Ratio Of Differential Cross Sections Research Articles

The hydrogen exchange reaction: Discrepancies between experimental state-resolved differential cross sections and 3-D quantun dynamics

Measured time-of-flight (TOF) distributions, corresponding to speed- and angle-resolved differential cross sections for the reaction D + H2 > HD + H, are compared with recently published 3-D quantum calculations. The comparison is made in the man- ner least susceptible to distortion: the energy-, angle- and state-resolved theoretical results in center-of-mass (c.m.) coordinates are projected onto the laboratory angle-time axis, and averaged over all experimental resolution parameters to predict the mea- sured TOF distributions. Features directly visible in the experimental data are: (1) relative populations of the v 1 = 0 and v 1 = 1 product vibrational states, (2) the extent of HD product rotational excitation, and (3) the ratio of differential cross sections near 180 ° c.m. to those near 70° c.m. Significant discrepancies with theory are found with respect to features (2) and (3).

Electron-impact excitation of the normal vibrational modes of NH3 in the intermediate region (12–50 eV)

Electron-impact excitation of the normal vibrational modes of NH3 in its ground electronic state has been studied by electron-energy-loss spectroscopy in the 12–50 eV impact energy range out of resonances. At 25 and 50 eV the differential cross sections (in arbitrary units) for the elastic scattering process and for the vibrationally inelastic v=0→1 transitions have been measured at various scattering angles ranging from 8° to 60°. The ratio of the vibrational differential cross sections to the elastic one, reported as a function of the impact energy, indicates that for energies above 10 eV, the vibrational excitation occurs mainly through a direct mechanism. At 50 eV the angular shape of the cross sections is strongly dependent on the specific normal mode excited. The ν2 differential cross section is forward peaked, whereas that of ν4 is isotropic. The differential cross section of ν1,3 composite has a minimum at 30°. At 25 eV the angular behavior of the differential cross sections is roughly similar for all the normal modes with a minimum at 30°, but the values (in arbitrary units) below and above 30° are quite different for each normal mode.

Electron scattering by atomic hydrogen

Close-coupling calculations that include the continuum and higher discrete states by two different methods, optical potentials and pseudostates, are found to be in fair agreement with existing absolute measurements of elastic and inelastic differential and total cross sections for electron-hydrogen scattering at 54.4, 100 and 200 eV. For elastic scattering the calculations essentially agree in absolute magnitude but differ from the experiments by 10 to 20% at different energies. Calculated values are too low for larger-angle inelastic scattering at 100 and 200 eV but agree for smaller angles. A new experiment and a very detailed coupled-channels-optical calculation have been performed in an effort to resolve the discrepancies. The experiment measures accurate ratios of differential cross sections for inelastic (n=2) and elastic scattering of electrons by atomic hydrogen at several scattering angles at 100 and 200 eV.

A-dependence of η-meson inclusive production at 10.5 GeV/ c

The experimental results are presented for ratios of ν-meson inclusive differential cross sections in 10.5 GeV/ c π +p, π +D and π +A collisions, R D/p=(d σ/d x F)( π + D→ ηX)/ (d σ/d x F ) π +p→ ηX), R A=(d σ/d x F)( π +D→ ηX) in the beam fragmentation region. The results are based on the statistics of ≈ 5 × 10 4 detected η → 2 γ decays. It is shown that the power α in the parametrisation R A ≈ A α( xf) does not change significantly with x F and its mean value is 0.50±0.02. The lower limit is obtained for the effective coefficient with string tension in the colour string model, κ ⩾ 3 GeV/fm. The observed growth of R A with x F can be explained by an assumption of a neutron halo with the factor H ≈ 4 in the nuclei.

Iteration wave function for describing the (e, 2e) spectrum of the helium atom

The wave function of the ground state of the helium atom is derived by the variational-iteration technique with the Hylleraas-Eckart momentum representation of the wave function as a first approximation. This function is used to calculate the ratios of the differential cross sections σ(n=2)/σ(n=1) and σ(2p)/σ(2s) for helium ionized by an electron impact. The calculation is conducted in the plane-wave impulse approximation for symmetric noncoplanar kinematics of the (e, 2e) process. The results are compared with previous calculations in which variational wave functions of the configurational interaction type were used. Good agreement with the existing experimental data for σ(n=2)/σ(n=1) is obtained. The results are generalized to helium ions.

Photon scattering from 206Pb.

Differential cross sections for the elastic scattering of tagged, monochromatic photons have been measured on a separated target of /sup 206/Pb between 12 and 30 MeV. The interpretation of these data implies that the total photoabsorption cross section in the region of the giant dipole resonance of /sup 206/Pb is nearly identical to that of /sup 208/Pb, except shifted slightly higher in energy. Fore-to-aft ratios of differential cross sections are ambiguous as to the existence of a giant quadrupole resonance between 20 and 30 MeV. This ambiguity is due in part to the influence of poorly known exchange effects and in part to uncertainties in the Delbrueck amplitude. Upper limits are placed on the relative photon-decay branch of the giant dipole resonance and isovector giant quadrupole resonance to the lowest 2/sup +/ and 3/sup -/ states, respectively. These limits are well above those predicted by current models for the coupling of giant resonances to surface vibrations.

A measurement of the n-p 180/90 degree cross section ratio at 65 and 50 MeV

Abstract A measurement of the 180° to 90° n-p differential cross section ratio is of interest because recent data from Louvain in the range 45 to 65 MeV showed a larger ratio than earlier data from Harwell and U.C. Davis. Here we use large area scintillation detectors to cover the range 5° to 30° (lab) and 40° to 46°. A ΔE - δE telescope covers the O° to 2° range. Position sensitive wire chambers cover the angular range of all three detectors, allowing a range of cross sections to be measured at the same time. The experimental arrangements, analysis and partial results to date are presented.

Precision test of QED by direct comparison of e+e− → γγ and e+e− → e+e− at 29 GeV

The ratio of differential cross sections for the reactions e + e − → γγ and e + e − → e + e − is measured at s = 29 GeV in the central polar angle region, |cos θ| < 0.55, and compared to the same ratio calculated by QED to order α 3. The ratio of these ratios, integrated over this angular region, is 1.007±0.009±0.008, demonstrating excellent agreement between theory and experiment. The 95% confidence limits on the QED cut-off parameters for the γγ final state are Λ + > 59 GeV and Λ - > 59 GeV.

Scaling of differential cross-section in high energy proton-helium scattering

Possible occurrence of scaling of differential cross-section for high energy hadronnucleus elastic scattering is demonstrated takingp-4He scattering as an example and using three well-known scaling variables proposed earlier for hadron-hadron scattering. The available data on differential cross-section ratio betweenE lab=45 and 393 GeV are found to scale in all the three variables reasonably well and the positions of the dip and the secondary maximum are found to follow the predicted patterns of behaviour as a function of energy. Extrapolating the fits to the available slope-parameter data onto higher energies and using the scaling curves, the positions of the dip and the secondary maximum and the differential cross-section ratio as a function of |t| are predicted for higher energies.

Elastic and inelastic scattering of uranium ions by holmium, gold, and bismuth targets.

Angular distributions for elastic scattering of /sup 238/U ions by /sup 165/Ho, /sup 197/Au, and /sup 209/Bi at 2380 MeV have been obtained in a 2..pi.. geometry using solid state nuclear track detectors. The angular distributions of the elastic differential cross section ratios sigma/sub el/(expt.)/sigma(Ruth) are analyzed using (a) the generalized Fresnel model and (b) the parametrized S-matrix method. Quarter-point angles obtained are converted to reaction parameters such as grazing angular momenta, interaction radii, and total reaction cross sections. Values of inelastic total reaction cross sections were obtained by directly counting the three-, four-, and five-prong events along with the two-prong inelastic events as observed in the 2..pi.. geometry. Experimental total reaction cross sections are compared with optical and sharp cutoff model calculations. There is good agreement among the total reaction cross sections evaluated from elastic and inelastic data as well as with model calculations.

Neutron density difference measurements for 26,24Mg and 36,34,32S using low-energy pions

The elastic scattering differential cross-section ratios of 36S/ 32S, 34S/ 32S and 26Mg/ 24Mg have been measured with 48.4 MeV and 43.9 MeV negative pions, respectively, using magnetic spectrometers. The data are analysed with optical potential calculations, using a Fourier-Bessel description for the neutron density of the heavier isotope. Neutron density and rms radius differences between the isotopes are determined and compared to shell-model calculations, and show reasonable agreement.

Elastic scattering of electrons from CO2in the intermediate energy range

Ratios of elastic differential cross sections of CO2 to those of N2 have been measured at electron impact energies of 500, 800 and 1000 eV in the angular range of 5 degrees to 120 degrees , using a crossed electron-beam-molecular-beam geometry and the relative flow technique. These ratios have been multiplied by previously known N2 elastic differential cross sections to obtain elastic differential cross sections for CO2. At 500 eV, the authors' experimental results agree quite well with the absolute values of Bromberg (1974). Comparison has also been made with the theoretical results obtained in the renormalised multicentre potential model approach of Botelho et al. and shows an agreement within 20% in the entire angular range. The elastic integral and momentum transfer cross sections have also been determined from the differential cross sections.

The helium (e, 2e) satellite spectrum

Two configuration-interaction-type wavefunctions each accounting for = 98% of the ground-state correlation energy in helium have been used to predict the differential (e, 2e) cross-section ratio leading to either the n = 2 or the n = 1 final ion states of helium. The findings are compared with known experimental data and two previous theoretical calculations. The predicted ratios using the various wavefunctions are in reasonable agreement with one another and with experiment up to q = 2.0 au. Thereafter, the dispersion for various wavefunctions increases significantly. Furthermore, the differential cross-section ratio for populating the He + (2p) to He + (2s) final ion states differ by an order of magnitude for correlated wavefunctions of equal quality in ground-state-energy terms. A reformation of the electron-impact cross-section theory beyond the plane-wave impulse approximation with the use of non-configuration-interaction-type correlated functions is required to assist the resolution of this problem.

Elastic scattering of electrons from SO2

Using a crossed electron beam–molecular beam scattering geometry and the relative-flow technique, ratios of elastic differential cross sections of SO2 to those of He have been measured at electron impact energies of 12, 20, 50, 100, 150, and 200 eV. At each energy, an angular range of 15° to 150° has been covered. These ratios have been multiplied by previously known He elastic differential cross sections to obtain elastic differential cross sections for SO2. From a knowledge of differential cross sections, integral and momentum transfer cross sections have been determined. Using the two-potential theory of e-molecule scattering, calculations were also performed and compared with the measurements.

Differential cross sections for elastic scattering of electrons by CH4in the energy range of 3 to 20 eV

Differential, integral and momentum transfer cross sections have been determined for the elastic scattering of electrons by CH4. With the help of a crossed electron beam, molecular beam apparatus using the relative flow technique, the ratios of the elastic differential cross sections (DCS) of CH4 to those of He were measured at electron impact energies of 3, 5, 6, 7.5, 9, 10, 15, and 20 eV for scattering angles from 30 to 140 degrees . From the ratios, the absolute DCS were determined by utilising the known DCS of He. Because pure rotational excitation could not be resolved, the elastic DCS are the sum of elastic and pure rotational excitations at room temperature. Integral and momentum transfer cross sections were calculated from the DCS. The CH4 DCS are similar in size and in angular behaviour to those of Ar at impact energies below 7.5 eV, and also agree approximately with a close-coupling calculation for electron scattering from polyatomic molecules. A broad maximum in the integral and momentum transfer cross sections is located at 7.5 eV. The angular distributions at energies up to about 7.5 eV are characteristic of a d-wave type of resonance.

Convergent polynomial expansion, scaling of differential cross-section and computation of scaling functions for elastic diffraction scattering processes

Existing data on the differential cross-section ratio at high energies for pp,\(\bar p\)p, π±p andK ±p scatering have been fitted by the proposed convergent polynomial expansion to determine the unknown coefficients in the scaling function. It is found that the data are very well represented within and somewhat outside the peak regions by only four or five terms in the proposed series in terms of Laguerre polynomials.

Measurement of the ratio of total and differential cross sections on neutrons and protons for charged-current neutrino events

Charged-current neutrino interactions have been analysed in a sample of pictures from BEBC equipped with a TST. Using a method independent of both the neutrino flux and nuclear interaction corrections, the ratio R= σ n/ σ p has been measured. The result is R=1.98±0.19 for the ratio of total cross sections. Bjorken x distributions for proton and neutron targets and for u and d quarks are compared.

The (e,2e) satellite spectrum of helium

A simple configuration interaction type wavefunction developed by Taylor and Parr (1952) has been used to predict the differential (e,2e) cross section ratio leading to the n=2 excited state or to the n=1 ground state of the helium ion. The cross section results obtained in the plane-wave impulse approximation for ion recoil momentum values in the range q, 0-3 au are in very good agreement with experiment and with an earlier theoretical finding using a more sophisticated correlated function. At higher q values however there are significant differences in the calculated cross section ratio using the two correlated functions. Furthermore, the calculated sigma (2p)/ sigma (2s) cross section ratio is strongly dependent upon the function used. Cross section data for the process leading to the 3s final state of helium are also presented. This work provides further information towards evaluating the sensitivity of the (e,2e) technique to discriminate between different wavefunctions.

Angular correlation measurements for the electron-excited 31P state of helium

Angular correlations between the scattered electrons resulting from the 11S-31P excitation process in helium and the photons emitted in the decay of the 31P state to the ground state have been measured. Data have been obtained at incident electron energies of 34.6, 45.6 and 75.6 eV for electron scattering angles up to 35 degrees . Analysis of the data gives the ratio of differential cross sections for excitation of the degenerate magnetic sublevels of the state, the magnitude of the phase difference between the corresponding excitation amplitudes and the Fano-Macek orientation and alignment parameters. Reasonable agreement is obtained between the present data at 45.6 and 75.6 eV and the original data of Eminyan et al. (1975) at 50 and 80 eV respectively. Even at these small scattering angles, no theoretical work yields values for these fundamental parameters in agreement with experiment.

Convergent polynomial expansion, energy dependence of slope parameters, scaling hypothesis and predictions forπ ± p andK + p scattering

A phenomenological representation for differential cross-section recently proposed using Mandelstam analyticity and convergent polynomial expansion (CPE) which has been found to be successful in describing scaling of the differential cross-section-ratio data for several elastic diffractive and inelastic nondiffractive processes is used to analyse the energy dependence of the slope-parameter data at high energies, extrapolate the slope parameter and predict the differential cross-section ratio as a function of |t| at higher energies forπ ± pndK + p scattering. Following the method of Hansen and Krisch it is found that, in spite of the existence of rather widely varying data points for nearbys values, a more systematic trend in the energy dependence of the slope parameter emerges when a statistical average of the existing high-energy data is used. Extrapolating the fits to the average data ontos → ∞ provides strong evidence in favour of a model-independent result that asymptotically theπ ± p slopes may be equal. There is also a strong indication to the effect that each of these two slopes may be equal to theK + p slope fors → ∞. Using the scaling curves generated by the existing data on differential cross-section ratio and extrapolated values of the slope parameter, the differential cross-section ratio for each of the three processes is predicted as a function of |t| for higher energies.