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At least 181 records · Page 10

Properties of states near 𝐸 𝑥 = 6 MeV in 18 Ne through 17 F +𝑝 scattering

The rate of energy production in the hot-CNO cycle and breakout to the rapid-proton capture process in Type I X-ray bursts is strongly related to the 14 O⁡(𝛼,𝑝)⁢ 17 F reaction rate. The properties of states in 18 Ne near 𝐸 𝑥 = 6.1–6.3 MeV are important for understanding the 14 O⁡(𝛼,𝑝)⁢ 17 F reaction rate. In order to study 18 Ne resonances around this energy region, the RESOLUT radioactive-ion beam facility at Florida State University was used to perform 17 F⁡(𝑝,𝑝)⁢ 17 F elastic scattering on a polypropylene target under inverse kinematics. Scattered protons were detected in a silicon-strip detector array while recoiling 17 F ions were detected in coincidence in a gas ionization detector. An 𝑅-matrix analysis of measured cross sections was conducted along with a reanalysis of data from previous 17 F +𝑝 measurements. All the data analyzed are well described by a consistent set of parameters with a 1 − assignment for a state at 6.14(1) MeV. A second comparable solution is also found with a 3 − assignment for the 6.14(1) MeV state. There is no conclusive evidence supporting one of the two solutions over the other. The rates of the 14 O⁡(𝛼,p)⁢ 17 F reaction that are determined from the two solutions differ by up to an order of magnitude.

6 ≤ A ≤ 19↗

Density matrix renormalization group description of the island of inversion isotopes F 28 – 33

Recent experiments have confirmed that the neutron-rich isotopes 28,29 F belong to the so-called island of inversion (IOI), a region of the nuclear chart around Z = 10 and N = 20 where nuclear structure deviates from the standard shell model predictions due to deformation and continuum effects. However, while the general principles leading to the IOI are relatively well understood, the details of the low-lying structure of the exotic fluorine isotopes 28–33 F are basically unknown. In this study, we perform large-scale shell model calculations including continuum states to investigate the properties of the neutron-rich isotopes 25–33 F, from a core of 24 O and using an effective two-body interaction with a small number of adjustable parameters in the central and tensor channels. We develop two models adjusted on experimentally confirmed states in 25,26 O and 25–27 F based on different assumptions concerning the positions of the neutron 0d 3/2 and 1p 3/2 shells, and solve the many-body problem using the density matrix renormalization group (DMRG) method for open quantum systems in an sd–fp model space. We obtain the first detailed spectroscopy of 25–33F in the continuum and show how the interplay between continuum effects and deformation explains the recent data on 28,29 F. Several deformed one- and two-neutron halo states are predicted in 29,31 F, and we provide some information about the possible structure of the heaviest fluorine isotopes. We also suggest several experimental studies of interest to constraint models and test the present predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measuring the properties of f - mode oscillations of a protoneutron star by third-generation gravitational-wave detectors

Core-collapse supernovae are among the astrophysical sources of gravitational waves that could be detected by third-generation gravitational-wave detectors. Here, we analyze the gravitational-wave strain signals from two- and three-dimensional simulations of core-collapse supernovae generated using the code FORNAX. A subset of the two-dimensional simulations has non-zero core rotation at the core bounce. A dominant source of time changing quadrupole moment is the l = 2 fundamental mode (f- mode) oscillation of the proto-neutron star. From the time-frequency spectrogram of the gravitational-wave strain we see that, starting ~ 400 ms after the core bounce, most of the power lies within a narrow track that represents the frequency evolution of the f-mode oscillations. The f-mode frequencies obtained from linear perturbation analysis of the angle averaged profile of the protoneutron star corroborate what we observe in the spectrograms of the gravitational wave signal. We explore the measurability of the f-mode frequency evolution of protoneutron star for a supernova signal observed in the third-generation gravitational-wave detectors. Measurement of the frequency evolution can reveal information about the masses, radii, and densities of the proto-neutron stars. We find that if the third generation detectors observe a supernova within 10 kpc, we can measure these frequencies to within ~90% accuracy. Here, we can also measure the energy emitted in the fundamental f-mode using the spectrogram data of the strain signal. We find that the energy in the f-mode can be measured to within 20% error for signals observed by Cosmic Explorer using simulations with successful explosion, assuming source distances within 10 kpc.

79 ASTRONOMY AND ASTROPHYSICS↗

CEFR simulation using diffusion code system RAST-F

In this study, the RAST-F code system, which is based on the two-step approach that couples a multi-group cross-section generation Monte-Carlo (MC) code and a multi-group nodal diffusion solver, was used for the neutronic simulation of the CEFR start-up experiments. The numerical solution of the RAST-F system was verified against the full core MC solution MCS at all control rods fully inserted and withdrawn states. The RAST-F solution of the selected experimental simulations was compared against the measurement data. A good agreement between RAST-F and MCS solutions was observed with less than 120 pcm discrepancies and 1.2% root-mean-square error in terms of k{sub eff} and power distribution, respectively. Meanwhile, the RAST-F result agreed well with the experimental data within two-sigma of experimental uncertainty. The good agreement of these results indicates that RAST-F can be used to neutronic steady-state simulations for small core-size SFR, which was challenged to deterministic code systems. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Performance Assessment for the E-Area Low-Level Radioactive Waste Disposal Facility at the Savannah River Site: Appendix F

As a supplement to Chapter 6, Section 6.1.1.3, Table F-1 through Table F-24 provide tabular results of the sensitivity analysis calculations for waste disposal timing (Sensitivity Case S6) in NR07E (Cases 3 and 4) and NR26E (Cases 1 through 4). The title of each table identifies the DU, sensitivity case, and performance measure. Section F.1.1 (Table F-1 through Table F-8) presents results for NR07E and Section F.1.2 (Table F-9 through Table F-24) presents results for NR26E. In each table, radionuclides are sorted from highest to lowest nominal concentration or dose factor. Nominal values are when waste disposal occurs at the start of operations; timeline values are when waste disposal occurs at the end of operations. The differences (Δ values) in the last column of each table equal the timeline concentration or dose factor minus the nominal concentration or dose factor, where DF and CF are shorthand designations for dose factor and concentration factor, respectively.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Hygroscopic Growth of UO 2 F 2 Particles

Hygroscopicity is an important physicochemical property of aerosol that describes the ability of a particle to uptake water. The hygroscopic properties of uranyl fluoride (UO 2 F 2 ) aerosol generated from a UF 6 hydrolysis reactor was investigated for the first time using a custom-built Humidified Tandem Differential Mobility Analyzer (HTDMA). The HTDMA is capable of measuring UO 2 F 2 particle growth determined by mobility size over a wide range of atmospheric humidity from dry conditions at <10% relative humidity (RH) to 85% RH. The hygroscopic properties were determined for nanoparticles as small as 3.5 nm in this study. Anhydrous UO 2 F 2 particles with a mobility diameter of 3.5 nm were shown to be highly hygroscopic with a deliquescence relative humidity (DRH) of 10%. Hydrates with a larger mobility diameter of 10 to 80 nm were non-hygroscopic with no observable DRH and limited water uptake up to 85% RH. These results demonstrate the hygroscopic properties of UO 2 F 2 particles are highly variable and based on both the mobility size and hydration state. Hygroscopicity affects the physicochemical properties of UO 2 F 2 particles, including the aerosol phase state and viscosity, with impacts on aerosol growth, coagulation, and deposition that is critical for understanding the fate and transport of UO 2 F 2 particles in the atmosphere.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Influence of the E region dynamo on equatorial spread F

The integrated E region Pedersen conductivity can be an important parameter in determining whether the bottomside of the equatorial F layer will be stable against the Rayleigh-Taylor gravitational instability. The F layer is observed to become unstable when it rises to great heights after sunset. One effect of this height rise is to decrease the stabilizing influence of ion-neutral collisions at F region heights. It is shown here that the same eastward electric field that raises the F layer also decreases the Pedersen conductivity of the E region, which further destabilizes convective overturning. Because the conductivity of magnetic tubes that penetrate the main F layer is large compared to the E layer contribution, these effects are important only for the bottomside of the equatorial F layer.

Hanson, W. B.↗

Evaluation of water cooled supersonic temperature and pressure probes for application to 2000 F flows

The development of water cooled supersonic probes used to study high temperature jet plumes is addressed. These probes are: total pressure, static pressure, and total temperature. The motivation for these experiments is the determination of high temperature supersonic jet mean flow properties. A 3.54 inch exit diameter water cooled nozzle was used in the tests. It is designed for exit Mach 2 at 2000 F exit total temperature. Tests were conducted using water cooled probes capable of operating in Mach 2 flow, up to 2000 F total temperature. Of the two designs tested, an annular cooling method was chosen as superior. Data at the jet exit planes, and along the jet centerline, were obtained for total temperatures of 900 F, 1500 F, and 2000 F, for each of the probes. The data obtained from the total and static pressure probes are consistent with prior low temperature results. However, the data obtained from the total temperature probe was affected by the water coolant. The total temperature probe was tested up to 2000 F with, and without, the cooling system turned on to better understand the heat transfer process at the thermocouple bead. The rate of heat transfer across the thermocouple bead was greater when the coolant was turned on than when the coolant was turned off. This accounted for the lower temperature measurement by the cooled probe. The velocity and Mach number at the exit plane and centerline locations were determined from the Rayleigh-Pitot tube formula.

Lagen, Nicholas T.↗

Numerical simulation of the flow about the F-18 HARV at high angle of attack

This report summarizes research done over the past two years as part of NASA Grant NCC 2-729. This research has been aimed at validating numerical methods for computing the flow about the complete F-18 HARV at alpha = 30 deg and alpha = 45 deg. At 30 deg angle of attack, the flow about the F-18 is dominated by the formation, and subsequent breakdown, of strong vortices over the wing leading-edge extensions (LEX). As the angle of attack is increased to alpha = 45 deg, the fuselage forebody of the F-18 contains significant laminar and transitional regions which are not present at alpha = 30 deg. Further, the flow over the LEX at alpha = 45 deg is dominated by an unsteady shedding in time, rather than strong coherent vortices. This complex physics, combined with the complex geometry of a full aircraft configuration, provides a challenge for current computational fluid dynamics (CFD) techniques. The following sections present the numerical method and grid generation scheme that was used, a review of prior research done to numerically model the F-18 HARV, and a discussion of the current research. The current research is broken into two main topics: the effect of engine-inlet mass-flow rate on the F-18 vortex breakdown position, and the results using a refined F-18 computational model to compute the flow at alpha = 30 deg and alpha = 45 deg.

Murman, Scott M.↗

Numerical simulation of the flow about the F-18 HARV at high angle of attack

This research has been aimed at validating numerical methods for computing the flow about the complete F-18 HARV at alpha = 30 deg and alpha = 45 deg. At 30 deg angle of attack, the flow about the F-18 is dominated by the formation, and subsequent breakdown, of strong vortices over the wing leading-edge extensions (LEX). As the angle of attack is increased to alpha = 45 deg, the fuselage forebody of the F-18 contains significant laminar and transitional regions which are not present at alpha = 30 deg. Further, the flow over the LEX at alpha = 45 deg is dominated by an unsteady shedding in time, rather than strong coherent vortices. This complex physics, combined with the complex geometry of a full-aircraft configuration, provides a challenge for current computational fluid dynamics (CFD) techniques. The following sections present the numerical method and grid generation scheme that was used, a review of prior research done to numerically model the F-18 HARV, and a discussion of the current research. The current research is broken into three main topics; the effect of engine-inlet mass-flow rate on the F-18 vortex breakdown position, the results using a refined F-18 computational model to compute the flow at alpha = 30 deg and alpha = 45 deg, and research done using the simplified geometry of an ogive-cylinder configuration to investigate the physics of unsteady shear-layer shedding. The last section briefly summarizes the discussion.

Murman, Scott M.↗

Experimental Investigation of an Air-Cooled Turbine Operating in a Turbojet Engine at Turbine Inlet Temperatures up to 2500 F

An experimental investigation was made of an air-cooled turbine at average turbine inlet temperatures up to 2500 F. A modified production-model 12-stage axial-flow-compressor turbojet engine operating in a static sea-level stand was used as the test vehicle. The modifications to the engine consisted of the substitution of special combustor and turbine assemblies and double-walled exhaust ducting for the standard parts of the engine. All of these special parts were air-cooled to withstand the high operating temperatures of the investigation. The air-cooled turbine stator and rotor blades were of the corrugated-insert type. Leading-edge tip caps were installed on the rotor blades to improve leading-edge cooling by diverting the discharge of coolant to regions of lower gas pressure toward the trailing edge of the blade tip. Caps varying in length from 0.15- to 0.55-chord length were used in an attempt to determine the optimum cap length for this blade. The engine was operated over a range of average turbine inlet temperatures from about 1600 to about 2500 F, and a range of average coolant-flow ratios of 0.012 to 0.065. Temperatures of the air-cooled turbine rotor blades were measured at all test conditions by the use of thermocouples and temperature-indicating paints. The results of the investigation indicated that this type of blade is feasible for operation in turbojet engines at the average turbine inlet temperatures and stress levels tested(maximums of 2500 F and 24,000 psi, respectively). An average one-third-span blade temperature of 1300 F could be maintained on 0.35-chord tip cap blades with an average coolant-flow ratio of about 0.022 when the average turbine inlet temperature was 2500 F and cooling-air temperature was about 260 F. All of the leading-edge tip cap lengths improved the cooling of the leading-edge region of the blades, particularly at low average coolant-flow ratios. At high gas temperatures, such parts as the turbine stator and the combustor liners are likely to be as critical as the turbine rotor blades.

Cochran, Reeves P.↗

Technical advance: identification of plant actin-binding proteins by F-actin affinity chromatography

Proteins that interact with the actin cytoskeleton often modulate the dynamics or organization of the cytoskeleton or use the cytoskeleton to control their localization. In plants, very few actin-binding proteins have been identified and most are thought to modulate cytoskeleton function. To identify actin-binding proteins that are unique to plants, the development of new biochemical procedures will be critical. Affinity columns using actin monomers (globular actin, G-actin) or actin filaments (filamentous actin, F-actin) have been used to identify actin-binding proteins from a wide variety of organisms. Monomeric actin from zucchini (Cucurbita pepo L.) hypocotyl tissue was purified to electrophoretic homogeneity and shown to be native and competent for polymerization to actin filaments. G-actin, F-actin and bovine serum albumin affinity columns were prepared and used to separate samples enriched in either soluble or membrane-associated actin-binding proteins. Extracts of soluble actin-binding proteins yield distinct patterns when eluted from the G-actin and F-actin columns, respectively, leading to the identification of a putative F-actin-binding protein of approximately 40 kDa. When plasma membrane-associated proteins were applied to these columns, two abundant polypeptides eluted selectively from the F-actin column and cross-reacted with antiserum against pea annexins. Additionally, a protein that binds auxin transport inhibitors, the naphthylphthalamic acid binding protein, which has been previously suggested to associate with the actin cytoskeleton, was eluted in a single peak from the F-actin column. These experiments provide a new approach that may help to identify novel actin-binding proteins from plants.

Non-NASA Center↗

Detached-Eddy Simulation Based on the V2-F Model

Detached-eddy simulation (DES) based on the v(sup 2)-f Reynolds-averaged Navier-Stokes (RANS) model is developed and tested. The v(sup 2)-f model incorporates the anisotropy of near-wall turbulence which is absent in other RANS models commonly used in the DES community. The v(sup 2)-f RANS model is modified in order the proposed v(sup 2)-f-based DES formulation reduces to a transport equation for the subgrid-scale kinetic energy isotropic turbulence. First, three coefficients in the elliptic relaxation equation are modified, which is tested in channel flows with friction Reynolds number up to 2000. Then, the proposed v(sup 2)-f DES model formulation is derived. The constant, C(sub DES), required in the DES formulation was calibrated by simulating both decaying and statistically-steady isotropic turbulence. After C(sub DES) was calibrated, the v(sub 2)-f DES formulation is tested for flow around a circular cylinder at a Reynolds number of 3900, in which case turbulence develops after separation. Simulations indicate that this model represents the turbulent wake nearly as accurately as the dynamic Smagorinsky model. Spalart-Allmaras-based DES is also included in the cylinder flow simulation for comparison.

Jee, Sol Keun↗

235-F GoldSim Fate and Transport Model: Uncertainty Quantification

Building 235-F was configured with two missions in mind: Actinide Billet Line (ABL) and the fabrication of Pu-238 oxide for space program applications. ABL produced Np-237 billets for use in SRS reactors, whereas the design process, fabrication, and examination of Pu-238 oxide powder occurred within the following areas, respectively: Plutonium Experimental Facility (PEF), Plutonium Fuel Form (PuFF), and Old Metallography Lab (OML). By 1990 production ceased and by 2006 de-inventory occurred; however, assays have shown significant holdup remains within ABL and PuFF. As a result, 235-F is a Category 2 nuclear facility, with plans to undergo deactivation and decommission (D and D) via In-Situ Disposal (ISD). The purpose of this project is to ensure United States Environmental Protection Agency (USEPA) groundwater radiation maximum contaminant level (MCL) and dosage standards are met during the D and D of 235-F by quantifying uncertainty through probabilistic modeling and evaluation of various ISD alternatives. GoldSim is a dynamic modeling software package with a graphical, object-oriented interface capable of capturing the influence of complex system input variability on probabilistic system outcomes. A GoldSim stochastic fate and transport model for 235-F was developed and matched with a PORFLOW deterministic model to simulate probabilistic release and flow of radionuclides from ABL and PuFF into the vadose zone, the Upper Three Runs (UTR) Aquifer, and UTR Creek. The GoldSim model was used to probabilistically evaluate four ISD scenarios against USEPA groundwater radiation MCLs and dosage standards. The deterministic 235-F GoldSim fate and transport model continues to be refined to match the results of the PORFLOW deterministic model to ensure the model accurately represents radionuclide movement through the groundwater system. The stochastic variables that are utilized within the GoldSim model are founded on the most current data; a conservative perspective is taken where needed. Alignment with the PORFLOW deterministic model, coupled with input stochastic variability, allows the probabilistic 235-F GoldSim model to capture the conservative breadth of possible outcomes for radionuclide fate within this particular system. This ensures that the USEPA MCLs and dosage limits hold even in the worst case scenarios.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Energetic and Electronic Properties of UX +/0/– for X = Li and Be and Comparison of the Properties of the Uranium Atom Binding to 2nd Row Elements Li–F

The bonding and spectroscopic properties of ULi +/0/– and UBe +/0/– to complete the series for UX +/0/– for X = Li to F were investigated by high-level ab initio SO-CASPT2 and CCSD(T) electronic structure calculations. The low-lying spin–orbit states were obtained at the SA-CASPT2/aQ-PP level; bond dissociation energies (BDEs), ionization energies (IEs), adiabatic electronic affinities (AEAs), and vertical detachment energies (VDEs) were calculated at the Feller-Peterson-Dixon (FPD) level. A dense manifold of low-lying states was predicted for ULi +/0/– and UBe +/0/– . Here, the calculated BDEs for ULi (37.7 kJ/mol) and UBe (8.0 kJ/mol) show that UBe is weakly bound. For redox processes, the BDEs increased for ULi + (109.3 kJ/mol), ULi – (47.4 kJ/mol), UBe + (35.6 kJ/mol), and UBe – (72.3 kJ/mol). The IE(ULi) = 4.650 eV is lower than IE(Li); the IE(UBe) = 5.901 eV is close to the IE(U) and to the IEs of UB, UC, UN, UO, and UF. The AEAs of ULi (0.708 eV) and UBe (0.989 eV) are lower than those for UB, UC, UN, and UO but higher than that for EA(UF). Natural bond orbital (NBO) calculations show that ULi has the 5f 3 6d 1 7s 2 configuration for U and 2s 1 for Li, with a small partial negative charge slightly delocalized on U. UBe arises from the U(5f 3 6d 1 7s 2 ) and Be(2s 2 ) electron configurations with no charge separation. The same calculations were made for WX (X = Li, Be, C–F) to enable detailed comparisons of the properties for UX with WX (X = Li–F). For WX, BDE(WX) is higher than that for UX for X = Li to N and lower than BDE(UX) for X = O and F, mostly due to the higher IE of W than U as ionic character becomes more important going from Li to F.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Charge completeness and the massless charge lattice in F-theory models of supergravity

We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Efficient Parameterization of Density Functional Tight-Binding for 5 f -Elements: A Th–O Case Study

Density functional tight binding (DFTB) models for f-element species are challenging to parametrize owing to the large number of adjustable parameters. The explicit optimization of the terms entering the semiempirical DFTB Hamiltonian related to f orbitals is crucial to generating a reliable parametrization for f-block elements, because they play import roles in bonding interactions. However, since the number of parameters grows quadratically with the number of orbitals, the computational cost for parameter optimization is much more expensive for the f-elements than for the main group elements. In this work we present a set of efficient approaches for mitigating the hurdle imposed by the large size of the parameter space. A novel group-by-orbital correction functions for two-center bond integrals was developed. With this approach the number of parameters is reduced, and it grows linearly with the number of elements, maintaining the accuracy and the number of parameters, in the case of f elements, by more than 40%. The parameter optimization step was accelerated by means of the mini-batch BFGS method. This method allows parameter optimizations with much larger training sets than other single batch methods. A stochastic optimizer was employed that helped overcome shallow local minima in the objective function. The proposed algorithm was used to parametrize the DFTB Hamiltonian for the Th–O system, which was subsequently applied to the study of ThO 2 nanoparticles. The training set consisted of 6322 unique structures, which is barely feasible with conventional optimization methods. The optimized parameter set, LANL-ThO, displays good agreement with DFT-calculated properties such as energies, forces, and structures for both clusters and bulk ThO 2 . Benefiting from the fewer number of parameters and lower computational costs for objective function evaluations, this new approach shows its potential applications in DFTB parametrization for elements with high angular momentum, which present a challenge to conventional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elliptic anisotropy measurement of the f 0 (980) hadron in proton-lead collisions and evidence for its quark-antiquark composition

Despite the f 0 (980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark ($q\bar{q}$) meson, a tetraquark ($q\bar{q}$$q\bar{q}$) exotic state, a kaon-antikaon ($K\bar{K}$) molecule, or a quark-antiquark-gluon ($q\bar{q}$g) hybrid. This paper reports strong evidence that the f 0 (980) state is an ordinary $q\bar{q}$ meson, inferred from the scaling of elliptic anisotropies (v 2 ) with the number of constituent quarks (n q ), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f 0 (980) state is reconstructed via its dominant decay channel f 0 (980) → π + π − , in proton-lead collisions recorded by the CMS experiment at the LHC, and its v 2 is measured as a function of transverse momentum (p T ). It is found that the n q = 2 ($q\bar{q}$ state) hypothesis is favored over n q = 4 ($q\bar{q}$$q\bar{q}$ or $K\bar{K}$ states) by 7.7, 6.3, or 3.1 standard deviations in the p T < 10, 8, or 6 GeV/c ranges, respectively, and over n q = 3 ($q\bar{q}$g hybrid state) by 3.5 standard deviations in the p T < 8 GeV/c range. This result represents the first determination of the quark content of the f 0 (980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗