Calculations Of Differential Cross Sections Research Articles

A study on neutron emission for proton-induced reactions in 90Zr, 91Zr, and 115In isotopes

Fusion energy heralds the potential of a transformative era, offering a significant solution to global challenges such as climate change, ozone depletion and environmental pollution. Despite its promising prospects, the commercialization of fusion faces several challenges, including high temperature, pressure, plasma stability, fuel supply, costs, etc. It is important to effectively analyze material behavior under plasma conditions, especially in environments where fusion reactions produce high-energy particles such as neutrons. This study investigates the angle-dependent neutron production mechanisms of proton-induced reactions involving the isotopes 90Zr, 91Zr and 115In, which are widely used in fusion reactor materials. Using the Monte Carlo codes PHITS 3.32 and FLUKA, as well as the TALYS 1.96 code, double differential cross-section calculations for neutron emission were performed considering various angles. The research contributes to a broader understanding of fusion processes by providing insights into the behavior of these isotopes under proton-induced reactions.

On the breakdown of eikonal approximation and survival of Reggeization in presence of dimension-5 Higgs-gluon coupling

We consider the one-loop effective vertex for the interaction of a gluon with a Reggeized gluon and a Higgs boson in the infinite-top-mass limit, which is described by a dimension-5 non-renormalizable operator. This vertex enters the calculation of differential cross sections for the forward inclusive production of a Higgs boson in high-energy proton-proton collisions, possibly in association with a backward jet or identified hadron, in a framework where next-to-leading logarithms of the energy are resummed to all orders. The effective vertex is extracted from the high-energy behavior of two-to-two amplitudes for the Higgs production in parton-parton collisions and relies on the validity of the Regge form for these amplitudes. We find that the usual eikonal approximation (Gribov prescription) for the Regge limit and the known region-expansion technique in this limit lead to an incomplete result for the amplitude. The discrepancy is traced back to the non-renormalizable nature of the involved operator. However, the Regge limit of the exact QCD amplitude agrees with the Regge-pole exchange form at one loop, nontrivially supporting the Reggeization hypothesis.

Double differential cross section calculations of (n,p) reactions on 27Al and 24Mg targets

In structural fusion material research, double differential sections are necessary to determine heating and damage due to secondary particles that may occur in structural materials. Therefore, in this study, the double differential proton emission cross sections of 27Al and 24Mg target nuclei were calculated theoretically with the TALYS nuclear reaction code at 14 MeV neutron energy. The calculated values were compared with existing experimental data in the EXFOR library. Additionally, the contribution of direct, compound and preequilibrium reactions in theoretical calculations was investigated.

Pineline: Industrialization of high-energy theory predictions

We present a collection of tools efficiently automating the computation of large sets of theory predictions for high-energy physics. Calculating predictions for different processes often require dedicated programs. These programs, however, accept inputs and produce outputs that are usually very different from each other. The industrialization of theory predictions is achieved by a framework which harmonizes inputs (runcard, parameter settings), standardizes outputs (in the form of grids), produces reusable intermediate objects, and carefully tracks all meta data required to reproduce the computation. Parameter searches and fitting of non-perturbative objects are exemplary use cases that require a full or partial re-computation of theory predictions and will thus benefit of such a toolset. As an example application we present a study of the impact of replacing NNLO QCD K-factors with the exact NNLO predictions in a PDF fit. Program summaryProgram Title:pinelineCPC Library link to program files:https://doi.org/10.17632/dyvns7gnwy.1Developer's repository link:https://nnpdf.github.io/pineline/Licensing provisions: GPLv3Programming language: Python, RustNature of the problem: The computation of theoretical quantities in particle physics often involves computationally-intensive tasks such as the calculation of differential cross sections in a systematic and reproducible way. Different groups often use different conventions and choices which makes tasks such as the fitting of physical parameters or quantities very computationally challenging and hard to reliably reproduce.Solution method: We create a pipeline of tools such that a user can define an observable and a theory framework and obtain a final object, containing all relevant theoretical information. Such objects can be then used in a variety of interchangeable ways (fitting, analysis, experimental comparisons).

Classical calculation of differential cross section for a beam deflected by a concentric refractive index field.

Ray tracing is a fundamental geometric-optics issue which gives a single ray path but seldom presents the collective behavior of light. The optical field distribution usually involves the calculation of an electromagnetic field and is rarely discussed from the perspective of geometric optics. However, in this paper, we show for a concentric medium with spherically symmetric refractive index, how the relative angular distribution of refractive beams can be obtained from the pure classical geometric optics method. As a measurement of the distribution, we introduce the concept of the differential cross section (DCS), which can be calculated from the relation between aiming distance and deflecting the angle of the ray. We present a general method to solve this relation from both Snell's law in a constant medium and the optical Binet equation (OBE) in a gradient-index (GRIN) medium. Even without observing the collective traces, the DCS can independently give a quantitative description for the deflected light density of concentric media at different directions. It may act as a reference index for the design of beam deflector.

Dynamic effective charge in the continuum of the CDW-EIS model for ionization in ion–atom collisions: angular and energy dependence

In this work, a dynamic charge is employed in the continuum distorted wave–eikonal initial state theoretical model to describe the non-Coulomb potential of the residual target for single ionization in bare ion–multielectron atom collisions. A comparison between the well-known Belkić prescription and the effective charge depending on emission angle and energy in the final residual-target continuum state is shown. The obtained results show that this effective charge improves the description of double-differential cross sections for backward emission angles over the whole emission energy range allowing the calculation of simple differential and total cross sections.

Elastic Neutrino–Atom Scattering as a Probe of Neutrino Millicharge and Magnetic Moment

Neutrino scattering on a target at low-energy transfer is one of the basic tools for searching for neutrino electromagnetic properties. We consider the effects of the neutrino millicharge and magnetic moment on the atomic recoil spectrum in elastic neutrino–atom scattering. The results of our calculations of differential cross sections for elastic collisions of tritium neutrinos with the H, 2H, 3He, and 4He atomic targets show that the corresponding experiments can achieve sensitivity to the indicated neutrino electromagnetic characteristics by orders of magnitude better than the available measurements of elastic neutrino–electron and neutrino–nucleus collisions.

Structure of low-lying states of 9Ве nucleus

Glauber's theory of multiple scattering is applied to the calculation of differential cross sections and polarization characteristics of particle scattering on light nuclei. All calculations were carried out within the framework of a reliable spectroscopic approach to nuclear reactions. Its essence consists in the use of nuclear models that reproduce practically all the spectroscopic characteristics of the nuclei under consideration. These include three-particle models of 6Li and 9Be nuclei, a many-particle shell model for nuclei with А = 6–14, and a particle-hole model of shells for nuclei with А = 15; three-body models for the 8Li and 9Li nuclei and a two-particle αt-model for the 7Li nucleus. As our experience shows, when implementing the spectroscopic approach, when the dominant mechanism of the process is also established, one can not only obtain a description of the main characteristics of the process, but also rely on the predictive nature of the theory. In the present work, the results obtained are supplemented by calculations of the structure of the low-lying 5/2+ and 5/2– levels. This allows us to draw a general conclusion: the negative parity levels in 9Be, in which the valence neutron is in the p state, do not have a halo structure; at the same time, low-lying levels of positive parity, in which the valence neutron passes into the next (2s-1d) shell, have such. A special place is occupied by our recent direct evidence of the halo structure of low-lying excited states of the 9Be nucleus with quantum numbers 1/2+ and 3/2+. Within the framework of the ααn model of the 9-Be nucleus, it was shown that a valence neutron with a high probability is located at 11 fm from the center of gravity of two α-particles, while in the 3/2- ground state this distance is several times smaller. The conclusions about the structure of low-lying levels of 9Be, obtained on the basis of the ααn model, are supported by calculations of p9Be scattering: only taking into account the halo structure makes it possible to reproduce the experimental data on inelastic scattering to positive parity levels.

Polarization phenomena in the reaction e++e−→N+N¯+π0 in the framework of the nonresonant mechanism

The dependence of the nucleon polarization in the reaction ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}N+\overline{N}+{\ensuremath{\pi}}^{0}$ over different invariant variables is derived for the nonresonant mechanism. The nucleon polarization is expressed in terms of six invariant complex amplitudes, assuming the conservation of the hadron electromagnetic currents and the P invariance of the hadron electromagnetic interaction. An inclusive experimental setup when the proton (or the antiproton) and the pion are detected in coincidence is considered. Numerical estimations are performed for the so-called normal polarization in the energy range from threshold up to $s=16\text{ }\text{ }{\mathrm{GeV}}^{2}$, using selected parametrizations of the nucleon electromagnetic form factors in frame of a formalism derived in a previous work for the calculation of the unpolarized differential cross section.

Inclusive and semi-inclusive production of spin- 3/2 hadrons in e+e− annihilation

We investigate the inclusive and semi-inclusive productions of spin-3/2 hadrons, such as $\Omega$, in unpolarized $e^+ e^-$ annihilation. The general differential cross sections are expressed in terms of structure functions in accordance to the polarization of the hadron and the azimuthal modulations. We derive a complete definition of quark transverse momentum dependent (TMD) fragmentation functions (FFs) to spin-3/2 hadrons for the first time from the decomposition of the quark-quark correlation matrix at leading twist, 14 of which are newly defined corresponding to rank-3 tensor polarized hadron. The collinear FFs are obtained from the $k_T$-integrated correlation matrix, and only two TMD FFs with rank-3 tensor polarization have nonvanishing collinear counterparts. Then we perform a leading order calculation of the unpolarized differential cross sections. In the single-hadron inclusive production, only two structure functions are found nonzero and none of the rank-3 tensor polarized FFs contributes. For the nearly back-to-back two-hadron production, half of the 48 structure functions are found nonzero even if the spin of the second hadron is not analyzed, and ten of the rank-3 tensor polarized TMD FFs contribute. Therefore, one can study the rank-3 tensor polarized FFs via the production of a spin-3/2 hadron and an unpolarized hadron in unpolarized $e^+ e^-$ collision experiments. These newly defined FFs can be further applied in semi-inclusive deep inelastic scattering processes for the study of nucleon structures.

Evolution equation for elastic scattering of hadrons

We turn high energy elastic scattering of hadrons into an initial value problem using an evolution equation based on the Regge Field Theory, which has a form of the complex nonlinear reaction–diffusion equation, with time being played by the logarithm of energy. The initial conditions are provided by the data-driven models for the real and imaginary parts of the amplitude. Numerical calculations of pp differential cross sections and forward quantities for LHC energies agree very well with experimental data extending up to, and including the diffractive cone. Furthermore, we show that at current accessible energies the non-linear effects play an important role, as the impact parameter space profiles approach the unitarity bound. The equation also predicts some other effects discussed in the literature, like the hollowness of nuclear matter or existence of stationary points in momentum transfer t.

Electron-impact excitation of the 5varvec{^2textbf{S}_{1/2} rightarrow 5^2textbf{P}_{1/2}} and 5varvec{^2textbf{P}_{3/2}} transitions in rubidium by 40 eV electrons: theory and experiment

We report on a series of detailed Breit-Pauli and Dirac B-spline R-matrix (DBSR) differential cross section (DCS) calculations for excitation of the 5,^2textrm{S}_{1/2} rightarrow 5,^2textrm{P}_{1/2} and 5,^2textrm{S}_{1/2}rightarrow 5,^2textrm{P}_{3/2} states in rubidium by 40 eV incident electrons. The early BP computations shown here were carried out with both 5 states and 12 states, while the DBSR models coupled 150 and 325 states, respectively. We also report corresponding results from a limited set of DCS measurements on the unresolved 5,^2textrm{P}_{1/2,3/2} states, with the experimental data being restricted to the scattered electron angular range 2–10^circ . Typically, good agreement is found between our calculated and measured DCS for excitation of the unresolved 5,^2textrm{P}_{1/2,3/2} states, with best accord being found between the DBSR predictions and the measured data. The present theoretical and experimental results are also compared with predictions from earlier 40 eV calculations using the nonrelativistic Distorted-Wave Born Approximation and a Relativistic Distorted-Wave model.Graphic abstract

Single-particle and cluster modes of 13C excited states of 3.09, 8.86 and 9.89MeV

The elastic and inelastic scatterings of deuterons from [Formula: see text]C are registered in a wide range of angles at the laboratory energy of 14.5[Formula: see text]MeV. Data on the differential cross-sections are treated within both the optical model and coupled-channels method. A new set of optical potential parameters is found. Analyses of the [Formula: see text] nuclear reactions are carried out for the levels of excitation 3.089, 8.86 and 9.87[Formula: see text]MeV. The single particle [Formula: see text], and cluster [Formula: see text] models are applied in calculations of differential cross-sections. The calculations show that the state 3.089[Formula: see text]MeV is populated with the single particle configuration, while the latter bands 8.86[Formula: see text]MeV and 9.87[Formula: see text]MeV mainly have the cluster [Formula: see text] excitation. The major contribution of the Hoyle state of the core [Formula: see text] is not observed, but the cluster [Formula: see text] configuration is ascertained to be the main contributor to the state 8.86[Formula: see text]MeV.

Theory Input for \(t\bar {t}j\) Experimental Analyses at the LHC

The precise measurement of the top quark mass, which is a fundamental SM parameter, constitutes one of the main goals of the LHC top physics program. One approach to measure this quantity uses the $\rho_\mathrm{s}$ distribution, an observable depending on the invariant mass of the $t\bar{t}j$ system. To fully exploit the experimental accuracy achievable in measuring top quark production cross sections at the LHC, the theory uncertainties associated to these measurements need to be well under control. To this end we present a study of the effect of varying the theoretical input parameters in the calculation of differential cross sections of the $t\bar{t}j$ process. Thereby we studied the influence of the jet reconstruction procedure, as well as the effect of various renormalization and factorization scale definitions and different PDF sets. The variation of the $R$ parameter in the jet reconstruction algorithm was found to have negligible influence on the scale variation uncertainty. A strong reduction of scale uncertainties and a better behaviour of the NLO/LO ratios using selected dynamical scales instead of a static one in the high energy tails of differential distributions was observed. This is particularly interesting in the context of the top quark mass measurements through the $\rho_\mathrm{s}$ distribution, in which the perturbative stability can be improved by applying the proposed dynamical scale definition.

Modified TMD Factorization and Sub-leading Power Corrections

Collinear factorization and transverse-momentum-dependent (TMD) factorization are two complementary approaches to perform QCD calculations of Drell-Yan differential cross sections. The former is designed to correctly describe the behavior of the observable at large values of the gauge boson transverse momentum qT, while the latter accounts for non-perturbative effects relevant at small qT. We present basic features and first numerical results of a novel factorization formalism which is related to both previous frameworks and allows for an improved description of the intermediate-qT region.

Modified TMD Factorization and Sub-leading Power Corrections

Collinear factorization and transverse-momentum-dependent (TMD) factorization are two complementary approaches to perform QCD calculations of Drell-Yan differential cross sections. The former is designed to correctly describe the behavior of the observable at large values of the gauge boson transverse momentum qT, while the latter accounts for non-perturbative effects relevant at small qT. We present basic features and first numerical results of a novel method which is related to both previous frameworks and allows for an improved description of the intermediate-qT region.

Calculation of double differential cross sections of electron–atom bremsstrahlung by the relativistic partial-wave method at electron energies greater than 3 MeV

This work describes an extension of the relativistic partial-wave (PW) method for calculation of the double differential cross sections (DDCS) of electron–atom bremsstrahlung at incident electron energies (T1) of the order of 10 MeV. The PW method is extended to higher energies by replacing some of the radial matrix elements with interpolated values, and by extrapolating the truncated PW series to a sufficiently high value of the maximum total angular momentum of the electron (jmax). Although the current analysis has been mostly limited to the cases with the outgoing electron energy T2≤10MeV and all values of Z from 1 to 100, this method allows to obtain accurate values of the DDCS even when T2>20MeV, using a relatively small number of partial waves (jmax<300), as demonstrated by a case study described in the present work (Z=1, T1=30MeV, T2=24MeV).

Differential study of proton-helium collisions at intermediate energies: Elastic scattering, excitation, and electron capture

In a series of papers we present a comprehensive investigation of the four-body proton-helium differential scattering problem using the two-center wave-packet convergent close-coupling approach in the intermediate energy region where coupling between various channels is important. The approach uses correlated two-electron wave functions for the helium target. For comparison, a recently developed method that reduces the target to an effective single-electron system is also used. In this paper we present calculations of angular differential cross sections for elastic-scattering, target excitation, and electron-capture processes. The results of the two-electron and effective single-electron methods exhibit a good level of agreement. They also agree well with available experimental data. It is concluded that both versions of the wave-packet convergent close-coupling approach are capable of providing a realistic differential picture of all interdependent and interconnected binary processes taking place in proton-helium collisions at intermediate energies.

Isotopic and vibrational-level dependence of H2 dissociation by electron impact

The low-energy electron-impact dissociation of molecular hydrogen has been a source of disagreement between various calculations and measurements for decades. Excitation of the ground state of H$_2$ into the dissociative $b ^3\Sigma_u^+$ state is now well understood, with the most recent measurements being in excellent agreement with the molecular convergent close-coupling (MCCC) calculations of both integral and differential cross sections (2018 Phys. Rev. A 98 062704). However, in the absence of similar measurements for vibrationally-excited or isotopically-substituted H$_2$, cross sections for dissociation of these species must be determined by theory alone. We have identified large discrepancies between MCCC calculations and the recommended $R$-matrix cross sections for dissociation of vibrationally-excited H$_2$, D$_2$, T$_2$, HD, HT, and DT (2002 Plasma Phys. Contr. F. 44 1263-1276,2217-2230), with disagreement in both the isotope effect and dependence on initial vibrational level. Here we investigate the source of the discrepancies, and discuss the consequences for plasma models which have incorporated the previously recommended data.

Electron transport in DNA bases: An extension of the Geant4-DNA Monte Carlo toolkit

The Geant4-DNA Monte Carlo toolkit is extended to include electron interactions with the four DNA bases using cross sections implemented in Geant-DNA CPA100 models. Electron cross sections for elastic scattering, ionisation, and excitation are calculated in the four DNA bases (adenine, thymine, guanine and cytosine) with relativistic energy range. These are implemented within the “option6” physics constructor to extend its capability of tracking electrons in DNA material in addition to liquid water. Differential and integrated cross sections calculations are in good agreement with the literature for all DNA bases. Stopping power, range and inelastic mean free path calculations in the four bases agree well with other studies, especially for high energy electrons with some deviations at low energies. Differences from water simulations emphasize the need to include DNA bases cross sections in track structure codes for better estimation of radiation effects on biological material.