Formula For Cross Section Research Articles

Interatomic Coulombic electron capture beyond the virtual photon approximation.

Via the interatomic Coulombic electron capture (ICEC) process, an electron can be captured by an atom or a molecule, while the binding and excess energy is transferred, via a long-range Coulomb interaction, to a neighboring atom or molecule. The transferred energy can be used to ionize or electronically excite the neighboring species. When the two species are asymptotically far apart, an analytical formula for the ICEC cross sections can be derived. The latter can then be estimated using only the energies and the photoionization cross sections of each species. In this work, we develop an analytical model that allows us to predict the ICEC cross sections when the size of the involved species is comparable to the distance between the two entities. Using abinitio R-matrix results for various systems, we show that the new model reduces the error of the asymptotic formula by two orders of magnitude on average while only using parameters that can be taken from the properties of each species.

Resonance ionization spectroscopy of neodymium for determining a highly efficient two-step ionization scheme

Two-color two-step resonance ionization spectroscopy of neodymium (Nd) was performed to identify more than 120 even-parity autoionizing levels and their candidate J-values. The analysis of the observed autoionizing Rydberg series yielded a value of 44,560.11 (43)stat (2)sys cm−1 as a more accurate ionization potential of Nd. The saturation method was used to measure the transition cross-sections for some intense ionization transitions. From the measured cross-sections, the ionization efficiencies of some two-step ionization schemes were evaluated using the scheme cross-section formula to obtain several promising schemes.

Analytical formula for the cross section of hadron production from e + e − collisions around the narrow charmouinum resonances

The paper reports an analytical formula for the production cross section of e + e − annihilation to hadrons in the vicinity of a narrow resonance, particularly in the τ-charm region, while considering initial state radiation. Despite some approximations in its derivation, comparison between the analytical formula and direct integration of ISR shows good accuracy, indicating that the analytical formula meets current experimental requirements. Furthermore, this paper presents a comparison of the cross section between the analytical formula and calculations using the ConExc Monte Carlo generator. The efficiency of the analytical formula in significantly reducing computing time makes it a favorable choice for the regression procedure to extract the parameters of narrow charmonium resonances in experiments.

Semi-empirical cross-section formulas for electron-impact ionization and rate coefficient calculations

We propose a semi-empirical formula for the cross section of ionization by electron impact. The formula involves adjustable parameters which are determined by comparison with measured or numerically calculated cross sections. In the latter case, the ions are perturbed by their environment which is a high-density plasma. As a consequence, the cross section is significantly modified. We investigate Be-like carbon, nitrogen and oxygen as well as aluminum ions. We also show that the formula is well-suited for interpolation and extrapolation. Knowing the cross section, we calculate the rate coefficient within the Boltzmann and Fermi–Dirac statistics. In the first case, the rate can be calculated analytically. In the second one, it can be expressed in terms of special functions, but the numerical evaluation is more convenient while providing accurate results. Our results are compared to experiment and to other calculations.

Systematic analysis of (n,3He) reaction cross sections at 14–15 MeV

Numerous research endeavours have delved into comprehending the dynamics of the (n,3He) reaction cross sections. In this study, a novel and straightforward empirical formula is put forth, aimed at swiftly computing the cross sections of the (n,3He) reaction in the neutron energy range of 14–15 MeV. This new formula has been obtained using outcomes from pre-existing cross section formulas in conjunction with experimental data. The present formulation, hinging on the interplay of A23 parameter, threshold energy (Eth) and incident neutron energy (En) factors, appears to furnish a satisfactory methodology for elucidating the cross sections of the neutron-induced (n,3He) nuclear reaction at 14–15 MeV. Finally, in this paper, a comparison is made between the results of the empirical formula and the experiment.

Analytical formula for multiple ionization cross sections of rare gas atoms by electron and positron impact

Analytical formula for multiple ionization cross sections of rare gas atoms by electron and positron impact

K-X rays induced by helium-like C ions in thick target atoms of different metals

The physical process and experimental phenomena of the interaction between highly charged heavy ions and atoms are very complex, particularly in the intermediate energy region, because of the limitation of accelerator and existing theoretical analysis, less systematic researches, incomplete atomic data, and not so high accuracy. The research of celestial element X-ray data is more scarce and the research of X-ray data of celestial elements is even more scarce. Helium-like C ions with 15–55 MeV kinetic energy provided by the HI-13 MV series accelerator of the China Institute of Atomic Energy are used to bombard Fe, Ni, Nb and Mo thick targets. The HpGe detectors are used to measure the K-X ray emission, and the corresponding K-X ray emission cross sections are obtained. Due to the different ionization degrees of the shell layers of various target atoms, the branching intensity ratio of K<sub><i>β</i> </sub>to K<sub><i>α</i></sub> X rays emitted by Helium-like C ions interacting with Fe and Ni target atoms decreases with the increase of the kinetic energy of the incident ions, while the branching intensity ratio of K-X rays emitted by Nb and Mo target atoms does not change significantly. The K-X ray emission cross section of target atom is calculated by using the formula of thick target cross section, and compared with the results of different theoretical models and proton. The results show that with the increase of the kinetic energy of helium-like C ions, the total emission cross section of the K<sub><i>β</i> </sub>and K<sub><i>α</i></sub> X ray emitted from Fe and Ni target atoms are most consistent with the BEA correction model considering multiple ionization, and the total emission cross section of K<sub><i>β</i> </sub>and K<sub><i>α</i></sub> X ray emitted from Nb and Mo target atoms are closest to the theoretical values of PWBA model. When the energy of proton is the same as that of single nucleon C ion, the cross section of K-X ray produced by proton is about three orders of magnitude smaller than that produced by helium-like C ion.

Estimating the efficiency and purityfor detecting annihilation and promptphotons for positronium imagingwith J-PET using toy Monte Carlosimulation

The positronium imaging technique represents a potential enhancement of the PET imaging method. Its core principle involves employing a β<sup>+</sup> radiation source that emits additional gamma (γ) quanta referred to as prompt gamma. Our aim is to evaluate the capability to differentiate between annihilation and prompt gamma emissions, a vital aspect of positronium imaging. For this purpose, the selected isotopes should enable high efficiency and purity in detecting both prompt gamma and annihilation gamma. The assessment of the efficiency in identifying prompt and annihilation photons for various isotopes, which are potentially superior candidates for <i>β<sup>+</sup></i> + γ emitters, is conducted through toy Monte-Carlo simulation utilizing the cross-section formula for photon-electron scattering. In this article, we have performed calculations for efficiency and purity values across different isotopes under ideal conditions and examined how these values evolve as we incorporate the fractional energy resolution into the analysis. Ultimately, the primary goal is to determine the energy threshold that optimizes both efficiency and purity, striking a balance between accurately identifying and recording events of interest while minimizing contamination from undesired events.

Empirical formula for (n, f) reaction cross sections of Uranium isotopes at 1–20 MeV neutrons

This article describes how to calculate neutron-induced fission reaction cross sections using a proposed empirical formula and the EMPIRE 3.2.3 and TALYS 1.95 computer codes for Uranium isotopes up to the third fission plateau. In this study, the excitation functions of 232U (n, f), 233U (n, f), 234U (n, f), 235U (n, f), 236U (n, f), 237U (n, f) and 238U (n, f) nuclear reactions were calculated at 1–20 MeV neutron energies. The results were contrasted to measured values from the Experimental Nuclear Reaction Data (EXFOR) as well as the evaluated data from Evaluated Nuclear Data File (ENDF) such as (EAF-2010, JEFF-3.3, ENDF/B-VIII.0 and TENDL-2019). Overall, the calculated, experimental, and evaluated fission cross-sections are in concordance.

The empirical coupled-channel model with the new analytical penetration formula for fusion cross-sections

The new analytical barrier penetration formula proposed by Li et al. [Int. J. Mod. Phys. E 19 (2010) 359] for potential barriers containing a long-range Coulomb interaction is adopted in the empirical coupled-channel (ECC) model for calculating fusion cross-sections. As compared with the Hill–Wheeler (HW) formula based on the parabolic approximation, this formula is more appropriate for the barrier penetration with incident energies much lower than the Coulomb barrier. The calculated results show that the ECC model with the new barrier penetration formula can describe the fusion cross-section data well, especially for light systems at energies much lower than the Coulomb barrier. Then the systematics of the difference between the ECC calculation with the new penetration formula and that with the HW formula is investigated. The results show that the difference between the results with the HW formula and the new penetration formula is less than one order of magnitude at [Formula: see text].

Systematic study of fusion barriers with energy dependent barrier radius

Considering energy dependence of the barrier radius in heavy-ion fusion reactions, a modified Siwek-Wilczyński (MSW) fusion cross section formula is proposed. With the MSW formula, the fusion barrier parameters for 367 reaction systems are systematically extracted, based on 443 datasets of measured cross sections. We find that the fusion excitation functions for about 60% reaction systems can be better described by introducing the energy dependence of the barrier radius which is due to the dynamical effects at energies near and below the barrier. Considering both the influence of the geometry radii and that of the reduced de Broglie wavelength of the colliding nuclei, the barrier heights are well reproduced with only one model parameter. The extracted barrier radius parameters linearly decrease with the effective fissility parameter, and the width of the barrier distribution relates to the barrier height, as well as the reduced de Broglie wavelength at energies around the Coulomb barrier.

A study of proton-induced reactions on natural Silicon targets

Experimental excitation functions of isotopes produced in reactions p + natSi are compared with the results of nuclear reaction program TALYS 1.95 and semi-empirical cross section formulas. We consider excitation functions of 7 isotopes (28Mg, 26Al, 24,22Na, 18F and 10,7Be) produced in reactions at bombarding energies of 20-144 MeV. They are compared with the predictions of the code TALYS 1.95, the semi-empirical formulas of Silberberg-Tsao (code yieldx) and SPACS. Comparisons of the results of the code TALYS 1.95 and previously published results of code ALICE are made. The predictive power of code TALYS 1.95 may be questioned for reaction products with mass number very much smaller than the target and of semi-empirical formulas at lower energies.

Electron impact ionization in the icy Galilean satellites’ atmospheres

Electron impact ionization is critical in producing the ionospheres on many planetary bodies and, as discussed here, is critical for interpreting spacecraft and telescopic observations of the tenuous atmospheres of the icy Galilean satellites of Jupiter (Europa, Ganymede, and Callisto), which form an interesting planetary system. Fortunately, laboratory measurements, extrapolated by theoretical models, were developed and published over a number of years by K. Becker and colleagues (see Deutsch et al. in Adv At Mol Opt Phys 57:87–155, 2009) to provide accurate electron impact ionization cross sections for atoms and molecules, which are crucial to correctly interpret these measurements. Because of their relevance for the Jovian icy satellites, we provide useful fits to the complex, semiempirical Deutsch–Märk formula for energy-dependent electron impact ionization cross sections of gas-phase water products (i.e., H $$_2$$ O, H $$_2$$ , O $$_2$$ , H, O). These are then used with measurements of the thermal plasma in the Jovian magnetosphere to produce ionization rates for comparison with solar photo-ionization rates at the icy Galilean satellites.

17.9 MeV’lik Enerjide (p,α) Tesir Kesiti Verileri üzerine Sistematik Bir İnceleme

Nuclear cross section data are needed in various applications such as radiation therapy, astrophysics, radioisotope production, fusion and fission. The systematics play a very important role in determining cross sections on neutron- and proton-induced reactions at incoming energies of which there are no experimental values. So, empirical systematics have been extensively used at present in the studies on cross section calculations. In this paper, we proposed empirical cross section formulas considering Q–value dependence on (p,α) reactions at proton energy of 17.9 MeV. The present formulas including Coulomb and odd-even effects are based on the statistical theory. In addition, these formulas are a modification to the Levkovskii’s original asymmetry parameter formulas for neutron induced reactions and the Tel et al.’s empirical formulas for proton reactions. Fitting parameters of formulas were determined by least-squares fitting to experimental excitation function data. It is seen that new empirical formulas give good fits with (p,α) experimental cross section values in the literature at 17.9 MeV.

Isotopic production cross sections in proton-16O and proton-12C interactions for energies from 10 MeV/u to 100 GeV/u

Proton interactions with16O or 12C nuclei are frequent nuclear interaction leading to secondary radiation in tissues for space radiationandcancer therapy with protons or ion beams. The fragmentation of these ionsby protons produces a large number of heavy ion (A > 4) target or projectile fragments often with high ionization density. Here we develop an analytical model of energy dependent proton-16O and proton-12C cross sections for isotopic nuclei production. Using experimental data and a 2nd order optical modelan accurate formula for the absorption cross section from <10 MeV/u to >10 GeV/u is obtained. The energy dependence of theelemental and isotopiccross sections is modeled as multiplicities scaled toabsorption cross section with average isotopic fractions estimated from experimental data. We show that this approach results in accurateanalytic formulae for isotopic fragmentation cross sections over the full energy range in hadron therapy and space radiation protection studies.

Dissociation cross sections of large-momentum charmonia with light mesons in hadronic matter

Momenta of charmonia created in Pb-Pb collisions at the Large Hadron Collider are so large that three or more mesons may be produced when the charmonia collide with light mesons in hadronic matter. We study the meson-charmonium collision in a mechanism where the collision produces two quarks and two antiquarks, the charm quark then fragmenting into charmed mesons, and the other three constituents as well as quarks and antiquarks created from vacuum give rise to two or more mesons. The absolute square of the transition amplitude for the production of two quarks and two antiquarks is derived from the $S$-matrix element, and cross-section formulas are derived from the absolute square of the transition amplitude and charm-quark fragmentation functions. With a temperature-dependent quark potential, we calculate unpolarized cross sections for inclusive $D^+$, $D^0$, $D^+_s$, or $D^{*+}$ production in scattering of charmonia by $\pi$, $\rho$, $K$, or $K^\ast$ mesons. At low center-of-mass energies of the charmonium and the light meson, the cross sections are very small. At high energies the cross sections have obvious temperature dependence, and are comparable to peak cross sections of two-to-two meson-charmonium reactions.

Empirical Description of Isotope Production in 0.01-2.5GeV p+natFe Reactions

Experimental excitation functions of isotopes produced in reactions are compared with the results of empirical cross section formulas. We consider excitation functions of 16 isotopes (36Cl, 38Ar, 42,43K, 44Ti, 46,47,48Sc, 48,51Cr, 52Fe, 52,54Mn and 55,56,57Co) produced in reactions at bombarding energies from threshold up to 2.6 GeV. They are compared with the predictions of the empirical formulas of Rudstam, Silberberg-Tsao and SPACS. In the middle-energy range, the formulas provide (in the stated order) a progressively improved description of the experimental excitation functions of the dominant isotopes. At the highest energies, the limiting values of the dominant excitation functions are well described by the EPAX formula (Version 2.1). The predictive power of these formulas could be questioned at low energies close to the threshold, reaction products with a mass much smaller than the target and possibly low cross section channels.

(d, 3n) Reaction cross-section calculation of some reactor materials

Nuclear reactions with charged particles have applications in many fields such as radioisotope production, industrial applications, astrophysics, etc. Therefore, examining the excitation functions performed and obtained by the activation technique is also important for understanding the nature of nuclear reactions. Also, it is especially necessary to study these reactions to estimate the effects of radiation damage on the fusion structural materials used in the construction of the first walls and core of the reactor. In this study, cross-section data have been calculated theoretically to 45Sc (d, 3n)44Ti, 63Cu (d, 3n)62Zn, 89Y (d, 3n)88Zr, and 100Mo (d, 3n)99Tc reactions in the range of 1–50 MeV energy via ALICE/ASH, TALYS 1.95 and Empire 3.2.2 nuclear reaction codes. Optical Model Parameters (OMP) calculation for deuteron-induced reaction results has been performed via TALYS 1.95 code and the calculated cross-section values are reproduced well. Also, empirically developed (d, 3n) cross section formula (Kavun, 2020) calculations have been performed at 20 MeV energy. Finally, experimental EXFOR data was compared with all results and were found to be compatible with each other.

New derivation of the twist-3 gluon fragmentation contribution to polarized hyperon production

A novel method of formulating the twist-3 gluon fragmentation function contribution to hyperon polarization in the proton-proton collision is presented. The method employs a covariant gauge and takes full advantage of the Ward-Takahashi identities before performing the collinear expansion. It provides a robust way of constructing the general cross section formula and also a clear understanding for the absence of the ghostlike terms in the twist-3 cross section in the leading order with respect to the QCD coupling constant.

Calculating the Atomic electron impact Ionization Cross Section for some elements

Inner-shell ionization cross section (ICS) by electron impact are of interest not only to the basic collision physics for complex atoms, but also to various practical applications in material science and electron microscopy. Theoretical difficulties in the past were between the threshold and the peak, which occur usually four to five times the threshold energy. Theories based on classical mechanics are somewhat better than on Born cross section, but such theories usually requires adjustable parameters. We used the Gryzinski formalism to calculate atomic electron impact ionization cross sections for the elements (Fe, Co, Mn, Ti, Zn, and Nb). Good to satisfactory agreement was found for all atoms with the exception of (Nb), where the distance between our cross section and Deutsch-Mark formula become larger at the high values of the overvoltage (U). Moreover, when compared to other to available ionization cross sections for these atoms, calculated using other methods and semiempirical formula, the Gryzinski formalism achieved a level of agreement with experimental data that is as good better than the predictions from the other methods.