Formula For Cross Section Research Articles

Possible sneutrino-pair signatures with R-parity breaking

If sneutrinos are the lightest supersymmetry partners and R-parity is not conserved, the process e +e − → tilde ν tilde ν can have striking signatures due to the decay modes tilde ν → ℓ +ℓ′ − or tilde ν → q q′ . We present cross section formulas and discuss event rates and detection at the upgraded e + e − collider LEP. Four-lepton signals should be detectable up to sneutrino mass m ̃ ν = 80 GeV and maybe beyond; four-jet signals should be detectable up to m ̃ ν = 70 GeV , but would probably be obscured thereafter by WW background.

Modeling transmission and scatter for photon beam attenuators

The development of treatment planning methods in radiation therapy requires dose calculation methods that are both accurate and general enough to provide a dose per unit monitor setting for a broad variety of fields and beam modifiers. The purpose of this work was to develop models for calculation of scatter and transmission for photon beam attenuators such as compensating filters, wedges, and block trays. The attenuation of the beam is calculated using a spectrum of the beam, and a correction factor based on attenuation measurements. Small angle coherent scatter and electron binding effects on scattering cross sections are considered by use of a correction factor. Quality changes in beam penetrability and energy fluence to dose conversion are modeled by use of the calculated primary beam spectrum after passage through the attenuator. The beam spectra are derived by the depth dose effective method, i.e., by minimizing the difference between measured and calculated depth dose distributions, where the calculated distributions are derived by superposing data from a database for monoenergetic photons. The attenuator scatter is integrated over the area viewed from the calculation point of view using first scatter theory. Calculations are simplified by replacing the energy and angular-dependent cross-section formulas with the forward scatter constant r2(0) and a set of parametrized correction functions. The set of corrections include functions for the Compton energy loss, scatter attenuation, and secondary bremsstrahlung production. The effect of charged particle contamination is bypassed by avoiding use of dmax for absolute dose calibrations. The results of the model are compared with scatter measurements in air for copper and lead filters and with dose to a water phantom for lead filters for 4 and 18 MV. For attenuated beams, downstream of the buildup region, the calculated results agree with measurements on the 1.5% level. The accuracy was slightly less in situations where the scatter component is very large, as for very large fields with very short filter to detector distances. The implementation of the model into treatment planning systems is discussed.

Observation of electromagnetic interactions of high energy muons deep underground.

The first experimental measurement of the spectrum of cascade showers produced by cosmic ray muon interactions deep underground in the transferred energy range 0.4--200 GeV has been performed by means of the NUSEX calorimeter at a depth of about 5000 hg/${\mathrm{cm}}^{2}$, the average muon energy being close to 360 GeV. The spectrum of energy transfers is in good agreement with calculations based on the commonly used theoretical formulas for muon interaction cross sections and on a conservative picture of the formation of muon energy spectrum at great depths. The present data do not confirm the deficit of the cross section at low energy transfers for the 1 TeV muon energy recently reported by the CCFR Collaboration. A possible explanation of the difference between the observed and the expected stochastic energy loss distributions presented by the CCFR group is discussed.

Possible pre-LEP200 SUSY threshold signals

If R-parity is not conserved, the SUSY-threshold production process e + e − → χ 1 0 χ 1 0 could be detectable with relatively low luminosity. Hence an interesting mass range for the lightest SUSY particle χ 1 0 could be explored at the CERN LEP collider during its intermediate energy development, even before the full LEP200 upgrade is completed. We present cross section formulas and discuss event rates and detection for the three distinct decay options: χ 1 0 → 2 charged leptons + neutrino, χ 1 0 → lepton + 2 quarks, and χ 1 0 → 3 quarks.

Electromagnetic scattering and absorption by finite wires

The scattering from a thin conducting wire is computed by representing the induced current as a sum of driven and resonant terms, the latter with complex propagation constant mk perturbed from its free space value k. Using Galerkin’s method, the central problem of determining m reduces to a minimization problem. For the limiting cases of highly conducting or highly absorbing wires simplifications are found. For short wires the Rayleigh cross sections are obtained; for longer wires with high absorption, accurate cross section formulas are constructed based on the unperturbed infinite wire currents. For general wire lengths and conductivities the method is computationally very simple and results are in excellent agreement with independent computations of both current and far field quantities, as well as experimental measurements.

L-resolved intercombination transitions in Rydberg atoms in collisions with electrons.

A systematic study of semiclassical and quantum cross sections of l-resolved intercombination transitions in Rydberg atoms due to collisions with fast electrons is performed in the Ochkur approximation for principal quantum numbers n\ensuremath{\le}15 and all possible orbital numbers l and changes \ensuremath{\Delta}l. The semiclassical approach provides reasonable estimates for cross sections over the angular-momentum range up to l\ensuremath{\sim}n/2. Intercombination transitions are shown to obey the ``Bethe rule'': at large l the transitions with n and l changing in the same direction dominate transitions with changes in opposite directions. It is also demonstrated that the more deeply inelastic the collision is, the higher the multipoles \ensuremath{\Delta}l that prevail in the total cross section. The semiclassical approach makes it possible to derive simple analytic formulas for cross sections with an explicit dependence on principal and orbital quantum numbers.

Neutrino-induced nuclear excitations.

We present an improved, compared to that of Belusevic and Rein, theoretical value of the cross section for the neutrino-induced nuclear excitation of iron. This result is based on a measurement of the photoabsorption cross section on the same nucleus, which can be related to the transverse part of the neutrino cross section via the conserved vector current hypothesis. The longitudinal part is related to the pion absorption cross section through the partial conservation of the axial-vector current, and thus reflects the spontaneous breaking of chiral symmetry. A general formula for the excitation cross section is derived, which is valid for both low and high incident neutrino energies. When caused by a weak neutral current, this process may play an important role in core-collapse supernovae. It can also be detected using low-temperature techniques with the purpose of cosmological and weak-interaction studies. A new estimate of the cross sections for neutrino-induced nonscaling processes described by Belusevic and Rein is discussed in the context of two experiments using iron targets, but at very different beam energies.

The triple regge limit of diffractive dissociation in deep inelastic scattering

We derive, within perturbative QCD, a formula for the inclusive cross section of the diffractive dissociation of the deep inelastic photon γ*+q→X+q in the triple Regge limits≫M 2≫Q 2≫Λ 2. We use the leading ln(s/M 2, ln(M 2/Q 2) approximation and derive an, expression for the triple Pomeron vertex. The Pomeron above this vertex is found to be of higher order than the BFKL Pomeron. The resulting formula for the cross section is infrared finite. We show that the Abramovsky-Gribov-Kanchelli cutting rules are satisfied, and we discuss implications for the Pomeron structure function.

An analytic calculation of the energy fluence spectrum of a linear accelerator

Calculation of photon dose by convolution methods requires a knowledge of the fluence spectrum of photons produced by the linear accelerator treatment head. But this spectrum is very difficult to measure accurately, and is often derived by Monte Carlo calculations modeling the elements of the treatment head. In this paper an analytic calculation technique and the corresponding computer tool for calculating the photon energy fluence spectral distribution at any point in a bremsstrahlung field are presented. Primary bremsstrahlung photon distributions are computed by modeling electron dispersion in layers in a thick target and using the thin target bremsstrahlung cross section formulas of Schiff. The first Compton scatter from all materials in a linear accelerator treatment head is computed analytically. Higher-order Compton scatter events and pair production annihilation photons are ignored, but the attenuation of both primary and first scattered photon fluence is computed. Predictions of the computer implementation of the model are compared to measurements of bremsstrahlung production in a thick target and to Monte Carlo calculations of the energy fluence emerging from a linear accelerator. Finally, the computer tool is used to investigate the source of collimator-dependent fluence fluctuations in air. In agreement with other measurements, the principal contribution to fluence outside the geometric field is found to be from scatter in the flattening filter.

Alignment and orientation for charge exchange in Li+-Na(3s, 3p) collisions: I. Differential and total cross sections

The alignment and orientation effects for charge exchange in 1-1.5 keV Li+-Na(3s, 3p) collisions are studied by semiclassical close-coupling calculations employing adiabatic molecular data and a common electron translation factor. The differential cross sections from Na(3s) to Li(2s) and Li(2p) are compared to experiment, a large orientation effect is predicted for charge exchange to Li(2p+or-1). From Na(3p) the charge exchange is important only to the Li(2p) channel, the corresponding alignment and orientation effects are calculated. The orientation effect follows the propensity rules. The formulae for total and differential cross sections for a transition from aligned p to p state or from oriented p to p state are derived. Two differential total cross sections for oriented p+or-1 to p+or-1 states can be defined, the same for aligned p+or-45 degrees to p+or-45 degrees states. The important role of the translation factor is discussed and a four state model is able to describe charge exchange from Na(3p) to Li(2p) at large impact parameters.

Inactivation cross section of ions for dry enzymes and viruses

In this note, a semi-empirical analytical formula for the inactivation cross section of ions for dry enzymes and viruses is developed based on the delta-ray theory of track structure. Using the experimental characteristic dose of gamma rays, the cross sections are calculated and compared with experimental results. The average ratio of the experimental to the calculated cross section is 0.96+or-0.17.

Implementation of the Doppler broadening of a Compton-scattered photon into the EGS4 code

A modification to the general-purpose Monte Carlo electron-photon transport code EGS4 [1] was made in order to include Doppler broadening of Compton-scattered photon energy due to electron pre-collision motion. The Compton-scattered photon energy is sampled from a cross section formula based on the Compton profile, and the Compton scattering is sustained if the energy imparted to the electron is less than its binding energy. The electron binding effect modifies the scattered photon energy, angular distribution, and total cross section of the Compton scattering, and affects the photon mean free path used in the calculations. In the improved EGS4 code, all of these electron binding effects in Compton scattering are treated consistently. A simulation of 40 keV photon scattering by C and Cu samples was performed using the improved EGS4 code; the calculated scattered photon spectra agreed well with the measurements.

Production ofK ?-mesons in proton-proton and proton-nucleus interactions at various energies

The experimental data on the production ofK−-mesons in pp-collisions are analyzed and a method of the unified description of these data in a broad energy range for primary protons is proposed. TheK−-mesons production in pA-collisions is considered. The simple formulas for inclusive cross sections of theK−-production in these collisions are given.

The antiproton-nuclei annihilation cross-section at the momentum range from 0.70 to 2.50 GeV/c

The results of the measurements of antiproton-nuclei annihilation cross-sections at the momentum range from 0.70 to 2.50 GeV/ c are presented. The A-dependence of the cross-sections is described by the formula σ 0 A α . The behavior of the parameters σ 0 and α indicates the possibility of Coulomb influence on the annihilation processes at low momenta. Comparison with the Glauber theory is carried out. The Coulomb corrections to the Glauber formula for the absorption cross-sections of hadrons by nuclei are calculated. The influence of the real part of the nuclear potential is taken into account. Calculations are made in the frame of the high-energy approach. A comparison with data of annihilation cross-sections of antiprotons on nuclei is made.

Molecular spectroscopy with light pulses of arbitrary pulse shape and field strength: A nonperturbative approach

We present a novel approach to molecular spectroscopy with light pulses of arbitrary strength and duration. The key quantity is the frequency-resolved net energy transfer dE/dω which reveals at which frequencies energy is transferred from the field to the molecule (absorption) or from the molecule to the field (stimulated emission). It is shown that dE/dω can be expressed as the Fourier transform of the cross-correlation function of the molecular polarization P(t) and the time derivative of the applied field, dℰ/dt. In this sense, it is formally equivalent to the absorption cross section under weak-field conditions which, as commonly known, can be represented as the Fourier transform of the autocorrelation function S(t). The time-dependent polarization P(t) is determined by exact integration of the time-dependent Schrödinger equation including the light-matter interaction to all orders. It is shown that under weak-field conditions the expression for dE/dω reduces to the well-known cross section formula in the time-dependent picture of spectroscopy, multiplied by the spectral intensity of the light pulse. Therefore, we consider the expression for the frequency-resolved energy transfer, which is valid for arbitrary electric fields, as the natural extension of the absorption cross section in the weak-field limit. Furthermore, dE/dω is shown to be formally equivalent to the change of the spectral intensity, ΔI(ω), of an optical pulse after transmission through a sample, the latter being derived by solving Maxwell’s equations under well-known approximations. The theory is applied to a simple one-dimensional model with two electronic states and the frequency-resolved energy transfer is investigated as a function of the field strength. For sufficiently strong fields, dE/dω exhibits transitions between essentially all vibrational levels in the ground and all states in the excited electronic manifold. The new expression distinguishes between absorption and emission and that is clearly seen in the spectra.

Light scattering cross-section - summing of Mie-series

Mie-series for cross-sections of light scattering from spherical particles are converted into integral form with a simple integrand. The transformation is due to essential compensations in the (electrically polarized) part of the Mie cross-section.A new approximate formula for cross-sections is obtained, having a wide region of validity, overlapping with that of van de Hulst's formula.

Postmortem validation of the automated coronary analyis (ACA) software package

Goal of this study was to compare the quantitative coronary arteriographic (QCA) results obtained with the Philips DCI/ACA analytical software package with those from postmortem casts in an animal experimental setting. Standard digital coronary arteriograms were obtained from 6 mongrel dogs. After the imaging procedure, the dogs were sacrificed and casts were made of the coronary trees by filling the vessels with a mixture of radio-opaque barium and silicone gel at a fixed pressure of 100 mmHg. Vessel diameters were measured from the digital arteriograms at a total of 118 selected locations with the ACA package. Thin slices were cut from the casts at these same measurement locations and the areas of the cross sections were obtained by manual tracing of the outline of each slice in an approximately 40 x magnified image. From these cross-sectional areas, cast diameters were derived using the formula for circular cross-sections. Cast diameters ranged in size from 0.69 to 3.30 mm. The systematic error between the measurements was found to be 0.058 mm; (p < 0.015) and the standard deviation of the signed difference 0.255 mm; the correlation coefficient was r = 0.91. The largest error sources are supposed to be the slight differences in the selection of identical positions in the X-ray images and on the casts, and the 'out-of-plane' magnification for a number of vessel locations. This postmortem study demonstrates that the diameters of coronary vessels can be measured from digital arteriograms with the DCI/ACA package with a high degree of accuracy and precision.

Principal value resummation

We present a new resummation formula for the Drell-Yan cross section. The formal resummation of threshold corrections in Drell-Yan hard-scattering functions produces an exponent with singularities from the infrared pole of the QCD running coupling. Our reformulation treats such “infrared renormalons” by a principal value prescription, analogous to a modified Borel transform. The resulting expression includes all large threshold corrections to the hard-scattering function as an asymptotic series in α s, but is a finite function of Q 2. We find that the ambiguities of the resummed perturbation theory imply the presence of higher twist corrections to quark-antiquark hard-scattering functions that begin at ʌ QCD /Q . This suggests an important role for higher twist in the phenomenology of hadron-hadron inclusive cross sections. We also discuss the numerical evaluation of the exponent and its asymptotic perturbation series for representative values of Q 2.

Hadronic diffractive cross sections and the rise of the total cross section.

A model for high-energy hadronic cross sections is proposed. It is based on Regge theory and perturbative QCD, and includes soft and hard mechanisms as well as diffractive processes. The validity range of Regge-pole theory in the description of total, elastic, single-, and double-diffractive cross sections is investigated and inconsistencies found already at CERN LHC and/or SSC energies. Examining unitarity constraints, modifications of the cross section formulas are proposed which allow a continued use of formulas in the Regge spirit to describe elastic and diffractive events. The nondiffractive cross section is allowed to rise at a rate consistent with unitarization of multiple parton-parton scatterings. However, in our picture, the rise of the total cross section with increasing energy is only partly due to the minijet cross sections; the diffractive topologies rise as well. Fully differential distributions are given and convenient parametrizations derived for the integrated rates of elastic and diffractive events. Predictions for the various partial cross sections at Fermilab Tevatron, LHC, and SSC energies are given and compared to other estimates.

Photodetachment cross section of H- in crossed electric and magnetic fields. I. Closed-orbit theory.

In this, the first of two papers, we obtain a simple analytic formula for the photodetachment cross section of ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ in crossed electric and magnetic fields. The three-dimensional semiclassical approximation predicts oscillations in the spectrum and these oscillations are correlated with closed classical orbits. In the following paper [A. D. Peters and J. B. Delos, Phys. Rev. A 47, 3036 (1993)] we derive fully-quantum-mechanical formulas for the cross section in perpendicular electric and magnetic fields and show how these results can be reduced to the semiclassical results of this paper.