Formula For Cross Section Research Articles

Inactivation cross section induced by heavy ions of different energies in Bacterial cells of E. coli: An analytical approach

An analytical inactivation cross section formula based on the radial dose distribution equation that proposed by Awad et al. (2018) is presented. The formula is a multi-hit model based on the track structure theory of Katz that was not updated since Katz and co-workers in 1970s. The formula was solved numerically to calculation the inactivation cross section, σ and action cross section for double strand break, σDSB for the two strains of vegetative E. coli cells (BS−1 and B/r) and their DNA bombarded with heavy ions of different energies. The inactivation cross section is affected by many parameters and the variations in σ in terms of these parameters were studied. The model predicts the measured inactivation cross sections for E. coli cells with good accuracy. It was found that as the ion charge increases as the inactivation probability increases and the corresponding inactivation cross section of the ion increases.

Improved calculation of fusion barrier distribution

The fusion barrier distribution (Dfus) for the systems 16O+144Sm and 16O+208Pb systems had been analyzed in this work to test the benefit of using second derivative of Wong’s formula for fusion cross section to extract Dfus from experimental data. The calculated Dfususing Wong’s formula compared with the result of three-point difference formula, which is the usual method for extract Dfus from experimental cross section. The results showed that this method generated the fusion barrier distribution for both systems in an acceptable approach with respect to the relative position of distribution peaks when it is compared with the theoretical calculations and three-point difference formula.

Nükleer Tıpta Kullanılan Bazı Radyofarmasötiklerin Üretim Reaksiyon Tesir Kesitlerinin Yoğunluğa Bağlı Yeni Parametrelerle Hesaplanması

In nuclear medicine, radiopharmaceuticals are used for diagnosis or treatment purposes. Radiopharmaceuticals containing radionuclide in their structure are produced by reactors, generators or cyclotrons and are generally used for scintigraphy or tomographic investigations. The produced radionuclides can be given to the human body together with organic or inorganic substances. In this study, the production reaction cross sections were calculated for two selected radiopharmaceutical nuclei (99Tc and 115In) using the semi-empirical cross section formula for the (n, α) reactions developed by Tel et al. (2008). The density depending on (n, α) reaction cross sections were also investigated with the four Skyrme Hartree Fock parameters (S3, T3, SKM and SKM*). While the calculated value from the semi-empirical formula developed by Tel et al. (2008) gave reasonable results, the density-dependent calculations were observed lower values than that of experimental values.

A new developed semi-empirical formula for the (α,p) reaction cross-section at 19±1 MeV

The aim of this study is to obtain a new semi-empirical formula for [Formula: see text] reactions concerning the possible usage areas of this reaction type, where the fusion reactor studies could be pointed as one of them. The formula development studies have been performed by considering the existing semi-empirical formula modification studies in the literature where an absence of [Formula: see text] reaction has been realized. The suitable experimental data, existing on the EXFOR database, have been used to generate the [Formula: see text] reaction cross-section systematics in the energy range of 19 [Formula: see text]1 MeV. Also, statistical analyses have been performed and the correlation coefficients [Formula: see text] generated by fit parameters have been given.

Transmission coefficients in compound-nucleus reaction theory

A recent article (D.A. Brown, et al., Phys. Rev. C98 024616 (2018)) rproposed a modification of the cross section formula used in practical calculations of compound nucleus reactions. We discuss the main concepts and approximations of statistical reaction theory and conclude that the standard practical implementations of the cross section formula remain the preferred choice.

Quantum photodetachment of hydrogen negative ion in a harmonic potential subjected to static electric field

Photodetachment of negative ions has attracted immense interest owing to its fundamental nature and practical implications with regard to technology. In this study, we explore the quantum dynamics of the photodetachment cross section of negative ion of hydrogen H− in the perturbed one dimensional linear harmonic potential via static electric field. To this end, the quantum formula for total photodetachment cross section of the H− ion is derived by calculating the dipole matrix element in spherical coordinates. In order to obtain the detached electron wave function, we have solved the time-independent Schrödinger wave equation for the perturbed Hamiltonian of the harmonic oscillator in momentum representation. To acquire the corresponding normalized final state detached electron wave function in momentum space, we have employed an approach analogous to the WKB (Wenzel–Kramers–Brillouin) approximation. The resulting analytical formula of total photodetachment cross section depicts interesting oscillator structure that varies considerably with incident-photon energy, oscillator potential frequency, and electric field strength as elucidated by the numerical results. The current problem having close analogy with the Stark effect in charged harmonic oscillator may have potential implications in atomic and molecular physics and quantum optics.

Empirical formula for bremsstrahlung cross-section in actinides

We have formulated the empirical formula for bremsstrahlung cross section in actinides. This formula produces bremsstrahlung cross sections for electrons with energies from 1 keV to 10 GeV incident on atoms with atomic numbers Z = 89 to 103. This formula produces bremsstrahlung cross sections with simple inputs of energy of incident electron (T), energy of emitted bremsstrahlung photon and atomic number of the target.

Empirical formula for bremsstrahlung cross-section in actinides

We have formulated the empirical formula for bremsstrahlung cross section in actinides. This formula produces bremsstrahlung cross sections for electrons with energies from 1 keV to 10 GeV incident on atoms with atomic numbers Z = 89 to 103. This formula produces bremsstrahlung cross sections with simple inputs of energy of incident electron (T), energy of emitted bremsstrahlung photon and atomic number of the target.

Photodetachment dynamics of negative ions near a moving surface

Photodetachment dynamics of negative ions near a moving surface is investigated for the first time. An analytical formula for the photodetachment cross section of negative ions induced by the moving surface has been put forward. This formula is universal and appropriate to any negative ion no matter the photodetachment is dominated by an s-wave source or a p-wave source. In contrast to the photodetachment of negative ion near a static surface, the returning kinetic energy of the detached electron is different from its initial value after it is bounced back by the moving surface; therefore, an additional modulation function related to the electron’s initial and returning momentum is multiplied in the oscillating cross section. As a demonstration, we calculate the photodetachment cross section of H− and Cl− ions near a moving surface. It is shown that the photodetachment cross section depends on the electron’s energy and the speed of the moving surface sensitively. Therefore, we can control the photodetachment dynamics of negative ion by a moving surface. Our work provides some insights into the behavior of photodetachment dynamics of negative ion near a moving surface and may guide the future experiments toward this field.

Reproducing heavy-ion fusion cross sections at extreme sub-barrier energies with a simple formula

Heavy-ion fusion hindrance occurs at extreme sub-barrier energies. This behavior is well reproduced with a simple cross section formula, which was developed by Siwek-Wilczynska et al., based on a single-Gaussian distribution of fusion barrier heights, before the discovery of the hindrance phenomenon. This expression has not yet been widely used and referenced in the literature. An analysis by using this simple formula is presented for 29 systems, from 16O + 18O to 64Ni + 124Sn , all being measured down to less than 10μb. The agreement with the data is even better than the ones from sophisticated Coupled-channels calculations. This simple expression also applies to fusion reactions in lighter systems. The three parameters contained in this formula vary in a relatively smooth fashion over the whole mass range, and can be used to extrapolate cross sections or to obtain an estimate of the excitation function for systems which have not been measured. Extensions and restrictions of this method are also discussed.

The influence of a strong infrared radiation field on the conductance properties of doped semiconductors

This work presents an analytic angular differential cross section formula for the electromagnetic radiation field-assisted electron scattering on impurities in semiconductors. These impurities are approximated with various model potentials. The scattered electrons are described with the well-known Volkov wave function, which has been used to describe strong laser field matter interaction for more than half a century, which exactly describes the interaction of the electron with the external oscillating field. These calculations show that the electron conductance in a semiconductor could be enhanced by an order of magnitude if an infrared electromagnetic field is present with 1011 W/cm2 < I < 1013 W/cm2 intensity.

Coherency and incoherency in neutrino-nucleus elastic and inelastic scattering

Neutrino-nucleus scattering $\nu A\to \nu A$, in which the nucleus conserves its integrity, is considered. We show that elastic interactions keeping the nucleus in the same quantum state lead to a quadratic enhancement of the corresponding cross-section in terms of the number of nucleons. Meanwhile, the cross-section of inelastic processes in which the quantum state of the nucleus is changed, essentially has a linear dependence on the number of nucleons. These two classes of processes are referred to as coherent and incoherent, respectively. The coherent and incoherent cross-sections are driven by factors $|F_{p/n}|^2$ and $(1-|F_{p/n}|^2)$, where $|F_{p/n}|^2$ is a proton/neutron form-factor of the nucleus, averaged over its initial states. The coherent cross-section formula used in the literature is revised and corrections depending on kinematics are estimated. As an illustration of the importance of the incoherent channel we considered three experimental setups with different nuclei. Experiments attempting to measure coherent neutrino scattering by solely detecting the recoiling nucleus, as is typical, might be including an incoherent background that is indistinguishable from the signal if the excitation gamma eludes its detection. However, as is shown here, the incoherent component can be measured directly by searching for photons released by the excited nuclei inherent to the incoherent channel. For a beam experiment these gammas should be correlated in time with the beam, and their higher energies make the corresponding signal easily detectable at a rate governed by the ratio of incoherent to coherent cross-sections. The detection of signals due to the nuclear recoil and excitation gammas provides a more sensitive instrument in studies of nuclear structure and possible signs of new physics.

Experimental investigation on octagonal concrete filled steel stub columns under uniaxial compression

Concrete filled steel tubes (CFST) have been widely used in modern constructions. The cross-section shapes of circular and rectangular are mostly used. This paper presents an investigation on CFST with a new cross-section shape - octagonal shape which combines both advantages from circular and square cross-sections. In this study, 21 CFST stub columns were tested accompanying with 9 plain concrete columns under uniaxial compression. Three cross-section shapes, octagonal, circular and square sections were considered. In parallel, 10 associated CFST stub columns with octagonal cross-sections from literature were also complied. The measured steel yield strength was between 383 MPa to 485 MPa. Both normal and high strength concrete were used with measured cylinder compressive strengths ranging from 38 MPa to 112 MPa. The key investigation focuses on the relationship between the cross-section shapes and confinement effectiveness which can provide an understanding on the difference in load bearing capacity of CFST with those three section shapes. Design formulae for the cross-section capacity in the current code of practice were assessed by the experimental results and modification was proposed to the existing formula for circular cross-section which could be adopted for the CFST with octagonal cross-section.

Higgs boson production at hadron colliders at N3LO in QCD

We present the Higgs boson production cross section at Hadron colliders in the gluon fusion production mode through N3LO in perturbative QCD. Specifically, we work in an effective theory where the top quark is assumed to be infinitely heavy and all other quarks are considered to be massless. Our result is the first exact formula for a partonic hadron collider cross section at N3LO in perturbative QCD. Furthermore, our result is an analytic computation of a hadron collider cross section involving elliptic integrals. We derive numerical predictions for the Higgs boson cross section at the LHC. Previously this result was approximated by an expansion of the cross section around the production threshold of the Higgs boson and we compare our findings. Finally, we study the impact of our new result on the state of the art prediction for the Higgs boson cross section at the LHC.

Subleading Regge limit from a soft anomalous dimension

Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in mathcal{N}=4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.

Simple empirical correction functions to cross sections of the photoelectric effect, Compton scattering, pair and triplet production for carbon radiation shields for intermediate and high photon energies

The general review of cross section formulas for the photoelectric effect, Compton scattering, pair and triplet production is presented in the intermediate and high photon energy spectrum for carbon (Z = 6). Using the classical Gaussian regression method, the empirical correction functions for the theoretical cross section formulas are calculated based on the existing experimental data. The simple formulas can be used to calculate the cross sections of four main radiation effects with a good accuracy. The proposed formulas are enough for practical calculations in the excel spreadsheet in e.g. radiation protection applications or radiation shields designing.

Post-prior equivalence for transfer reactions with complex potentials

In this paper, we address the problem of the post-prior equivalence in the calculation of inclusive breakup and transfer cross sections. For that, we employ the model proposed by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)], conveniently generalized to include the part of the cross section corresponding the transfer to bound states. We pay particular attention to the case in which the unobserved particle is left in a bound state of the residual nucleus, in which case the theory prescribes the use of a complex potential, responsible for the spreading width of the populated single-particle states. We see that the introduction of this complex potential gives rise to an additional term in the prior cross section formula, not present in the usual case of real binding potentials. The equivalence is numerically tested for reaction induced by deuterons.

Equivalent photons at the LHC: pp(γγ) → ppl+l-, Pb Pb (γγ) → Pb Pb l+l-

The Large Hadron Collider is considered as a photon-photon collider with the photons produced in ultraperipheral collisions of protons or heavy ions. The equivalent photon approximation is applied to derive analytical formulae for the fiducial cross sections of reactions pp(γγ) → pp μ+μ- and Pb Pb (γγ) → Pb Pb μ+μ-. The results are compared to the measurements reported by the ATLAS collaboration.

Cross sections for inelastic meson-meson scattering

We study two kinds of inelastic meson-meson scattering. The first kind is inelastic 2-to-2 meson-meson scattering that is governed by quark interchange as well as quark-antiquark annihilation and creation. Cross-section formulas are provided to get unpolarized cross sections for $\pi K \to \rho K^\ast$ for $I=1/2$, $\pi K^\ast \to \rho K$ for $I=1/2$, $\pi K^\ast \to \rho K^\ast$ for $I=1/2$, and $\rho K \to \rho K^\ast$ for $I=1/2$. Near threshold, quark interchange dominates the reactions near the critical temperature. The second kind is 2-to-1 meson-meson scattering with the process that a quark in an initial meson and an antiquark in another initial meson annihilate into a gluon and subsequently the gluon is absorbed by the other antiquark or quark. The transition potential for the process is derived. Four Feynman diagrams at tree level contribute to the 2-to-1 meson-meson scattering. Starting from the $S$-matrix element, the isospin-averaged unpolarized cross section with transition amplitudes is derived. The cross sections for $\pi \pi \to \rho$ and $\pi K \to K^*$ decrease with increasing temperature.

Solar and nuclear physics uncertainties in cosmic-ray propagation

Recent data released by the AMS experiment on the primary spectra and secondary-to-primary ratios in cosmic rays (CRs) can pose tight constraints to astrophysical models of CR acceleration and transport in the Galaxy, thereby providing a robust baseline of the astrophysical background for dark matter search via antimatter. However, models of CR propagation are affected by other important sources of uncertainties, notably from solar modulation and nuclear fragmentation, that cannot be improved with the sole use of the AMS data. The present work is aimed at assessing these uncertainties and their relevance in the interpretation of the new AMS data on the boron-to-carbon (B/C) ratio. Uncertainties from solar modulation are estimated using improved models of CR transport in the Heliosphere constrained against various type of measurements: monthly-resolved CR data collected by balloon-born or space missions, interstellar flux data from the Voyager-1 spacecraft, and counting rates from ground-based neutron monitor detectors. Uncertainties from nuclear fragmentation are estimated using semiempirical cross-section formulae constrained by measurements on isotopically-resolved and charge-changing reactions. We found that a proper data-driven treatment of solar modulation can guarantee the desired level of precision, in comparison with the improved accuracy of the recent data on the B/C ratio. On the other hand, nuclear uncertainties represent a serious limiting factor over a wide energy range. We therefore stress the need for establishing a dedicated program of cross-section measurements at the $\mathcal{O}$(100 GeV) energy scale.