per particle of the homogeneous symmetric nuclear matter, one is related to the nuclear surface tension, two are related to the symmetry energy and its density dependence, one is related to the strength of the spin-orbit interaction, and one is the coupling constant of the pairing interaction. Finally, we identify additional phenomenological parameters that have little effect on ground-state properties but can be used to fine-tune features such as the Thomas-Reiche-Kuhn sum rule, the excitation energy of the giant dipole and Gamow-Teller resonances, the static dipole electric polarizability, and the neutron skin thickness.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions

Quantum Monte Carlo methods have recently been employed to study properties of nuclei and infinite matter using local chiral effective-field-theory interactions. In this paper, we present a detailed description of the auxiliary field diffusion Monte Carlo algorithm for nuclei in combination with local chiral two- and three-nucleon interactions up to next-to-next-to-leading order. We show results for the binding energy, charge radius, charge form factor, and Coulomb sum rule in nuclei with $3{\le}A{\le}16$. Particular attention is devoted to the effect of different operator structures in the three-body force for different cutoffs. Finally, the outcomes suggest that local chiral interactions fit to few-body observables give a very good description of the ground-state properties of nuclei up to $^{16}\mathrm{O}$, with the exception of one fit for the softer cutoff which predicts overbinding in larger nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗