Nuclear Commons^™

Beam Spin Asymmetries In Deeply Virtual Compton Scattering (Dvcs) With Clas At 4.8 Gev, G. Gavalian, Gerard P. Gilfoyle, Et. Al.

Physics Faculty Publications

We report measurements of the beam spin asymmetry in deeply virtual Compton scattering (DVCS) at an electron beam energy of 4.8 GeV using the CLAS detector at the Thomas Jefferson National Accelerator Facility. The DVCS beam spin asymmetry has been measured in a wide range of kinematics, 1.0 < Q² < 2.8 (GeV/c)², 0.12 < x_B < 0.48, and 0.1 < −t < 0.8 (GeV/c)², using the reaction ep → e' p X. The number of H(e, e' γ p) and H(e, e'π⁰p) events are separated in each (Q², x_B, t …

High-K Multi-Quasiparticle States And Rotational Bands In 255103Lr., H. B. Jeppesen, R. M. Clark, K. E. Gregorich, A. V. Afanasjev, M. N. Ali, J. M. Allmond, C. W. Beausang, M. Cromaz, M. A. Deleplanque, I. Dragojevic, J. Dvorak, P. A. Ellison, P. Fallon, M. A. Garcia, J. M. Gates, S. Gros, I. Y. Lee, A. O. Macchiavelli, S. L. Nelson, H. Nitsche, L. Stavsetra, F. S. Stephens, M. Wiedeking

Physics Faculty Publications

Two isomeric states have been identified in ²⁵⁵Lr. The decay of the isomers populates rotational structures. Comparison with macroscopic-microscopic calculations suggests that the lowest observed sequence is built upon the [624]9/2⁺ Nilsson state. However, microscopic cranked relativistic Hartree-Bogoliubov (CRHB) calculations do not reproduce the moment of inertia within typical accuracy. This is a clear challenge to theories describing the heaviest elements.

Heavy-Flavor Production At Accelerators, Nikolaos Kidonakis

Faculty Articles

I discuss heavy flavor production at hadronic facilities. I present total cross sections and differential distributions for top quark, bottom quark, and charm quark production at the rrevatron and LHC colliders, and at fixed-target experiments such as HERA-B. The calculations include complete next-to-leading order corrections as well as higher-order soft-gluon corrections which are important near kinematical threshold.

Deep Inelastic Scattering With Leading Protons Or Large Rapidity Gaps At Hera, S. Chekanov, M. Derrick, S. Magill, B. Musgrave, D. Nicholass, J. Repond, R. Yoshida, Margarita C. K. Mattingly, P. Antonioli, G. Bari, L. Bellagamba, D. Boscherini, A. Bruni, G. Bruni, G. Cara Romeo, F. Cindolo, M. Corradi, G. Iacobucci, A. Margotti, T. Massam, R. Nania, A. Polini, S. Antonelli, M. Basile, M. Bindi, L. Cifarelli, A. Contin, F. Palmonari, S. De Pasquale, G. Sartorelli, A. Zichichi

Faculty Publications

The dissociation of virtual photons, γ{star operator} p → X p, in events with a large rapidity gap between X and the outgoing proton, as well as in events in which the leading proton was directly measured, has been studied with the ZEUS detector at HERA. The data cover photon virtualities Q2 > 2 GeV2 and γ{star operator} p centre-of-mass energies 40 < W < 240 GeV, with MX > 2 GeV, where MX is the mass of the hadronic final state, X. Leading protons were detected in the ZEUS leading proton spectrometer. The cross section is presented as a function of t, the squared four-momentum transfer at the …

High-Energy Amplitudes In Gauge Theories In The Next-To-Leading-Order, Giovanni Antonio Chirilli

Physics Theses & Dissertations

Scattering processes play a central role in physics, and high-energies experiments give us an insight into the fine structure of matter. The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky-Kovchegov (BK) equation. In order to see if this equation is relevant for existing or future deep inelastic scattering (DIS) accelerators (like Electron Ion Collider (EIC) or Large Hadron electron Collider (LHeC)) one needs to know how large are the next-to-leading order (NLO) corrections. In addition, the NLO corrections …

Π+ Photoproduction On The Proton For Photon Energies From 0.725 To 2.875 Gev, M. Dugger, Gerard P. Gilfoyle, Et. Al.

Physics Faculty Publications

Differential cross sections for the reaction γp → nπ⁺ have been measured with the CEBAF Large Acceptance Spectrometer (CLAS) and a tagged photon beam with energies from 0.725 to 2.875 GeV. Where available, the results obtained here compare well with previously published results for the reaction. Agreement with the SAID andMAID analyses is found below 1 GeV. The present set of cross sections has been incorporated into the SAID database, and exploratory fits have been made up to 2.7 GeV. Resonance couplings have been extracted and compared to previous determinations. With the addition of these cross sections to the …

Two-Loop Soft Anomalous Dimensions And Next-To-Next-To-Leading-Logarithm Resummation For Heavy Quark Production, Nikolaos Kidonakis

Faculty Articles

I present results for two-loop soft anomalous dimensions for heavy quark production which control soft-gluon resummation at next-to-next-to-leading-logarithm accuracy. I derive an explicit expression for the exact result and study it numerically for top quark production via e(+) e(-) -> t (t) over bar t, and I construct a surprisingly simple but very accurate approximation. I show that the two-loop soft anomalous dimensions with massive quarks display a simple proportionality relation to the one-loop result only in the limit of vanishing quark mass. I also discuss the extension of the calculation to single top and top pair production in hadron …

Effect Of Advanced Synthetically Enhanced Detector Resolution Algorithm On Specificity And Sensitivity Of Portable High Purity Germanium Gamma Detector Spectra, Latosha M. Bell

Theses and Dissertations

The ability to identify special nuclear material is one of the necessary prevention mechanisms for preventing proliferation of special nuclear materials. Additionally, if a nuclear event were to occur, information about the nuclear material used may be extracted from gamma spectra, provided it is obtained quickly and accurately. This can be made possible with the use of the exceptional resolution of the HPGe detector. This experiment applied the Advanced Synthetically Enhanced Detector Resolution Algorithm (ASEDRA) to a portable HPGe detector's spectra, to investigate whether improvements in specificity and sensitivity can be obtained. This method has been used to improve performance …

Relative 235U(N,Γ) And (N,F) Cross Sections From 235U(D,Pγ) And (D,Pf), J. M. Allmond, L. A. Bernstein, C. W. Beausang, L. Phair, D. L. Bleuel, J. T. Burke, J. Escher, K. E. Evans, B. L. Goldblum, R. Hatarik, H. B. Jeppesen, S. R. Lesher, M. A. Mcmahan, J. O. Rasmussen, N. D. Scielzo, M. Wiedeking

Physics Faculty Publications

The internal surrogate ratio method allows for the determination of an unknown cross section, such as (n,γ), relative to a better-known cross section, such as (n,f), by measuring the relative exit-channel probabilities of a surrogate reaction that proceeds through the same compound nucleus. The validity of the internal surrogate ratio method is tested by comparing the relative γ and fission exit-channel probabilities of a ²³⁶U^∗ compound nucleus, formed in the ²³⁵U(d,p) reaction, to the known ²³⁵U(n,γ) and (n,f) cross sections. A model-independent method for measuring the …

Neutron Production Analysis On Inertial Electrostatic Deuterium-Deuterium Fusion, Louis Franzel

Theses & Honors Papers

The basic principle of fusion is combining two light nuclei to form one nucleus that is lighter than the combination of the original two. This loss of mass is converted into energy (E=mc² ) which can be harnessed for various applications. Fusion can take many different and varied forms including: aneutronic fusion, magnetic confinement (MFE), and inertial electrostatic confinement (IEC) to name a few. Fusion is highly adaptable because it can use several different types of fuel such as Deuterium-Tritium, Tritium-Helium-3, Proton-Boron₁₁, and Deuterium-Deuterium mixtures. On top of this, each of the fusion techniques mentioned uses different …

Evaluation Of Low-Temperature Fluoride Routes To Synthesize Actinide Nitrides And Oxide Solid Solutions, Gunanda Waduge Chinthaka Silva

UNLV Theses, Dissertations, Professional Papers, and Capstones

Actinide mononitrides have been considered as a possible nuclear fuel for the Generation-IV nuclear reactor systems. In the process of evaluating these actinide mononitrides as nuclear fuel, it is important to study different chemical and physical characteristics of these compounds. Synthesis of the materials is thus important. Carbothermic reduction is one of the techniques that have been used to synthesize actinide mononitrides. In this method, a mixture of actinide oxide such as UO ₂ and excess carbon is heat treated at temperatures greater than 1700 °C under a nitrogen atmosphere. The technique is however not promising in synthesizing the actinide …

Surrogate Ratio Method In The Actinide Region Using The (Α,Α'F) Reaction, S. R. Lesher, J. T. Burke, L. A. Bernstein, H. Ai, C. W. Beausang, D. L. Bleuel, R. M. Clark, F. S. Dietrich, J. Escher, P. Fallon, J. Gibelin, B. L. Goldblum, I. Y. Lee, A. O. Macchiavelli, M. A. Mcmahan, K. Moody, E. B. Norman, L. Phair, E. Rodriguez-Vieitez, N. D. Scielzo, M. Wiedeking

Physics Faculty Publications

In the Surrogate Method, the measured decay probability of a compound nucleus formed via a direct reaction is used to extract the cross section for a reaction with a different entrance channel that proceeds through the same compound nucleus. An extension of the Surrogate Method, the Surrogate Ratio Method (SRM), uses a ratio of measured decay probabilities to infer an unknown cross section relative to a known one. To test the SRM we compare the direct-reaction-induced fission probability ratio of ²³⁴U(α, α’ f ) to ²³⁶U(α, α’f ) with the ratio of cross sections …

Effects Of Hze Irradiation On Chemical Neurotransmission In Rodent Hippocampus, Mayumi Machida

Theses and Dissertations in Biomedical Sciences

Space radiation represents a significant risk to the CNS (central nervous system) during space missions. Most harmful are the HZE (high mass, highly charged (Z), high energy) particles, e.g. ⁵⁶Fe, which possess high ionizing ability, dense energy deposition pattern, and high penetrance.

Accumulating evidence suggests that radiation has significant impact on cognitive functions. In ground-base experiments, HZE radiation induces pronounced deficits in hippocampus dependent learning and memory in rodents. However, the mechanisms underlying these impairments are mostly unknown.

Exposure to HZE radiation elevates the level of oxidation, resulting in cell loss, tissue damage and functional deficits through direct ionization …

Search For The Photoexcitation Of Exotic Mesons In The Π​+Π​+Π- System, M. Nozar, Gerard P. Gilfoyle, Et. Al.

Physics Faculty Publications

A search for exotic mesons in the π⁺π⁺π^- system photoproduced by the charge exchange reaction γp → π⁺π⁺π^- was carried out by the CLAS Collaboration at Jefferson Lab. A tagged-photon beam with energies in the 4.8 to 5.4 GeV range, produced through bremsstrahlung from a 5.744 GeV electron beam, was incident on a liquid-hydrogen target. A partial wave analysis was performed on a sample of 83 000 events, the highest such statistics to date in this reaction at these energies. The main objective of this study was to look …

Measurement Of Direct Ƒ0(980) Photoproduction On The Proton, M. Battaglieri, Gerard P. Gilfoyle, Et. Al.

Physics Faculty Publications

We report on the results of the first measurement of exclusive ƒ₀(980) meson photoproduction on protons for E_γ = 3.0–3.8 GeV and -t = 0.4–1.0 GeV^2. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The resonance was detected via its decay in the π⁺ π^- channel by performing a partial wave analysis of the reaction γ p → pπ⁺π^-. Clear evidence of the ƒ₀(980) meson was found in the interference between P and S waves at M_{π⁺π …}

Estimation Of Weapon Yield From Inversion Of Dose Rate Contours, Buckley E. O'Day Iii

Theses and Dissertations

This research studies the uncertainty in yield estimation from inversion of dose rate contours. The Hazard Prediction and Assessment Capability (HPAC) and a simple FORTRAN95 based Fallout Deposition Code (FDC) are used to recreate dose rate contours from historic nuclear tests. Fallout footprints from six atomic tests are recreated using balloon wind soundings and high resolution mesoscale weather reanalysis data. Dose rate contour plots are created for different yields for a single set of weather conditions. Dose rate contours are compared to determine uncertainty in yield estimation from inversion of dose rate contour plots. Results of these dose rate recreations …

Multi-Quasiparticle States In 256Rf, H. B. Jeppesen, I. Dragojevic, R. M. Clark, K. E. Gregorich, M. N. Ali, J. M. Allmond, C. W. Beausang, D. L. Bleuel, M. Cromaz, M. A. Deleplanque, P. A. Ellison, P. Fallon, M. A. Garcia, J. M. Gates, J. P. Greene, S. Gros, I. Y. Lee, H. L. Liu, A. O. Macchiavelli, S. L. Nelson, H. Nitsche, J. R. Pavan, L. Stavsetra, F. S. Stephens, M. Wiedeking, R. Wyss, F. R. Xu

Physics Faculty Publications

Excited states in ²⁵⁶Rf were populated via the ²⁰⁸Pb(⁵⁰Ti,2n) fusion–evaporation reaction. Delayed γ-ray and electron decay spectroscopy was performed and three isomeric states in ²⁵⁶Rf have been identified. A fourth low-energy nonyrast state was identified from the γ-ray decay of one of the higher lying isomers. The states are interpreted as multi-quasiparticle excitations.

Electroproduction Of Pπ+​Π- Off Protons At 0.2 < Q2 < 0.6 Gev2 And 1.3 < W < 1.57 Gev With The Clas Detector, G. V. Fedotov, Gerard P. Gilfoyle, Et. Al.

Physics Faculty Publications

This paper reports on the most comprehensive data set obtained on differential and fully integrated cross sections for the process ep → e'pπ⁺π ⁻. The data were collected with the CLAS detector at Jefferson Laboratory. Measurements were carried out in the as yet unexplored kinematic region of photon virtuality 0.2 < Q² < 0.6 GeV² and invariant mass of the final hadron system W from 1.3 to 1.57 GeV. For the first time, nine independent one-fold differential cross sections were determined in each bin of W and Q² covered by the measurements. A phenomenological analysis of the data …

Energy And System Size Dependence Of Φ Meson Production In Cu + Cu And Au + Au Collisions, B. I. Abelev, M. M. Aggarwal, Z. Ahammed, B. D. Anderson, D. Arkhipkin, G. S. Averichev, Y. Bai, J. Balewski, O. Barannikova, L. S. Barnby, S. Bültmann

Physics Faculty Publications

We study the beam-energy and system-size dependence of ϕ meson production (using the hadronic decay mode ϕ → K ⁺ K ⁻ ) by comparing the new results from Cu + Cu collisions and previously reported Au + Au collisions at √^sNN = 62.4 and 200 GeV measured in the STAR experiment at RHIC. Data presented in this Letter are from mid-rapidity ( | y | < 0.5 ) for 0.4 < PT < 5 GeV /c . At a given beam energy, the transverse momentum distributions for ϕ mesons are observed to be similar in yield and shape for Cu + Cu and Au + …

New Compact Tem-Type Deflecting And Crabbing Rf Structure, J. R. Delayen, H. Wang

Physics Faculty Publications

A new type of rf structure for the deflection and crabbing of particle beams is presented. The structure is comprised of a number of parallel TEM resonant lines operating in opposing phase from each other. One of its advantages is its compactness compared to conventional crabbing cavities operating in the TM₁₁₀ mode, thus allowing low frequency designs. This geometry would also be effective for the deflection of beams propagating at velocities substantially less than that of light.

Moments Of The Spin Structure Functions G(1)(P) And G(1)(D) For 0.05 < Q2 < 3.0 Gev2, Clas Collaboration, Y. Prok, K. V. Dharmawardane, G. E. Dodge, S. E. Kuhn, M. J. Amaryan, H. Bagdasaryan, M. Bektasoglu, S. Bültmann, S. L. Careccia, G. Gavalian, N. Guler, C. E. Hyde-Wright, H. G. Juengst, N. Kalantarians, A. Klein, J. Lachniet, R. A. Niyazov, L. M. Qin, S. Sabatie, S. Tkachenko, L. B. Weinstein, J. Zhang

Physics Faculty Publications

The spin structure functions g1 for the proton and the deuteron have been measured over a wide kinematic range in x and Q² using 1.6 and 5.7 GeV longitudinally polarized electrons incident upon polarized NH3 and ND3 targets at Jefferson Lab. Scattered electrons were detected in the CEBAF Large Acceptance Spectrometer, for 0.05 < Q² < 5GeV² and W < 3 GeV. The first moments of g1 for the proton and deuteron are presented – both have a negative slope at low Q², as predicted by the extended Gerasimov–Drell–Hearn sum rule. The first extraction of the generalized forward spin polarizability of the proton γ p 0 the Q² evolution of the first moment of g1 shows agreement in leading order with Heavy …

Beam-Energy And System-Size Dependence Of Dynamical Net Charge Fluctuations, B. I. Abelev, M. M. Aggarwal, Z. Ahammed, B. D. Anderson, D. Arkhipkin, G. S. Averichev, Y. Bai, J. Balewski, S. Bueltmann, Star Collaboration

Physics Faculty Publications

We present measurements of net charge fluctuations in Au+Au collisions at √sNN=19.6, 62.4, 130, and 200 GeV, Cu+Cu collisions at √sNN=62.4 and 200 GeV, and p+p collisions at √s=200GeV using the dynamical net charge fluctuations measure ν_+−,dyn. We observe that the dynamical fluctuations are nonzero at all energies and exhibit a modest dependence on beam energy. A weak system size dependence is also observed. We examine the collision centrality dependence of the net charge fluctuations and find that dynamical net charge fluctuations violate 1/N_ch scaling but display approximate 1/N_part scaling. We also study the azimuthal and …

Beam Spin Asymmetries In Deeply Virtual Compton Scattering (Dvcs) With Clas At 4.8 Gev, G. Gavalian, M. J. Amaryan, H. Bagdasaryan, M. Bektasoglu, S. Bültmann, S. L. Careccia, K. V. Dharmawardane, G. E. Dodge, N. Guler, C. E. Hyde, H. G. Juengst, N. Kalantarians, A. Klein, S. E. Kuhn, J. Lachniet, M. R. Niroula, R. A. Niyazov, L. M. Qin, F. Sabatié, S. Tkachenko, L. B. Weinstein, J. Yun, J. Zhang, Clas Collaboration

Physics Faculty Publications

We report measurements of the beam spin asymmetry in deeply virtual Compton scattering (DVCS) at an electron beam energy of 4.8 GeV using the CLAS detector at the Thomas Jefferson National Accelerator Facility. The DVCS beam spin asymmetry has been measured in a wide range of kinematics, 1.02<2.8 (GeV/c)², 0.12<_xB<0.48, and 0.1<−t<0.8 (GeV/c)², using the reaction →ep→e′pX. The number of H(e,e′γp) and H(e,e′π⁰p) events are separated in each (Q²,_xB,t) bin by a fit to the line shape of the H(e,e′p)X M²_x distribution. The validity of the method was studied in detail …

Virtual Compton Scattering And Neutral Pion Electroproduction In The Resonance Region Up To The Deep Inelastic Region At Backward Angles, G. Laveissiere, N. Degrande, S. Jaminion, C. Jutier, L. Todor, G. E. Dodge, C. E. Hyde, K. Mccormick, P. E. Ulmer, L. B. Weinstein, Jefferson Lab Hall A Collaboration

Physics Faculty Publications

We have made the first measurements of the virtual Compton scattering (VCS) process via the H(e, e′p)γ exclusive reaction in the nucleon resonance region, at backward angles. Results are presented for the W-dependence at fixed Q²=1 GeV² and for the Q² dependence at fixed W near 1.5 GeV. The VCS data show resonant structures in the first and second resonance regions. The observed Q² dependence is smooth. The measured ratio of H(e, e′p)γ to H(e, e′p)π⁰ cross sections emphasizes the different sensitivity of these two reactions to the various nucleon resonances. Finally, when compared …

Electroproduction Of P Π⁺Π⁻ Off Protons At 0.2 < Q² < 0.6 Gev² And 1.3 < W < 1.57 Gev With The Clas Detector, M. J. Amaryan, H. Baghdasaryan, M. Bektasoglu, S. Bültmann, S. L. Careccia, G. E. Dodge, G. Gavalian, N. Guler, C. E. Hyde, W. Kim, A. Klein, F. J. Klein, A. Klimenko, S. E. Kuhn, S. Tkachenko, L. B. Weinstein, Et Al., Clas Collaboration

Physics Faculty Publications

This paper reports on the most comprehensive data set obtained on differential and fully integrated cross sections for the process ep → e'pπ⁺π^-. The data were collected with the CLAS detector at Jefferson Laboratory. Measurements were carried out in the as yet unexplored kinematic region of photon virtuality 0.2 < Q² < 0.6 GeV² and invariant mass of the final hadron system W from 1.3 to 1.57 GeV. For the first time, nine independent one-fold differential cross sections were determined in each bin of W and Q² covered by the measurements. A phenomenological analysis of the data allowed …

The Potential Contribution Of Organic Salts To New Particle Growth, Kelley Barsanti, Peter H. Mcmurry, J. N. Smith

Civil and Environmental Engineering Faculty Publications and Presentations

Field and lab measurements suggest that low-molecular weight (MW) organic acids and bases exist in accumulation and nucleation mode particles, despite their relatively high pure-liquid vapor pressures. The mechanism(s) by which such compounds contribute to the mass growth of existing aerosol particles and newly formed particles has not been thoroughly explored. One mechanism by which low- MW compounds may contribute to new particle growth is through the formation of organic salts. In this paper we use thermodynamic modeling to explore the potential for organic salt formation by atmospherically relevant organic acids and bases for two system types: one in which …

Search For The Photoexcitation Of Exotic Mesons In The Π+Π+Π- System, Clas Collaboration, M. J. Amaryan, H. Bagdasaryan, S. Bektasoglu, S. Bültmann, G. E. Dodge, G. Gavalian, N. Guler, C. E. Hyde-Wright, N. Kalantarians, A. Klein, S. E. Kuhn, J. Lachniet, M. R. Niroula, L. M. Qin, S. Tkachenko, L. B. Weinstein, J. Zhang

Physics Faculty Publications

A search for exotic mesons in the π⁺π⁺π⁻ system photoproduced by the charge exchange reaction γp→π⁺π⁺π⁻(n) was carried out by the CLAS Collaboration at Jefferson Lab. A tagged-photon beam with energies in the 4.8 to 5.4 GeV range, produced through bremsstrahlung from a 5.744 GeV electron beam, was incident on a liquid-hydrogen target. A partial wave analysis was performed on a sample of 83 000 events, the highest such statistics to date in this reaction at these energies. The main objective of this study was to look for the …

Spin Structure Of The Deuteron, Nevzat Guler

Physics Theses & Dissertations

Double spin asymmetries for the proton and the deuteron have been measured in the EG1b experiment using the CLAS detector at Jefferson Lab. Longitudinally polarized electrons at energies 1.6, 2.5, 4.2 and 5.7 GeV were scattered from longitudinally polarized NH3 and ND3 targets. The double spin asymmetry A|| for the proton and the deuteron has been extracted from these data as a function of W and Q² with unprecedented precision. The virtual photon asymmetry A₁ and the spin structure function g1 can be calculated from these measurements by using parametrization to the world data for the virtual …

Neutron Structure Functions Measured With Spectator Tagging, Svyatoslav Tkachenko

Physics Theses & Dissertations

We know much less about the neutron than the proton due to the absence of free neutron targets. Neutron information has to be extracted from data on nuclear targets like deuterium. This requires corrections for off-shell and binding effects which are not known from first principles and therefore are model-dependent. As a consequence, the same data can be interpreted in different ways, leading to different conclusions about important questions such as the value of the d/u quark ratio at large momentum fraction x. The Barely Off-shell NUcleon Structure (BONUS) experiment at Jefferson Lab addressed this problem by tagging spectator protons …

Evaluation Of Extraction Chromatography Resins For Rapid Actinide Analysis, Julie Marisa Gostic

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this work, physical and chemical parameters associated with extraction chromatography separation procedures were investigated for rapid actinide analysis. A vacuum box system was designed in-house and was characterized in terms of flow rate reproducibility, matrix effects on flow rate for sequential elution, and actinide separation efficiency using different types of resin (TEVA, DGA and TRU). Results indicated that the columnar kinetics of the resins were sufficiently rapid to run high purity samples through the unit over a wide range of flow rates for all resin types. Single matrix interferences at a metal ion ratio of 1:10 6 relative to …