Photon Cross Section Research Articles

Nuclear modification factor of isolated prompt photons in pp and PbPb collisions at [formula omitted] with the CMS detector

High-transverse-momentum prompt photons, as colorless objects, do not interact strongly with the medium and provide a direct way to test perturbative QCD and the nuclear parton distribution functions (nPDFs). The transverse energy spectra and the nuclear modification factors of isolated photons are measured in pp and PbPb collisions at sNN=5.02TeV using the CMS detector. The data are compared to jetphox next-to-leading-order calculations and found to be consistent with the prediction of the nuclear modification factor. The measurements significantly improved the accuracy compared to the previous CMS results at sNN=2.76TeV. No significant modification of isolated photon cross-sections in PbPb collisions with respect to pp collisions is observed in the pseudorapidity range |η| < 1.44 for EγT between 25 and 200 GeV at various collision centrality intervals.

Photon and electron ionization of the HeH+ Molecule

With the first detection of HeH+ in nearby interstellar space, various molecular ionization and recombination processes are now being calculated to better understand the dynamics of the first molecule in the universe. We use a configuration-average distorted-wave method to compute the photon and electron ionization cross sections of HeH+ based on an earlier molecular structure tabulation.

An insight into the charge carriers transport properties and electric field distribution of CH3NH3PbBr3 thick single crystals

Thanks to their unique combination of semiconducting properties and a large cross section for energetic photons, metal halide perovskites could theoretically achieve high x-ray to charge carriers conversion rates, making them materials of high interest for the direct x-ray detection. In this work, we focus on the transport properties of methylammonium lead tribromide (MAPbBr3) single crystals. Time of Flight measurements and x-ray focused experiments along the edge of the samples were carried out. We report homogenous holes transit throughout the thickness of the samples as well as poor electrons transit. We also report the continuity of the electric field throughout the thickness of the MAPbBr3 samples, and we present preliminary fitting results to discuss its nature.

Investigation of γ-ray attenuation coefficients, effective atomic number and electron density for ZnO/HDPE composite

Bulk and nano ZnO/HDPE composite with different weight fractions (10, 20, 30 and 40%) of ZnO as a filler were prepared and studied for radiation shielding properties against γ-ray. The structural, morphological and functional properties of the composites were identified using x-ray diffraction (XRD), scanning electron microscope (SEM) and Fourier transform infrared specrtroscopy (FTIR). The results confirmed the formation of ZnO nanoparticles with crystallite size of 27 nm and revealed their good dispersion within the polymer matrix compared to bulk ZnO as well as interaction mechanism between the filler and the polymer matrix. The mass attenuation coefficient (μm) for the composite was measured experimentally using a well calibrated high purity germanium cylindrical detector (HPGe) at energies (59.54, 356.01, 661.66, 1173.33 and 1332.50 keV) for different radioactive point sources (241Am, 133Ba, 137Cs and 60Co). The obtained attenuation coefficients were used to determine the values of total molecular cross section σmol, the total atomic cross section σatm (cm2/atom), total electronic cross-section σel (cm2/electron) effective atomic number Zeff, and effective electron number Neff. Using NIST XCOM photon cross section database, the theoretical radiation parameters were calculated for bulk ZnO/HDPE composite and compared with the experimental results of both bulk and nano ZnO/HDPE composite. The obtained results revealed good agreement compared to theoretical values. μm, σmol, and σatm values decreased with incident photon energy and increased with weight percentage of both bulk and nano ZnO filler. However, these values were greater for nano ZnO/HDPE composite compared to bulk ZnO/HDPE composite with the same weight percentage. Whereas, σel, Zeff and Neff values decreased with weight percentage and revealed a plateau region which appeared with further increase in energy.

Monte Carlo and water calorimetric determination of kilovoltage beam radiotherapy ionization chamber correction factors

The in-phantom calibration method for radiotherapy kilovoltage x-ray beams requires ionization chamber correction factors. The overall ionization chamber correction factor accounts for changes in the chamber response due to the displacement of water by the chamber cavity and wall, the presence of the stem and the change in incident photon energy and angular distribution in the phantom to that in air. A waterproof sheath, if required, is accounted for in a sheath correction factor. The aim of this study is to determine chamber correction factors through Monte Carlo (MC) simulations and water calorimetry measurements. Correction factors are determined for the PTW TM30013, NE2571, IBA FC65-G, IBA FC65-P and Exradin A12 ionization chambers. They are compared to experimental values obtained at the German national metrology institute Physikalisch-Technische Bundesanstalt (PTB) with their water calorimetry-based absorbed dose to water primary standard and at other national metrological institutes. An uncertainty analysis considers the contributions to the uncertainty on the chamber correction factors from the field size, photon cross sections, photon fluence spectra and chamber wall and central electrode dimensions. The MC calculated chamber correction factors are within 2.2% of unity with a standard uncertainty of 0.3%. For the 50 kV and 100 - 140 kV radiation beam qualities, the calculated correction factors deviate from the measured correction factors (with a standard uncertainty of 1%) by up to 2.6%. The calculated chamber correction factors for the PTW TM30013 and Exradin A12 are consistent with those derived from the BIPM kilovoltage primary standard. The inconsistencies between the calculated and experimental chamber correction factors indicate the need to further investigate the accuracy of kilovoltage absorbed dose to water primary standards and the use of MC simulations to determine kilovoltage beam chamber correction factors.

One-photon absorption by inorganic perovskite nanocrystals: A theoretical study

The one-photon absorption cross section of nanocrystals (NCs) of the inorganic perovskite CsPbBr$_{3}$ is studied theoretically using a multiband $\mathbf{k}\cdot\mathbf{p}$ envelope-function model combined with a treatment of intercarrier correlation by many-body perturbation theory. A confined exciton is described first within the Hartree-Fock (HF) approximation, and correlation between the electron and hole is then included in leading order by computing the first-order vertex correction to the electron-photon interaction. The vertex correction is found to give an enhancement of the near-threshold absorption cross section by a factor of up to 4 relative to the HF (mean-field) value of the cross section, for NCs with an edge length $L=9$-12 nm (regime of intermediate confinement). The vertex-correction enhancement factors are found to decrease with increasing exciton energy; the absorption cross section for photons of energy $\omega=3.1$ eV (about 0.7 eV above threshold) is enhanced by a factor of only 1.4-1.5 relative to the HF value. The $\mathbf{k}\cdot\mathbf{p}$ corrections to the absorption cross section are also significant; they are found to increase the cross section at an energy $\omega=3.1$ eV by about 30% relative to the value found in the effective-mass approximation. The theoretical absorption cross section at $\omega=3.1$ eV, assuming a Kane parameter $E_{P}=20$ eV, is found to be intermediate among the set of measured values (which vary among themselves by nearly an order of magnitude) and to obey a power-law dependence $\sigma^{(1)}(\omega)\propto L^{2.9}$ on the NC edge length $L$, in good agreement with experiment. The dominant contribution to the theoretical exponent 2.9 is shown to be the density of final-state excitons. The main theoretical uncertainty in these calculations is in the value of the Kane parameter $E_{P}$.

Absorption spectra of Müller cell intermediate filaments: Experimental results and theoretical models.

Experimental spectra of Müller cell (MC) intermediate filaments (IFs) isolated from porcine retina are reported in this work. The absorption spectra recorded at different MC IF concentrations were used to estimate their absorption cross-sections at different wavelengths. The average absorption cross-section of a single MC IF was ca. (0.97 … 2.01)×10-10cm2 in the 650-445nm spectral range. To interpret these experimental absorption spectra, we made ab initio calculations of the optical spectra of α-helix polypeptides, and also used a simplified theoretical approach that modeled an IF by a conductive wire. The energy spectra of the refractive index, extinction coefficient (absorption cross-section), energy loss and reflectivity functions for different photon polarizations, with strong anisotropy with respect to the system axis, were calculated ab initio for polyglycine α-helix molecule containing 1000 glycine residues. Strong anisotropy of these parameters was explained by photons interacting with different electronic transitions. Note that similarly strong anisotropy was also obtained for the optical absorption cross-sections in the simplified model. Both modeling approaches were used for calculating the absorption cross-sections of interest. As a result, the absorption cross-section for photons propagating axially along MC IFs was much larger than their geometrical cross-section. The latter result was explained taking into account the density of electronic states, with numerous electrons contributing to the transition intensity at a given energy. We found that the simple conductive wire model describes the MC IF absorption spectrum better than the ab initio spectra. The latter conclusion was explained by the limitations of ab initio analysis, which only took into account one α-helix with 1000 aminoacids, whereas each porcine Müller cell IF is assembled of thousands of protein molecules, reaching the total length of ca. 100μm. The presently reported results contribute to the understanding of the quantum mechanism of high-contrast vision of vertebrate eyes.

Forbidden atomic carbon, nitrogen, and oxygen emission lines in the water-poor comet C/2016 R2 (Pan-STARRS)

Context.The N2and CO-rich and water-depleted comet C/2016 R2 (Pan-STARRS) – hereafter “C/2016 R2” – is a unique comet for detailed spectroscopic analysis.Aims.We aim to explore the associated photochemistry of parent species, which produces different metastable states and forbidden emissions, in this cometary coma of peculiar composition.Methods.We reanalyzed the high-resolution spectra of comet C/2016 R2 obtained in February 2018 using the UVES spectrograph of the European Southern Observatory Very Large Telescope. Various forbidden atomic emission lines of [CI], [NI], and [OI] were observed in the optical spectrum of this comet when it was at 2.8 au from the Sun. The observed forbidden emission intensity ratios are studied in the framework of a couple-chemistry emission model.Results.The model calculations show that CO2is the major source of both atomic oxygen green and red doublet emissions in the coma of C/2016 R2 (while for most comets it is generally H2O), whereas, CO and N2govern the atomic carbon and nitrogen emissions, respectively. Our modeled oxygen green-to-red-doublet and carbon-to-nitrogen emission ratios are higher by a factor of three than what is found from observations. These discrepancies could be due to uncertainties associated with photon cross sections or unknown production and/or loss sources. Our modeled oxygen green-to-red-doublet emission ratio is close to what is seen in observations when we consider an O2abundance with a production rate of 30% relative to the CO production rate. We constrained the mean photodissociation yield of CO, producing C(1S) at about 1%, a quantity which has not been measured in the laboratory. The collisional quenching is not a significant loss process for N(2D) though its radiative lifetime is significant (~10 h). Hence, the observed [NI] doublet-emission ratio ([NI] 5198/5200) of 1.22, which is smaller than the terrestrial measurement by a factor 1.4, is mainly due to the characteristic radiative decay of N(2D).

The synthesis of −1, −3, −5, −7, −8 aryl substituted boron-dipyrromethene chromophores: Nonlinear optical and photophysical characterization

A convenient protocol enabled the synthesis of novel Arylated Borondipyrromethene (BODIPY) compounds was applied that synthesis yields found to be higher than classical alkyl substituted analogues. The nonlinear properties of the target molecules were investigated systematically in terms of aryl substitution to the pyrrole side and the meso substitution on the indacene core. It was found that, −3, −5 positions of the indacene core are effective positions for charge transfer, which is essential for two photon absorption (TPA). The greatest two photon cross section (TPCS) value (178 GM) is obtained for BDP3 compound, while TPCS value of BDP4 compound is 27 GM at near infrared wavelength (800 nm). Arylated chromophores exhibited the broader red-shifted absorption and fluorescence bands with higher stokes shifts with regard to reference Borondipyrromethene compound (4,4′-difluoro-8-phenyl-1,3,5,7-tetramethyl-4-bora-3a,4a-diaza-s-indacene, TMB). Our results are helpful for designing new photosensitizers and for applications in the study of the molecular photochemistry.

Tensor Pomeron and low- x deep inelastic scattering

The tensor-pomeron model is applied to low-x deep-inelastic lepton-nucleon scattering and photoproduction. We consider c.m. energies in the range 6 - 318 GeV and Q^2 < 50 GeV^2. In addition to the soft tensor pomeron, which has proven quite successful for the description of soft hadronic high-energy reactions, we include a hard tensor pomeron. We also include f_2-reggeon exchange which turns out to be particularly relevant for real-photon-proton scattering at c.m. energies in the range up to 30 GeV. The combination of these exchanges permits a description of the absorption cross sections of real and virtual photons on the proton in the same framework. In particular, a detailed comparison of this two-tensor-pomeron model with the latest HERA data for x < 0.01 is made. Our model gives a very good description of the transition from the small-Q^2 regime where the real or virtual photon behaves hadron-like to the large-Q^2 regime where hard scattering dominates. Our fit allows us, for instance, a determination of the intercepts of the hard pomeron as 1.3008(+73,-84), of the soft pomeron as 1.0935(+76,-64), and of the f_2 reggeon. We find that in photoproduction the hard pomeron does not contribute within the errors of the fit. We show that assuming a vector instead of a tensor character for the pomeron leads to the conclusion that it must decouple in real photoproduction.

Probing entanglement in Compton interactions

This theoretical research aims to examine areas of the Compton cross section of entangled annihilation photons for the purpose of testing for possible break down of theory, which could have consequences for predicted optimal capabilities of Compton PET systems. We provide maps of the cross section for entangled annihilation photons for experimental verification. We introduce a strategy to derive cross sections in a relatively straight forward manner for the Compton scattering of a hypothetical separable, mixed and entangled states. To understand the effect that entanglement has on the cross section for annihilation photons, we derive the cross section so that it is expressed in terms of the cross section of a hypothetical separable state and of a hypothetical forbidden maximally entangled state. We find lobe-like structures in the cross section which are regions where entanglement has the greatest effect. We also find that mixed states do not reproduce the cross section for annihilation photons, contrary to a recent investigation which reported otherwise. We review the motivation and method of the most precise Compton scattering experiment for annihilation photons, in order to resolve conflicting reports regarding the extent to which the cross section itself has been experimentally verified.

Experimental evidence of molecular coherence effects in the bremsstrahlung radiation processes

The first experimental evidence of Young-type interferences is presented in bremsstrahlung (BS) processes by measuring the double differential cross sections (DDCS) of BS photons emitted from a two-centre N2 molecule under impact of 4.0 keV electrons. The spectra were recorded for emission of photons in the angular range of 45°–120° and the energy range of 2.0–3.8 keV using a Si PIN photodiode detector (FWHM = 165 eV at 5.9 keV). The measured variation of DDCS ratio of N2 to Ar as a function of photon energy shows no obvious signature of interference structure. However, the measured angular distribution of the intensity ratio of BS photons of N2 to Ar is found to exhibit the noticeable oscillations. Furthermore, a clear oscillatory structure is observed in the angular distribution of BS photons if the intensity of photons emitted from N2 molecules at angle θ to the intensity of photons emitted at angle 90°, i.e. I(θ)/I(90°) is plotted as a function of emission angle. Noting the fact that, only one theoretical work on coherence effects in BS processes under low-energy electron impact with homonuclear diatomic molecules is reported in the literature by Borie et al (1970 Phys. Rev. A 2 1443) which fails to explain the observed oscillations and shows orders of magnitude difference in the amplitude and mismatch in the shape of oscillations. The presence of observed oscillations is suggested to arise due to coherent superposition of BS photons of a given energy emitted in scattering of 4.0 keV electrons with a two-centre N2 molecule. Strong disagreement between our measurements and the calculations from Borie et al theory clearly suggests that a more refined and adequate theoretical model together with additional experimental investigations are needed to verify the present observations.

An Efficiency Studying of an Ion Chamber Simulation Using Vriance Reduction Techniques with EGSnrc.

Background:Radiotherapy is an important technique of cancer treatment using ionizing radiation. The determination of total dose in reference conditions is an important contribution to uncertainty that could achieve 2%. The source of this uncertainty comes from cavity theory that relates the in-air cavity dose and the dose to water. These correction factors are determined from Monte Carlo calculations of ionization chambers. The main problem of this type of calculation is the extremely long computation time to achieve reasonable statistics. Objective:The main purpose of this work is to present a combination with variance reduction techniques for the case of an ionization chamber in water. Methods:The egs_chamber code allows for very efficient computation of ionization chamber doses and dose ratios by using various variance reduction techniques, and also permits realistic simulations of the experimental setup due to the use of EGSnrc C++ library. Russian roulette and Photon Cross Section Enhancement were used with egs_chamber code. Tests were performed to obtain the parameters of variance reduction techniques resulting in a maximum efficiency. Results:It can be seen that the parameters which result in improved Monte Carlo calculation of the efficiency values are XCSE 64 and Russian Roulette (RR) 128. Conclusion:This study determines the parameters of variance reduction techniques that result in an optimal computational efficiency.

An Efficiency Studying of an Ion Chamber Simulation Using Vriance Reduction Techniques with EGSnrc

Background: Radiotherapy is an important technique of cancer treatment using ionizing radiation. The determination of total dose in reference conditions is an important contribution to uncertainty that could achieve 2%. The source of this uncertainty comes from cavity theory that relates the in-air cavity dose and the dose to water. These correction factors are determined from Monte Carlo calculations of ionization chambers. The main problem of this type of calculation is the extremely long computation time to achieve reasonable statistics.Objective: The main purpose of this work is to present a combination with variance reduction techniques for the case of an ionization chamber in water.Methods: The egs_chamber code allows for very efficient computation of ionization chamber doses and dose ratios by using various variance reduction techniques, and also permits realistic simulations of the experimental setup due to the use of EGSnrc C++ library. Russian roulette and Photon Cross Section Enhancement were used with egs_chamber code. Tests were performed to obtain the parameters of variance reduction techniques resulting in a maximum efficiency.Results: It can be seen that the parameters which result in improved Monte Carlo calculation of the efficiency values are XCSE 64 and Russian Roulette (RR) 128.Conclusion: This study determines the parameters of variance reduction techniques that result in an optimal computational efficiency.

Development of a Monte Carlo Modeling Approach to Determine the Enrichment of UF6 Typical Cylinders

Precise assay of uranium enrichment without time-consuming analysis is a crucial factor in nuclear safeguards process. This paper aims at a computational development using innovative Monte Carlo (MC) method for 235U mass enrichment (%E) verification for the UF6 cylinder. This new approach focuses mainly on using different UF6 physical properties (effective volume and density) and extra 235U gamma- and X-ray transitions as input parameters for efficient calculations of %E assay. In this work, we used the measured values of the dose rate (μSv/h) due to the emitted gamma- and X-rays of 235U content at the cylinder external surface for enrichment calculations. The attenuation of the main 235U gamma- and X-energies due to the cylinder wall (5B-Type Ni Inconel alloy) was also estimated to wide range of energies using XCOM: Photon Cross Sections Database software. Using this suggested model for 235U enrichment calculation, the calculated value of 19.46 ± 1.28% is within one standard deviation of the certified value of 19.75 ± 0.40%. The mass of 235U was also estimated and found to be 2.6814 kg. Based on this improved approach, the total uranium activity of the investigated UF6 cylinder was calculated and found to be (5.52 GBq), which is 98.6% from the declared activity value (5.6 GBq). These accurate and confident calculated values are direct functions in the improved parameters and the developed MC code.

Olivine mineral used in concrete for gamma-ray shielding

The aim of this study is assessing the concretes containing olivine, which is an abundant and locally mined mineral in Turkey, in terms of several essential photon shielding parameters, which are total mass attenuation coefficients (μ/ρ), mean free paths (mfp), half and tenth value layer thicknesses (HVL and TVL, respectively), effective atomic numbers (Zeff), and electron densities (Nel). For this purpose, two types of concretes with and without olivine content have been produced and studied by photon transmission experiments, simulations and theoretical calculations. In the experimental part, photon transmission technique has been performed using a 16k 3″ × 3″ NaI(Tl) detector system and so, μ/ρ, mfp, HVL, and TVL values of concretes have been determined experimentally at 511 and 1275 keV photon energies. Aforesaid parameters have also been estimated by simulations at the same energies using Geant4 Monte Carlo code. For theoretical calculations, the web version of NIST XCOM photon cross-section library has been utilized. By this way, all parameters have been calculated at 1 keV–100 GeV energy region and compared with data from experiments and simulations. It has been observed that olivine addition affected the aforementioned radiation shielding parameters of concretes positively at 511 and 1275 keV energies. Also, results from each method have been found to be in a reasonably good agreement, especially for the ones from XCOM and Geant4. So, it has been concluded that Geant4 code is a powerful tool in such studies.

A study on the investigation of gamma shielding properties of some metal borides

In this study, the gamma radiation absorption capabilities of some metal borides were studied by using Monte Carlo simulation method. So, the mass attenuation coefficients, μm, the half value layer, HVL, the tenth value layer, TVL and the mean free path, MFP values of the NdB6, SmB6 and GdB6 were calculated by means of EGSnrc particle transport code and XCOM program theoretically within the energy range 0.125–5 MeV. It was seen that there is a quite successful consistency (t = 0.00049, p = 0.99961) between the simulated results and calculated values obtained by NIST's XCOM photon cross-section database. Those computational results for the synthesized compounds have also been compared with lead and vermiculite which have concluded that NdB6, SmB6, and GdB6 are good candidates for gamma shielding applications. These materials were sythesized by magnesiothermic reduction in open air. Stoichiometric amounts of M2O3, B2O3 and Mg (20% excess) were mixed, where MIII is a lanthanide metal (NdIII, SmIII and GdIII) ion. Mixture was heated to 700 °C, 800 °C and 900 °C. Optimum reaction temperature and reaction time were found by X-Ray Diffraction (XRD) analysis and Scannning Electron Microscopy (SEM). By fixing the reaction temperature, reaction time has changed as 1, 2, 3, 4 and 5 h to obtain nano crystals with homogeneous morphology. It was found that optimum reaction temperature and reaction time of NdB6 is 700 °C and 3 h, for SmB6 700 °C and 1 h for GdB6 900 °C.

Constraining unintegrated gluon distributions from inclusive photon production in proton–proton collisions at the LHC

We compute the leading order (LO) qg→qγ and next-to-leading order (NLO) gg→qq¯γ contributions to inclusive photon production in proton–proton (p+p) collisions at the LHC. These channels provide the dominant contribution at LO and NLO for photon transverse momenta kγ⊥ corresponding to momentum fractions of x≤0.01 in the colliding protons. Our computations, performed in the dilute–dense framework of the Color Glass Condensate effective field theory (CGC EFT), show that the NLO contribution dominates at small-x because it is sensitive to k⊥-dependent unintegrated gluon distributions in both of the protons. We predict a maximal 10% modification of the cross section at low kγ⊥ as a direct consequence of the violation of k⊥-factorization. The coherence effects responsible for this modification are enhanced in nuclei and can be identified from inclusive photon measurements in proton–nucleus collisions. We provide numerical results for the isolated inclusive photon cross section for kγ⊥≤20 GeV in p+p collisions that can be tested in the future at the LHC.

Characterisation of the attenuation properties of 3D-printed tungsten for use in gamma camera collimation

BackgroundThe aim of this work was to characterise the attenuation properties of 3D-printed tungsten and to assess the feasibility for its use in gamma camera collimator manufacture.Method3D-printed tungsten disks were produced using selective laser melting (SLM). Measurements of attenuation were made through increasing numbers of disks for a Tc-99m (140 keV) and I-131 (364 keV) source. The technique was validated by repeating the measurements with lead samples. Resolution measurements were also made with a SLM tungsten collimator and compared to Monte Carlo simulations of the experimental setup. Different collimator parameters were simulated and compared against the physical measurements to investigate the effect on image quality.ResultsThe measured disk thicknesses were on average 20% above the specified disk thicknesses. The measured attenuation for the tungsten samples were lower than the theoretical value determined from the National Institute of Standards and Technology (NIST) cross-sectional database (Berger and Hubbell, XCOM: photon cross-sections on a personal computer, 1987). The laser scan strategy had a significant influence on material attenuation (up to 40% difference). Results of these attenuation measurements indicate that the density of the SLM material is lower than the raw tungsten density. However, an improved performance compared to a lead collimator was observed. The SLM tungsten collimator was adequately simulated as 80% density and 110% septal thickness. Scatter and septal penetration were 17% less than a similar lead collimator and 33% greater than tungsten at 100% density.ConclusionsSLM manufacture of tungsten collimators is feasible. Attenuation properties of SLM tungsten are superior to the lead alternative and the opportunity for bespoke collimator design is appealing.

Measurement of differential cross sections for inclusive isolated-photon and photon+jet production in proton-proton collisions at sqrt{s} = 13,text {TeV}

Measurements of inclusive isolated-photon and photon+jet production in proton–proton collisions at sqrt{s} = 13,text {TeV} are presented. The analysis uses data collected by the CMS experiment in 2015, corresponding to an integrated luminosity of 2.26,text {fb}^{-1}. The cross section for inclusive isolated photon production is measured as a function of the photon transverse energy in a fiducial region. The cross section for photon+jet production is measured as a function of the photon transverse energy in the same fiducial region with identical photon requirements and with the highest transverse momentum jet. All measurements are in agreement with predictions from next-to-leading-order perturbative QCD.