Born Cross Section Research Articles

Electron-impact ionization cross section of rubidium

A theoretical model for electron-impact ionization cross section has been applied to Rb and the theoretical cross section (from the threshold to 1 keV in incident energy) is in good agreement with the recent experimental data obtained using Rb atoms trapped in a magneto-optical trap. The theoretical model, called the binary-encounter--dipole (BED) model, combines a modified Mott cross section with the high-energy behavior of Born cross sections. To obtain the continuum dipole oscillator strength $df/dE$ of the $5s$ electron required in the BED model, we used Dirac-Fock continuum wave functions with a core polarization potential that reproduced the known position of the Cooper minimum in the photoionization cross section. For inner-shell ionization, we used a simpler version of $df/dE$, which retained the hydrogenic shape. The contributions of the $4\stackrel{\ensuremath{\rightarrow}}{p}4d$, $5s$, and $5p$ autoionizing excitations were estimated using the plane-wave Born approximation. As a by-product, we also present the dipole oscillator strengths for the $5\stackrel{\ensuremath{\rightarrow}}{s}{\mathrm{np}}_{1/2}$ and $5\stackrel{\ensuremath{\rightarrow}}{s}{\mathrm{np}}_{3/2}$ transitions for high principal quantum numbers $n$ near the ionization threshold obtained from the Dirac-Fock wave functions with the same core polarization potential as that used for the continuum wave functions.

Mott scattering in strong laser fields

Qualitative and quantitative results of a complete relativistic calculation of the $S$-matrix transition amplitudes and first Born cross sections for the Mott scattering of an electron in the presence of an ultraintense single-mode laser field are compared in detail to a spinless and a nonrelativistic treatment. The role of the fermion character of the electron leading to spin-orbit and spin-laser interactions is discussed depending on the laser intensity and on the incoming electron kinetic energy. The differences between radiative transfer spectra of the electron energy in the relativistic and nonrelativistic regimes are addressed.

Multiple Gluon Effects in $q+\bar{q}\rightarrow t+\bar{t}+X$ at FNAL Energies: Semi-Analytical Results

We apply our Yennie–Frautschi–Suura exponentiated cross-section formulas for the parton process [Formula: see text] to the process [Formula: see text] at FNAL energies, where G is a QCD gluon. We use semi-analytical methods to compute the ratio [Formula: see text], where [Formula: see text] is our soft gluon YFS exponentiated cross-section and [Formula: see text] is the Born cross-section. For mt=0.176(0.199) TeV, we get r expt =1.65(1.48), respectively, for q=u for example. We show that these parton level results, when properly synthesized with the DGLAP structure function evolution, lead to the conclusion that the YFS exponentiated hadron level cross-section for [Formula: see text] is increased by ~0.6–0.8% beyond the Born cross-section due to the re-summation of soft gluon effects beyond those in the exact [Formula: see text] correction when mt=176 GeV. These results are not inconsistent with the recent observations by CDF and D0.

Small angle Bhabha scattering at LEP1. Wide-narrow angular acceptance

Analytical method is applied for description of the small angle Bhabha scattering at LEP1. Inclusive event selection for asymmetrical wide-narrow circular detectors is considered. The QED correction to the Born cross-section is calculated with leading and next-to-leading accuracy in the second order of perturbation theory and with leading one --- in the third order. All contributions in the second order due to photonic radiative corrections and pair production are calculated starting from essential Feynman diagrams. The third order correction is computed by means of electron structure function. Numerical results illustrate the analytical calculsations.

Gluonic three-jet cross section in hadron collisions at O(α4 s ) with cone jet definition

The next-to-leading order three-jet cross section in hadron collisions is calculated in the simplified case, when the matrix elements of all QCD subprocesses are approximated by the pure gluon matrix element. The cone jet definition is used. Distribution of the three-jet invariant mass distribution is compared with experimental data obtained at the TEVATRON. The important property of reduced renormalization and factorization scale dependence of the next-to-leading order physical cross sections as compared to the Born cross section is demonstrated.

Calorimeter event selection for small-angle Bhabha scattering at LEP1

An analytical method is applied for description of calorimeter event selection in small-angle electron-positron scattering at LEP1. The selections CALO1 and CALO2 are investigated specifically. The first-order correction to the Born cross section is given in the case of wide-narrow angular acceptance.

Three-Jet Cross Section in Hadron Collisions at Next-to-Leading Order: Pure Gluon Processes.

The next-to-leading order three-jet cross section in hadron collisions is calculated in the simplified case when the matrix elements of all QCD subprocesses are approximated by the pure gluon matrix element. The longitudinally-invariant $k_\perp$ jet-clustering algorithm is used. The important property of reduced renormalization and factorization scale dependence of the next-to-leading order physical cross section as compared to the Born cross section is demonstrated.

Electron-impact vibrational excitation of water molecules

Cross sections (differential and integral) for the electron-impact vibrational excitation of H2O are calculated at the collision energies 6-50 eV. Excitation of the three fundamental modes of vibration, (100), (010) and (001), is considered separately. The calculation is based on the rotationally sudden and a vibrationally close-coupling method taking an ab initio electrostatic potential. The effects of electron exchange and target polarization are taken into account approximately. The resulting cross sections are compared with the experimental data available. A comparison is also made with the Born cross section, which is often cited in experimental papers. Qualitatively, the present differential cross sections well reproduce the experimental data, particularly the angular dependence of the cross section. Quantitatively, on the other hand, there are some disagreements between the present calculation and the experimental data.

QCD corrections to Higgs boson production: Nonleading terms in the heavy quark limit.

We compute analytic results for the QCD corrections to Higgs boson production via gluon fusion in hadronic collisions in the limit in which the top quark is much heavier than the Higgs boson. The first non-leading corrections of $\O(\alpha_s^3 \mh^2/m_t^2)$ are given and numerical results presented for both LHC and SSC energies. We confirm earlier numerical results showing that the dominant corrections have the same mass dependence as the Born cross section.

Fast electron scattering from Rydberg states of Na

Inelastic cross sections for fast electrons scattered from Na atom targets prepared in the 30s Rydberg level are calculated in the Born plane wave approximation. The resulting cross sections for the dominant dipole transitions are in good agreement with a recent experiment and with an earlier semiclassical version of the Born approximation. Cross sections for dipole-forbidden transitions are also computed and are found to be a few orders of magnitude smaller than the corresponding dipole-allowed cross sections for incident electron velocities from 80 to 200 times the mean orbital speed of the target electron. Variations of the Born cross sections with target quantum defect are also investigated systematically by comparison with the corresponding transitions using hydrogen atom wavefunctions.

High energy approximations for the total Born cross section for pair production in a screened Coulomb field.

We derive the high energy limit of the momentum distribution associated with the total Born approximation cross section for pair production in a static screened Coulomb field. This high energy distribution is free of the ``large'' terms which appear in the exact momentum distribution and cancel leaving a remainder of relative order (m/k${)}^{2}$, the cancellation having been performed analytically. (k is the incident photon energy, m the electron rest mass.) The high energy distribution is used to derive the total pair production cross section both for an unscreened Coulomb field and in the limit of complete screening, and the results are compared with expressions given in the literature. It is shown that the largest corrections to the high energy limit of the total cross section [of relative orders (2m/k${)}^{2}$${\mathrm{ln}}^{3}$(2k/m) and (2m/k${)}^{2}$${\mathrm{ln}}^{2}$(2k/m)] are independent of screening, and these are given analytically.

Electroweak radiative corrections to high-energy Compton scattering

The Compton scattering cross section with arbitrary electron and photon polarizations is calculated within the electroweak standard model including the complete O(α) virtual and soft-photonic radiative corrections for centre-of-mass energies in the GeV and TeV region. While the weak corrections are negligible for energies below the masses of the electroweak gauge bosons, they are of the order of 10% and 1% above the Z threshold for left- and right-handed electrons, respectively. The dominant contributions are due to Feynman diagrams involving non-abelian gauge couplings, which vanish for right-handed electrons. Finally the results for the unpolarized Born cross sections of e − γ → W − ν e, e −Z, e − γ and the radiative corrections to the latter two processes are compared.

Vibrational effects on cross sections for elastic scattering of X-rays and fast electrons by H 2O molecules

Waller-Hartree and first Born cross sections for the elastic scattering of X-rays and fast electrons by H 2O are calculated for 80 geometries of the H 2O molecule using self-consistent-field electronic wave functions of good quality. The cross sections are then averaged over the five lowest vibrational states with wave functions calculated using the discrete variable representation. The differences between the vibrationally averaged cross sections and their equilibrium counterparts are less than 1.3% and 3% for X-ray and electron scattering respectively. The effects are greater in states with a stretch excited than a bend.

Electron-impact excitation of the Rb 7 (2)S1/2, 8 (2)S1/2, 5 (2)D3/2, and 6 (2)D3/2 states.

Electron-impact cross sections for excitation of the 7 $^{2}$${\mathit{S}}_{1/2}$, 8 $^{2}$${\mathit{S}}_{1/2}$, 5 $^{2}$${\mathit{D}}_{3/2}$, and 6 $^{2}$${\mathit{D}}_{3/2}$ states of rubidium have been measured from threshold to 1000 eV. The optical-excitation-function method has been employed in a crossed atom- and electron-beam apparatus. Relative, total (cascade including) experimental cross sections are made absolute by comparison with the known total cross section of the Rb D1 line. Total excitation cross sections are compared with theoretical calculations employing first Born approximation and theoretical branching ratios. Born cross sections for the 7 $^{2}$${\mathit{S}}_{1/2}$ and 8 $^{2}$${\mathit{S}}_{1/2}$ states are obtained from the literature, while Born cross sections for the 5 $^{2}$${\mathit{D}}_{3/2}$, 6 $^{2}$${\mathit{D}}_{3/2}$, and all cascading states are calculated in this paper. At high energies, the measured total $^{2}$${\mathit{D}}_{3/2}$ state cross sections show 1/E behavior and converge to first Born theory; for Eg100 eV, experiment and theory agree within 6.7% for 5 $^{2}$${\mathit{D}}_{3/2}$ and within 3.7% for 6 $^{2}$${\mathit{D}}_{3/2}$. The total cross sections for the $^{2}$${\mathit{S}}_{1/2}$ states do not converge to Born theory even at 1000 eV, and it is shown that this cannot be attributed to cascading. At low energies, $^{2}$${\mathit{S}}_{1/2}$ and $^{2}$${\mathit{D}}_{3/2}$ state total excitation cross sections have similar shapes with sharply peaked maxima at about 0.9 eV above threshold. After cascading is corrected using first Born theory, estimated experimental cross sections for direct excitation of higher fine-structure states of rubidium are given.

Second-order Born cross sections for positronium formation in positron-hydrogen collisions.

The second-order Born cross sections of positronium formation are calculated for positron-hydrogen collisions in the energy region below 100 eV and compared with the recent measurement of Sperber et al. [Phys. Rev. Lett. 68, 3690 (1992)]. Better agreement is achieved above 25 eV than other existing theoretical values including elaborate close-coupling calculations. This result implies that continuum states that are not taken into account fully in other theoretical calculations are contributing significantly to positronium formation through a second-order process.

Heavy-quark correlations in hadron collisions at next-to-leading order

We present a calculation of the fully exclusive parton cross sections for heavy-quark production at order O( α S 3) in QCD. Our result includes the Born cross section for producing a Q Q pair, of order O( α S 2), the virtual corrections to the Born cross section, of order O( α S 3), and the cross section for producing a Q Q pair plus a light parton, of order O( α S 3). We can therefore compute distributions in which correlations among the heavy quarks (and, if present, the associated jet) are correctly taken into account up to order O( α S 3). We present some applications of phenomenological interest to top, bottom and charm production at hadron colliders.

E +e − annihilation into heavy fermion pairs at high-energy colliders

We discuss the process e + e − → f f in the zero-width approximation for massive fermions which is complete at the electroweak 1-loop level. We present a detailed calculation of the electroweak loop diagrams in the massive fermion case. The formulae are applicable to the standard fermion production including a heavy top but also to heavy fermions of a possible next generation. Specific results are given for e + e − → t t in the standard model. Compared to the Born cross section the typical size of the weak corrections is about 10% if the top is light and has a wide range depending on the Higgs boson mass if the top is heavy. In particular close to threshold the influence of virtual Higgs bosons is quite significant for heavy top quarks with large Yukawa couplings culminating in weak corrections of the order of 40% if the Higgs is light. We also include QED corrections for the massive case complete in the virtual 1-loop part and in the soft-photon approximation for the real photon part.

Electron-positron pair production in relativistic heavy-ion collisions.

First-order Born cross sections for electron-positron pair production in relativistic heavy-ion collisions are calculated. Sommerfeld-Maue wave functions are employed to describe the continuum state of the emitted electron and positron in the field of the heavy target nucleus. Double-differential, single-differential, and total cross sections are presented in a wide energy regime from 1 GeV/u up to 20 TeV/u. We compare our results with first-Born calculations using a partial-wave expansion and with lowest-order QED calculations. The target-charge dependence is investigated.

Exact second-order Born calculations for relativistic electron capture.

Second-order Born cross sections for electron capture in relativistic collisions have been calculated without further approximations for a large number of projectile-target combinations and energies. Within the regime of high-Z target atoms and energies of a few GeV/u, the exactly evaluated cross sections are considerably larger than first-order cross sections, which already overestimate the experimental results. This shows that the Born expansion is not a suitable perturbation series in the charge and energy regime considered. At the same time it is demonstrated that previous evaluations using peaking approximations and \ensuremath{\alpha}Z expansions are in error by more than an order of magnitude. For p+H collisions the differential cross section exhibits a peak at the classical relativistic Thomas angle.

Second Born approximation for relativistic electron capture: Exact Monte Carlo calculations forC6+-Au andAr18+-Ag collisions

The second-order Oppenheimer-Brinkman-Kramers approximation for relativistic electron capture is formulated, and rigorously calculated K-K cross sections are presented for the first time. Theoretical cross sections for electron capture in collisions of ${\mathrm{C}}^{6+}$-Au at 400 MeV/u and ${\mathrm{Ar}}^{18+}$-Ag at 400 and 1050 MeV/u projectile energy are compared with the experimental data and other approximate second Born results. It is shown that exact second Born cross sections grossly overestimate the experimental data.