# Haut PDF Modelisation of the fission cross section

### Modelisation of the fission cross section

Chapter 4 Treatment of the fission channel 4.1. Double humped fission barriers The main concepts of nuclear ﬁssion theory are based essentially on the liquid -drop model. According to this model, the competition between the surface tension forces of a nuclear liquid drop and the Coulomb repulsion forces related to the nuclear charge leads to the formation of a single humped energy barrier which can determine spontaneous decay of the nucleus. The penetrability of the barrier determines the half-life for spontaneous ﬁssion. Early studies showed that the liquid-drop model cannot explain the major peculiarity of spontaneous and low-energy ﬁssion of the actinides, namely the asymmetric mass distribution of ﬁssion fragments, nor the sub-barrier fission of fertile actinides or the isomeric fission. The spontaneously – ﬁssioning americium isomers and the intermediate resonance structures observed in neutron-induced ﬁssion cross sections, required radical changes in the ﬁssion model. Calculations of nuclear deformation energies based on the shell correction method by Strutinsky ( Strutinsky, 1967 and 1968 ) played a crucial role. Applying the Strutinski shell corrections a double humped barrier is obtained. The ﬁssion barriers calculated for the actinides consisted of a double-hump curve with a rather deep potential well between the humps.
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### Scaling tests of the cross section for deeply virtual compton scattering

(F ), C I (F eff ), C I + ∆C I  (F)} as independent pa- rameters. In Kin-1 and Kin-2, due to the lower photon energy E γ (Table I), our acceptance, trigger, and readout did not record a comprehensive set of ep → eπ 0 X events. For those events we were able to reconstruct, we found only a few percent contribution to dΣ, but a larger con- tribution to dσ. For Kin-1,2, we only present results on dΣ. Our systematic errors in the cross-section measure- ments are dominated by the following contributions: 3% from HRS×PbF 2 acceptance and luminosity; 3% from H(e, e ′ γ)γX (π 0 ) background; 2% from radiative correc- tions; and 3% from inclusive H(e, e ′ γ)N π . . . background. The total, added in quadrature, is 5.6%. The dΣ results contain an additional 2% systematic uncertainty from the beam polarization. In order to compute the BH contri- bution in the dσ analysis we used Kelly’s parametrization of form factors [26], which reproduce elastic cross-section world data in our t range with 1% error and 90% CL.
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### Simple method for measuring the spectral absorption cross-section of microalgae

3.2. Culture characterization The cell size distribution of C. vulgaris was measured using 165 microscope images captured using a digital camera (AxioCam MRc) mounted on an optical microscope (Zeiss Axio Scope A1). The dia- meters of 2873 cells were measured manually using an image pro- cessing software (Axio Vision Routine) and their volume equivalent sphere radius was reported for the sake of completeness. These results were not used in either experimental approaches investigated. The culture dry biomass concentration X (in g/L) was determined gravimetrically by ﬁltering 5 mL of culture through a pre-dried and pre-weighed 0.45 μ m pore size glass- ﬁber ﬁlter (Whatman GF/F). The ﬁlters were dried overnight in an oven at 105 °C and weighed, in an analytical balance (Mettler Toledo XA204, Columbus, OH) with a sensitivity of 0.1 mg, after being cooled in a desiccator for 10 min. The samples were analyzed in triplicates and the reported biomass con- centration corresponded to the mean value. In addition, the cell density N T (in #/m 3 ) was counted using a 200 μ m deep Malassez
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### Measurement of the antineutrino flux and cross section at the near detector of the T2K experiment

factors F i only depend on x. This behaviour goes under the name Bjorken scaling. 2.2 Neutrino-nucleus scattering Theoretical modelling of the neutrino-nucleus scattering face many complications. The first is the initial state of the nucleons inside a nucleus. They are indeed constantly moving around inside the nuclear potential, changing their momentum and direction in relation to an incoming neutrino, which affects both the kinematics and the cross-section. Unfortunately the initial momentum spectra of nucleons is not well known, and can vary significantly even between similar mass nuclei. An additional complication is that the neutrino can interact not only with individual nucleons, but the interaction can include correlated nucleon pairs or any combination of nucleons in a quasi-bound state. After the final-state particles have been created from an interaction, they need to propagate out through the nucleus. During the propagation they can interact with the other nucleons inside the nucleus. These processes, called “final state interactions” (FSI), can alter the particles type and number.
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### Rosenbluth separation of the $\pi^0$ Electroproduction Cross Section off the Neutron

tions: D(e, e 0 π 0 )X = d(e, e 0 π 0 )d+n(e, e 0 π 0 )n+p(e, e 0 π 0 )p. (5) We subtract the p(e, e 0 π 0 )p yield from the deuterium data by normalizing our H(e, e 0 π 0 )X data to the lumi- nosity of the LD2 data. The Fermi-momentum ~ p F of bound protons inside the deuteron is statistically added to the LH2 data following the distribution given in [22] since this effect is intrinsically present in the M X 02 spec- trum of the LD2 data. The result of the subtraction of the H(e, e 0 π 0 )X data from the D(e, e 0 π 0 )X yield is shown in Fig. 2. The d(e, e 0 π 0 )d and n(e, e 0 π 0 )n chan- nels are in-principle kinematically separated by ∆M X 02 = t(1 − M/M d ) ≈ t/2 where M d is the deuteron mass. This kinematic shift is exploited in the procedure described below to separate the contributions of the quasi-free neu- tron and coherent deuteron channels in the total π 0 elec- troproduction cross section.
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### Proton inelastic cross section at ultrahigh energies

It should be noted that both the total and elastic cross section datasets include discordant data from different experiments. This is quantified by a simple consistency check that fits generic quadratic polynomials in log s to each dataset and computes the resulting χ 2 . Table I shows the results with both the elastic and total cross sections running up χ 2 =d:o:f noticeably greater than 1. Thus, one obtains a minimum combined χ 2 of 47.1. This is a well- known problem with these data, first addressed in [30] and later in [31] . At present, however, the number of data points is simply too small to identify individual outliers, and hence there is little one can do for lack of better experimental results. We shall thus neither filter nor sieve the data, but remember that the best possible χ 2 is rather high.
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### Fission yields and cross sections: correlated or not?

Following this line of research, some quantities have still been left aside from this global correlation effort, namely fission yields. In the following, the term “fission yield” will designate without distinction independent or cumu- lative fission yields (called FY). It is a known deficiency that current evaluated libraries do not provide correlation matrices for fission yields, neither for a specific fission- ing isotope (such as all fission yields from 235 U(n,f)), or between fissioning isotopes. This represents a practical problem for nuclear data users, as uncertainties on quanti- ties dependent of FY (e.g. long-lived fission products from spent fuel) are believed to be too large, due to the lack of FY correlations [ 31 – 34 ]. As mentioned before, the current evaluation format is not defined to propose such correla- tions for FY; there are nevertheless efforts to update such format.
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### Validation of the $^{238}$U inelastic scattering cross section through the excalibur dedicated experiment

5 Sensitivity / uncertainty analysis 5.1. Calculation of sensitivity coefficients The correlated sampling [7] feature of the TRIPOLI4 code was used to calculate sensitivity coefficients, defined as the relative change in the ITR i due to a relative change of 1% in the cross section σ i of 238 U - with σ i = capture, fission, elastic, inelastic or (n,xn) reactions (for the time being, it is not possible to get the sensitivity coefficient due to prompt neutron multiplicity neither due to double differential data like for instance the energy or angular distribution of inelastic scattering). The 1-group sensitivity coefficients for 238 U and 235 U reactions are presented in Table 5 while the sensitivity profile as a function of neutron incident energy is plotted in Fig. 5 for the ITR obtained from the activation of 54 Fe. The sensitivity coefficient breakdown shows a
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### The Total Cross Section at the LHC: Models and Experimental Consequences

The inner band of Fig. 1 shows the best guess, and it is based on a series of statistical indica- tors explained in [4]. It corresponds to a universal triple-pole (log 2 s) parametrisation. One should note that the multiple-pole fits have some peculiar properties: in the triple-pole case, the contribution of the pomeron f alls with s for energies smaller than 6 GeV, whereas in the double-pole case, it actually becomes negative below 9.5 GeV. Simple poles seem to be excluded, but they can be con- sidered again if the lower cut-off on the energy is raised to 10 GeV. The multiple-pole parametrisa- tions have been used successfully [5] to reproduce low-x data in deeply inelastic scattering (DIS), showing that universality does not seem to hold in general, as the coefficient of the triple pole de- pends on Q 2 . More recently, multiple poles have
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### Challenging fission cross section simulation with long standing macro-microscopic model of nucleus potential energy surface

CHAPTER 7. CONCLUSION & PERSPECTIVES 7.1. OVERVIEW OF THE WORK felt by the nucleons. This parameterized potential is chosen to be consistent with the former macroscopic description. This model is the outcome of many successive improve- ments that have refined the original liquid-drop model. Implementing this model in the CONRAD code has been a colossal work because of the model complexity and the related 50 year of legacy. An operational FRLDM has been added to the CONRAD toolbox and verified by various means. Despite this pragmatical choice, deepest care has been brought in the implementation in order to meet the speed requirements of evaluation. Advanced numerical and computational (hardware) solutions have been found and put into effect. The PES obtained using the macroscopic-microscopic FRLDM describes the deformation energy of a nucleus allowed to deform according to a related geometrical shape parame- terization. At least three parameters are necessary to satisfactorily describe the shape of the fission barrier: elongation, neck size and mass-asymmetry. The corresponding mul- tidimensional PES must be reduced into a one-dimensional deformation potential. Two algorithms have been implemented in the CONRAD code to obtain such a one-dimensional path: the least-energy and least-action paths searching methods. To study the barrier penetrability, the deformation inertia “along” the fission path must be defined. In many studies this parameter is explicitly or implicitly chosen to be deformation-independent. The natural fission abscissa describing the position along the path provided by these meth- ods has been discussed. The present conclusions advocate for the least-action method as both the fission abscissa and the inertia parameter are naturally provided by the model. Yet the least-energy path provides, for the time being, results closer to the experimental data. It is this pragmatical approach that has been selected in the last section of this chapter to investigate the impact of some parameters on the eventual fission cross sec- tion. The one-dimensional deformation potential and the related inertia parameter are obtained with both of the reduction methods and their effect on barrier penetrability has been compared with special focus set on the impact of the deformation dependency of the inertia parameter.
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### Measurement of the ttbar production cross section using dilepton events in ppbar collisions

We also determine the number of events with an iso- lated muon arising from jets in the eµ and µµ channels. This number is estimated as n µ f = N loose f µ , where N loose is the number of events in the same sign sample with loose isolation criteria on the muon: E T µ,iso /p µ T < 0.5 and p µ,iso T /p µ T < 0.5, and f µ is the misidentification rate for isolated muons. In the µµ final state, we apply these loose isolation criteria only to one randomly cho- sen muon. In the eµ channel, the number of events with jets misidentified as electrons in the same sign sample is subtracted from N loose . The misidentification rate, f µ , is determined in a dimuon sample with at least one jet. In this sample we require one muon to be close to the jet (R(µ, jet) < 0.5) with reversed isolation criteria E T µ,iso /p µ T > 0.15 and p µ,iso T /p µ T > 0.15. The other muon defined as the probe, should pass the loose isolation crite- ria E T µ,iso /p µ T < 0.5 and p µ,iso T /p µ T < 0.5. We compute f µ as the ratio of the number of events in which the probe muon passes the tight isolation criteria to the total num- ber of events in this same sign sample. The systematic uncertainty on the f µ determination is about 10% and results mainly from the statistical uncertainty due to the limited size of the sample used for the muon misidenti- fication rate calculation and the potential dependence of the misidentification rate on p T and / p T .
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### Quantum scattering by a disordered target - The mean cross section

5. Numerical study The fact that the set of equations to be solved in order to obtain one value of the cross section is finite when the scatterers are pointlike makes this type of scatterer especially suitable for numerical studies in which a large number of such values is needed. In this section we present and discuss the results of a numerical study about the scattering by a disordered target consisting of pointlike scatterers. The target has been modelled by a set of N scatterers having each an equal probability of being at any position inside a sphere whose radius R may be modified; samples fitting in the same volume have been assigned the same value of the density ρ = 3N/4πR 3 . We have studied the variation of
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### Combination of measurements of the top-quark pair production cross section from the Tevatron Collider

is approximately 85% from quark-antiquark annihilation (q ¯q → t¯t) and 15% from gluon-gluon fusion (gg → t¯t). SM predictions for inclusive t¯t production at the Tevatron, calculated to different orders in perturbative quantum chromodynamics (QCD), are available in Refs. [16 –24] . The first calculations at full next-to-leading-order (NLO) QCD were performed before the discovery of the top quark [16] , and have been updated using the more recent CTEQ6.6 parton distribution functions (PDF) [17] . These full NLO calculations were further improved by adding resummations of logarithmic corrections to the cross section from higher-order soft-gluon radiation, in particular by including next-to-leading logarithmic (NLL) soft-gluon resummation [18] and the more recent PDF [19] . Also available are NLO calculations with soft-gluon resum- mation to next-to-next-to-leading logarithmic (NNLL) accuracy, and approximations at next-to-next-to-leading- order (NNLO) obtained by reexpanding the result from NLO þ NNLL in a fixed-order series in the strong coupling constant α s (NNLO approx ) [20–23,25,26] . Differences
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### Determination of Galloping for Non-Circular Cross-Section Cylinders

(sinφ θ /ω) ¯ M θ , (2.31) As can be seen in equation (2.31), the stiffness term is now incorporated in the flow-induced dam- ping term. From a physical point of view, equation (2.31) shows that the phase-lag-related damping is associated to the time needed for the viscous flow to adjust to position changes of the structure. The second term of equation (2.31) demonstrates that the unsteady effects can not be neglected. In order to use the quasi-steady theory to analyze torsional galloping properly, the phase delay needs to be considered. However, there is no reliable tool to predict the phase delay. Nakamura and Mizota [20] experimentally measured the M θ ˙ for different aspect ratios. Their results showed that
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### Improvement of cross section model in COCAGNE code of the calculation chain of EDF

The first category’s methods have been proven suitable for the simulation on a “standard” domain where the parameter-values are rather close to the nominal condition. Of course, when they are far away from this condition, their accuracy is lost since the heuristics used around nominal values may not be valid anymore. The second ones are more general but high accuracy requires a lot of pre- calculated data. For instance, the multilinear approach that is used at EDF, relies on the acquisition of the values of the various cross sections on a Cartesian grid of the (standard or extended) domain in the parameter-phase space, i.e. in R 5 from the lattice code. This nuclear library has a cardinal equal to N d , where N stands for the number of discretized points in each phase direction. Then the reconstruction allows us to build an approximation of each cross section at any point by: i) locating this point to one of the cells of the Cartesian grid (to which this point belongs), here each cell is seen as a d dimensional object and its vertices are the points on which the value of each cross section is available, ii) averaging the previous values in a convex way to provide a linear approximation in each dimension. This is a very simple methods, and its accuracy (second oder in L 2 or L ∞ norms scaling like O(N −2 )) in terms of size of the cell that implies to have a quite large library on standard domains and very - even too much - large nuclear library on extended domains.
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### Compton Scattering Cross Section on the Proton at High Momentum Transfer

couple to a single quark. The fixed-θ cm scaling power is considerably larger than that predicted by perturbative QCD. We thank P. Kroll, J. M. Laget, and G. Miller for pro- ductive discussions, and acknowledge the Jefferson Lab staff for their outstanding contributions. This work was supported the US Department of Energy under contract DE-AC05-84ER40150, Modification No. M175, under which the Southeastern Universities Research Associa- tion (SURA) operates the Thomas Jefferson National Accelerator Facility. We acknowledge additional grants from the U.S. National Science Foundation, the UK Engi- neering and Physical Science Research Council, the Ital- ian INFN, the French CNRS and CEA, and the Israel Science Foundation.
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### Combination of measurements of the top-quark pair production cross section from the Tevatron Collider

The largest weight in the BLUE combination of CDF measurements is 70% for the ℓ+jets channel LJ-ANN re- sult. The dilepton result has a weight of 22%, and the measurement using b-jet identification in the ℓ+jets chan- nel has a weight of 15%. The measurement in the all-jets channel has a weight of −7%. Such negative weights can occur when the correlation between the two mea- surements is larger than the ratio of their total uncer- tainties [56]. The correlation matrix, including statis- tical and systematic effects, is given in Table III. The largest correlation is 51% between the DIL and HAD measurements, due to the correlation between system- atic uncertainties on detector modeling (primarily b-jet identification), signal modeling, jet energy scale, and lu- minosity. Next largest is the 50% correlation between the LJ-ANN and LJ-SVX measurements, which arises from a subset of common events and correlation between sys- tematic uncertainties from signal modeling, jet energy scale, and normalization of the Z/γ ∗ cross section. The
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### First measurement of the WZ production cross section with the CMS detector at the LHC

The drift cells of each chamber are offset by a half-cell width with respect to their neigh- bor to eliminate dead spots in the efficiency, providing the muon time measurement with excellent resolution. In the 2 endcap regions, the muon rates and background levels are high and the magnetic field is less uniform. Cathode strip chambers (CSC) are used in this region covering the |η| range between 0.9 and 2.4, thanks to their fast response time, fine segmentation, and radiation resistance. In each endcap 4 stations of CSCs are hosted, with chambers po- sitioned perpendicular to the beam line and interspersed between the flux return plates. In each chamber, a precision measurement in the r − φ bending plane is provided by the cathode strips running radially outward, while the anode wires run approximately perpendicular to the strips and measure η and the beam-crossing time of a muon.
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### The flow-induced vibration of an elliptical cross-section at varying angles of attack

This raises a question: how ubiquitous is the flow-induced vibration behaviour of a purely circular cylinder? Navrose et al. ( 2014 ) studied the vortex-induced vibration of an elliptical cross section using two-dimensional direct numerical simulations for ellipses of varying aspect ratio. They found that the response regimes present, characterised by amplitude of oscillation, forces, and vortex shedding modes, were a strong function of the aspect ratio. To understand the response of circular cylinders yawed with respect to the incoming flow, Franzini et al. ( 2009 ) conducted an experimental study on the vortex-induced vibration of an elliptical cylinder with an aspect ratio of 1.41, the same aspect ratio as the cross section of a cylinder yawed at an angle of π / 4. With the long axis aligned with the flow, this study showed that the response of the body was reduced compared to the circular cross section. It was hypothesised that this reduction is due to the increased added mass of the flatter transversely oscillating body. Both of these studies investigated situations where the ellipse was mounted symmetrically with respect to the incoming flow, i.e, with the major or minor axis aligned with the flow.
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### The flow-induced vibration of an elliptical cross-section at varying angles of attack

This raises a question: how ubiquitous is the flow-induced vibration behaviour of a purely circular cylinder? Navrose et al. ( 2014 ) studied the vortex-induced vibration of an elliptical cross section using two-dimensional direct numerical simulations for ellipses of varying aspect ratio. They found that the response regimes present, characterised by amplitude of oscillation, forces, and vortex shedding modes, were a strong function of the aspect ratio. To understand the response of circular cylinders yawed with respect to the incoming flow, Franzini et al. ( 2009 ) conducted an experimental study on the vortex-induced vibration of an elliptical cylinder with an aspect ratio of 1.41, the same aspect ratio as the cross section of a cylinder yawed at an angle of π / 4. With the long axis aligned with the flow, this study showed that the response of the body was reduced compared to the circular cross section. It was hypothesised that this reduction is due to the increased added mass of the flatter transversely oscillating body. Both of these studies investigated situations where the ellipse was mounted symmetrically with respect to the incoming flow, i.e, with the major or minor axis aligned with the flow.
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