Formula For Cross Section Research Articles

Ionization of nS, nP, and nD lithium, potassium, and cesium Rydberg atoms by blackbody radiation

The results of theoretical calculations of the blackbody ionization rates of lithium, potassium, and cesium atoms residing in Rydberg states are presented. The calculations are performed for nS, nP, and nD states in a wide range of principal quantum numbers, n = 8−65, for blackbody radiation temperatures T = 77, 300, and 600 K. The calculations are performed using the known quasi-classical formulas for the photoionization cross sections and for the radial matrix elements of transitions in the discrete spectrum. The effect of the blackbody-radiation-induced population redistribution between Rydberg states on the blackbody ionization rates measured under laboratory conditions is quantitatively analyzed. Simple analytical formulas that approximate the numerical results and that can be used to estimate the blackbody ionization rates of Rydberg atoms are presented. For the S series of lithium, the rate of population of high-lying Rydberg levels by blackbody radiation is found to anomalously behave as a function of n. This anomaly is similar to the occurrence of the Cooper minimum in the discrete spectrum.

Ionization of heavy ions in relativistic collisions with neutral atoms

The problem of ionization of ions in ion-ion and ion-neutral relativistic collisions is considered. Formulas for ionization cross sections are derived in the Born approximation in terms of the momentum transfer without allowance for magnetic interactions. Using these formulas implemented in the LOSS-R code, the ionization cross sections are calculated for the K shells of neutral atoms colliding with protons and also for 1s and 2p electrons of multiply charged heavy ions (nuclear charge Z = 80−90) colliding with bare nuclei and neutral atoms. The calculation results are compared with experimental data and calculations of other authors.

Erratum: Improved analysis of black hole formation in high-energy particle collisions [Phys. Rev. D71, 104028 (2005)

We investigate formation of an apparent horizon (AH) in high-energy particle collisions in four- and higher-dimensional general relativity, motivated by TeV-scale gravity scenarios. The goal is to estimate the prefactor in the geometric cross section formula for the black hole production. We numerically construct AHs on the future light cone of the collision plane. Since this slice lies to the future of the slice used previously by Eardley and Giddings (gr-qc/0201034) and by one of us and Nambu (gr-qc/0209003), we are able to improve the prefactor estimates. The black hole production cross section increases by 40-70% in the higher-dimensional cases, indicating larger black hole production rates in future-planned accelerators than previously estimated. We also determine the mass and the angular momentum of the final black hole state, as allowed by the area theorem.

A New Comparison of Empirical and Semi-empirical Formulae for the (n, 3He) Reaction Cross-sections at 14–15 MeV

New empirical and semi-empirical formulae have been suggested for the (n, 3He) reaction cross-sections with dependent on asymmetry parameter, S = (N − Z)/A. The (n, 3He) reaction cross-sections at the energy of 14–15 MeV have been investigated for two different parameters groups by the classification of nuclei into 31 ≤ A ≤ 103 and 133 ≤ A ≤ 181. The obtained results have been compared with the other systematics and experimental data for the (n, 3He) reaction cross-sections. Some improvement has been got in describing the (n, 3He) reaction cross-sections compared with the existing relations.

Calculation of 14–15 MeV (n, d) Reaction Cross Sections Using Newly Evaluated Empirical and Semi-empirical Systematics

In this study, we have investigated the asymmetry term effect for the (n, d) reaction cross sections at 14–15 neutron incident energy. It has been discussed the odd–even effect and the pairing effect considering binding energy systematic of the nuclear shell model for the new experimental data and new cross section formulae developed by Tel et al. for (n, d) reactions. We have determined different parameter groups by the classification of nuclei into even–even, even–odd and odd–even for (n, d) reactions cross sections. The obtained empirical and semi-empirical formulae by fitting two parameters for (n, d) reactions were given. By using the new cross sections formulae for (n, d) reactions the obtained results have been discussed and compared with the available experimental data.

Double Ionization of H−Ions by Electron Impact in the Solar Atmosphere

The double ionization of H− ions by the generalized Lorentzian distribution of electrons in the solar atmosphere is investigated. The Born-Bethe formula for the multielectron ionization cross section is employed in order to obtain the double-ionization rate for H− as a function of the spectral index and thermal energy. It is shown that the double-ionization rates of H− are greater in non-Maxwellian plasmas than in Maxwellian plasmas in the low-temperature region. It is also shown that the nonthermal character of the solar plasma increases the double-ionization rates of H− in the solar photosphere and chromosphere. In addition, we found that the double-ionization rates of H− in the solar photosphere and chromosphere increase with increasing the plasma temperature. It is also shown that the high-energy corrections enhance the double-ionization rates in non-Maxwellian plasmas, and that the high-energy corrections on the double-ionization rate increase with increasing the plasma temperature.

Nonthermal effects on multielectron ionization processes in Lorentzian plasmas

The nonthermal effects on multielectron ionization by electron impact are investigated in generalized Lorentzian distribution plasmas. The Born-Bethe-type formula for the multielectron ionization cross section is employed in order to obtain the multiple-ionization rate as a function of the spectral index, ionization degree, and thermal energy. It is found that the ionization rate increases with an increase of the nonthermal character of the plasma. It is also found that the ionization rate increases with an increase of the plasma temperature. In addition, it is shown that the thermalization of the plasma strongly suppresses the multiple-ionization process.

Surface polaritons of small coated cylinders illuminated by normal incident TM and TE plane waves

The surface polariton properties of TM or TE plane wave scattered by a coated cylinder are investigated in this paper. The coated cylinder (whose outer radius is much smaller than the wavelength) is assumed to be electrically small and low dissipative. Analytical formulas of the plasmonic resonances are derived and found to agree well with those obtained from exact expressions in the classical scattering theory. The behaviors of the scattering coefficients at resonances are also discussed and compared for different cases. While a single cylinder has the resonance at the relative permittivity of epsilon(r) = -1 (or relative permeability of mu(r) = -1) for the TE (or TM) polarization, the resonances of the coated cylinders change with different n values (where n denotes the series term or mode of the field), and also the inner and outer radii. It is shown that the scattered field in the near zone can be enhanced significantly compared to the incident wave. For the TE incident case, we take a silver coated nano-cylinder as an example to illuminate the near-field optical effect. Also, we have studied the peak values of the nth order scattered field for different n values and electrical parameter k0b (where k0 is the wavenumber of the free space and b denotes the outer radius of the cylinder) around the cylinder. The derived new formulas for total cross sections are given and they may provide us with some potential photonic applications such as surface cleaning and etching.

Charged current cross section for massive cosmological neutrinos impinging on radioactive nuclei

We discuss the cross section formula for both massless and massive neutrinos on stable and radioactive nuclei. The latter could be of interest for the detection of cosmological neutrinos whose observation is one of the main challenges of modern cosmology. We analyse the signal-to-background ratio as a function of the ratio mν/Δ, i.e. the neutrino mass over the detector resolution and show that an energy resolution Δ ⩽ 0.5 eV would be required for sub-eV neutrino masses, independently of the gravitational neutrino clustering. Finally, we mention the non-resonant character of neutrino capture on radioactive nuclei.

Open system of interacting fermions: Statistical properties of cross sections and fluctuations

Statistical properties of cross sections are studied for an open system of interacting fermions. The description is based on the effective non-Hermitian Hamiltonian that accounts for the existence of open decay channels preserving the unitarity of the scattering matrix. The intrinsic interaction is modeled by the two-body random ensemble of variable strength. In particular, the crossover region from isolated to overlapping resonances accompanied by the effect of the width redistribution creating superradiant and trapped states is studied in detail. The important observables, such as average cross section, its fluctuations, autocorrelation functions of the cross section, and scattering matrix, are very sensitive to the coupling of the intrinsic states to the continuum around the crossover. A detailed comparison is made of our results with standard predictions of statistical theory of cross sections, such as the Hauser-Feshbach formula for the average cross section and Ericson theory of fluctuations and correlations of cross sections. Strong deviations are found in the crossover region, along with the dependence on intrinsic interactions and the degree of chaos inside the system.

The second-order S-matrix element for the elastic scattering of photons by K-shell bound electrons: the nonrelativistic limit

The right expressions of the nonrelativistic K-shell Rayleigh scattering amplitudes and cross-sections are obtained by using the Coulomb Green's function method. Our analytical result does not have the spurious poles that occur in the old nonrelativistic result with retardation (Gavrila and Costescu 1970 Phys. Rev. A 2 1752). Starting from the expression of the second-order S-matrix element for the case of the elastic scattering of photons by K-shell bound electrons, we obtain the correct nonrelativistic Rayleigh angular distribution (valid for photon energies ω up to αZm) by removing the relativistic higher order terms in αZ and ω/m. The imaginary part of the Rayleigh amplitudes is obtained for any scattering angles in a closed form in terms of elementary functions. Thereby a simple formula for the exact nonrelativistic photoeffect total cross-section is obtained via the optical theorem, giving significantly better predictions than Fischer's nonrelativistic photoeffect formula. Comparing the predictions given by our formulae with the full relativistic numerical calculations of Kissel et al (Phys. Rev. 1980 A 22 1970), and with experimental results, a fairly good agreement within 10% is found for the angular distribution of Rayleigh scattering for photon energies up to 200 keV and both below and above the first resonance.

Effects of Accelerator-Driven Transmutation System on Radiotoxicity of High-Level Radioactive Wastes

We have developed a computation tool, WAste COMposition (WACOM) for performing a scoping study of the effects of the accelerator-driven transmutation of waste (ATW) system with a lead-bismuth-eutectic-cooled transmuter on actinide inventory and radiotoxicity reduction. WACOM consists of a simplified burnup model for a chain of 18 actinide isotopes and a fuel cycle model to evaluate high-level waste (HLW) generation from the reference ATW plant. Interpolation formulas for effective one-group cross sections as a function of the actinide mass fraction have been developed. Three kinds of HLW generation were considered: (a) HLW from uranium separation for light water reactor (LWR) spent fuel, (b) HLW from the partitioning process in multicycle ATW operation, and (c) the last core of the transmuter at the decommissioning of the ATW system. The latter two HLW sources resulting from multicycle ATW operation have been found to be greater than the first source. Potential benefits of ATW deployment have been found to be (a) reduction of the total actinide toxicity by a factor of 48 at the time of waste generation and (b) conversion of the actinide mixture into a more proliferation-resistant configuration, by effective transmutation of 239Pu, 241Am, and 237Np included in the LWR spent fuel. The total actinide radiotoxicity further decreases to 1/260 for the time period of 100 000 yr, which would improve the performance of the Yucca Mountain Repository.

Neutrino-electron scattering in a magnetic field with allowance for polarizations of electrons

We present an analytic formula for differential cross section (DCS) of neutrino-electron scattering (NES) in a magnetic field (MF) with allowance for longitudinal polarizations of initial and final electrons (IAFE). The DCS of NES in a MF is sensitive to the spin variable of the IAFE and to the direction of the incident and scattered neutrinos (IASN) momenta. Spin asymmetries and field effects in NES in a MF enable us to use initial electrons having a left-hand circular polarization (LHCP) as polarized electron targets in detectors for detection of low-energy neutrinos or relic neutrinos and for distinguishing neutrino flavor (NF). In general, gas consisting of only electrons having a LHCP and gas consisting of only electrons having a right-hand circular polarization (RHCP) are heated by neutrinos asymmetrically. The asymmetry of heating (AH) is sensitive to NF, MF strength, energies (Landau quantum numbers and third components of the momenta) of IAFE, final electron chemical potential, the final temperature of gas consisting of only electrons having a LHCP (RHCP), polar angles of IASN momenta, the difference between the azimuthal angles of IASN momenta, the angle {phi}, and IASN energies. In the heating process of electrons by neutrinos the dominant role belongs tomore » electron neutrinos compared with the contribution of muon (tauon) neutrinos. Electrons having a LHCP in NES in a MF are heated by {nu}{sub e} and {nu}{sub {mu}}({nu}{sub {tau}}) unequally when both the IASN fly along or against the MF direction. For magnetars and neutrinos of 1 MeV energy, within the considered kinematics, the AH in an electron neutrino-electron scattering is 2.23 times that in a muon neutrino-electron scattering or in a tauon neutrino-electron scattering.« less

Antineutrino–electron scattering in a magnetic field with allowance for polarizations of electrons

We present analytic formula for the differential cross section (DCS) of the antineutrino–electron scattering (AES) in a magnetic field (MF) with allowance for the longitudinal polarizations of the initial and final electrons, analyze polarization effects and show possible applications of the obtained results. The DCS of AES in MF is sensitive to the spin variable of the initial and final electrons and to the direction of the incident and scattered antineutrinos. Spin asymmetries and field effects in AES in MF enable us to use initial electrons with right-hand circular polarization (RHCP) as polarized electron targets in detectors for detection of antineutrinos of low energy or relic antineutrinos, and for distinguishing antineutrino flavour. In general, the gas consisting of the electrons having a left-hand circular polarization (LHCP) and the gas consisting of the electrons having RHCP are heated by antineutrinos asymmetrically. The asymmetry of heating is sensitive to the antineutrino flavour. In the heating process of electrons by antineutrinos the dominant role belongs to electron antineutrinos compared with the contribution of muon (tauon) antineutrinos. In AES in a MF, electrons with LHCP are heated by , and equally when both the initial and final antineutrinos fly along or against MF direction. Electrons with RHCP in AES in a MF are heated by and unequally when both the initial and final antineutrinos fly along or against MF direction.

Present status of radiation interaction with DNA–strand-break cross-section and fragment-size distributions

A cross-section formula for single strand brakes via radiation in the DNA molecule is reviewed and discussed, showing that it describes well-existing data for a wide range of linear energy transfer (LET). Recently published DNA fragment-size distributions (FSDs) data, obtained by irradiation of plasmids with electrons and neutrons, are presented. These results are analyzed and interpreted on the basis of a model developed by the Sao Paulo group, in which by introducing a long-range correlation among the jumps in a random walk, a power-law function is obtained for the probability distribution. The power-law exponent is a function of both the correlation potential and the degree of freedom of the system. It is shown that plasmidial DNA behaves as a nonextensive system, with FSDs described by power laws but not by exponential functions (as in extensive statistics). A pronounced crossover for electron-irradiation data and a change from 1 to 3 in the degree of freedom for neutron irradiation at a high dose were observed. A likely interpretation for these two features is presented and discussed. Perspectives for further developments in this area are presented and addressed.

Master formula for twist-3 soft-gluon-pole mechanism to single transverse-spin asymmetry

Abstract Perturbative QCD relates the single transverse-spin asymmetries (SSAs) for hard processes at large transverse-momentum of produced particle to partonic matrix elements that describe interference between scattering from a coherent quark–gluon pair and from a single quark, generated through twist-3 quark–gluon correlations inside a hadron. When the coherent gluon is soft at the gluonic poles, its coupling to partonic subprocess can be systematically disentangled, so that the relevant interfering amplitude can be derived entirely from the Born diagrams for the scattering from a single quark. We establish a new formula that represents the exact rules to derive the SSA due to soft-gluon poles from the knowledge of the twist-2 cross-section formula for unpolarized processes. This single master formula is applicable to a range of processes like Drell–Yan and direct-photon production, and semi-inclusive deep inelastic scattering, and is also useful to manifest the gauge invariance of the results.

A universal algorithm for calculating the backscattering factor in Auger-electron spectroscopy

We describe a universal Monte Carlo algorithm that can be used for the efficient calculation of backscattering factors (BFs) for quantitative Auger-electron spectroscopy (AES). This algorithm makes use of the continuous slowing-down approximation and the electron stopping power instead of simulation of individual inelastic-scattering events. This approach is attractive because it can be applied to any material with an empirical formula for the stopping power, available data for differential elastic-scattering cross sections, and an empirical formula for inner-shell ionization cross sections. We report BFs for the Si KL 23L 23, Cu L 3M 45M 45, Ag M 5N 45N 45, and Au M 5N 67N 67 Auger transitions in the corresponding elemental solids. These BFs were calculated for normal incidence of the primary beam, primary energies from near threshold for ionization of the relevant core levels to 20 keV, and Auger-electron emission angles of 10°, 60°, and 80°. We found satisfactory agreement between these BFs and values obtained from a more accurate algorithm in which individual inelastic-scattering events were simulated. Percentage deviations between BFs from the two algorithms were <2% for Au, <5% for Ag, <7% for Cu, and <10% for Si for primary energies likely to be used in practical AES. These deviations arise mainly from our use of stopping powers from the empirical formula rather than more reliable values calculated from experimental optical data.

Twist-3 formalism for single transverse spin asymmetry reexamined: Semi-inclusive deep inelastic scattering

We study the single spin asymmetry (SSA) for the pion production in semi-inclusive deep inelastic scattering, e p ↑ → e π X , in the framework of the collinear factorization. We derive the complete cross section formula associated with the twist-3 quark–gluon correlation functions for the transversely polarized nucleon, including all types of pole (hard-pole, soft-fermion-pole and soft-gluon-pole) contributions which produce the strong interaction phase necessary for SSA. We prove that the partonic hard part from each pole contribution satisfies certain constraints from Ward identities for color gauge invariance. We demonstrate that the use of these new constraints is crucial to reorganize the collinear expansion of the Feynman diagrams into manifestly gauge-invariant form so as to obtain the factorization formula for the cross section in terms of a complete set of the twist-3 distributions without any double counting. It also provides a simpler method for the actual calculation. We also present a simple estimate of SSA based on our cross section formula, using a model for the “soft-gluon-pole function” that represents the relevant twist-3 quark–gluon correlation, and compare the magnitude of the terms involving the derivative of the soft-gluon-pole function with that of the “nonderivative” terms.

Semi-empirical systematics of (n, 3He) reaction cross-section at 14.6 and 20 MeV

A new semi-empirical formula for the evaluation of (n, 3He) reaction cross-sections at the energy of 14.6 and 20 MeV is presented. Formula was derived using the analytical expression for the evaluation of the 3He spectrum within the frame of pre-equilibrium exciton model. The systematics obtained is compared with the empirical formula for the (n, 3He) reaction cross-section.

INVESTIGATION OF THE NEUTRALINO PAIR PRODUCTION AT LHC

In this article, we investigate the Drell–Yan process of the light neutralino pair [Formula: see text] (i,j = 1,2) productions at proton-proton collisions and we present the general formulae for the differential cross sections. We conduct an extensive examination of the dependence of the total cross section of the subprocesses [Formula: see text] on the beam energy, on the mass of the squarks and also on the M2 gaugino for the three extremely different scenarios. For all three cases, the outcomes are as follows: The dependence of the total cross section of the subprocesses [Formula: see text] on the beam energy is dominated by one of the subprocesses, [Formula: see text]. On the other hand, the dependence of the total cross section of the subprocesses [Formula: see text] on the mass of the squarks is dominated by one of the subprocesses, [Formula: see text]. We derive there from that our findings may lead to new insights relating to experimental investigations and these dependencies may be used as bases of an experimental research for the neutralino pair at LHC.