Small-angle Peak Research Articles

Small-angle maxima and cation-cation distances. Differences between iron nitrate and perchlorate solutions

X-ray diffraction data of aqueous solutions of iron(III) nitrate show a small-angle peak at an s value of about 0.5–0.9 A−1. A constant relationship between peak position and concentration leads to reject the hypothesis of a quasi-lattice structure for the solutions investigated. On the contrary, no peak is present in the same s range of diffraction data of iron (III) perchlorate solutions.

Factorized distorted-wave approximation for the (e, 2e) reaction on atoms: Coplanar symmetric

The coplanar symmetric ($e, 2e$) cross section has been studied in the intermediate-energy region for the valence states of the inert gases He, Ar, and Ne. Experimental measurements at 200, 400, 800, and 1200 eV for He, and at 400, 800, and 1200 eV for Ne and Ar, are compared with calculations based on the factorized half-off-shell distorted-wave impulse approximation. Calculations are carried out using partial-wave-expanded optical-model wave functions which describe elastic scattering for the distorted waves, the eikonal approximation, and the plane-wave approximation. The latter two significantly overestimate the cross sections at small angles and the valence $s$-orbital cross section relative to the valence $p$-orbital one. They also predict the small-angle peak in the $p$-orbital cross section to be at an angle significantly smaller than is observed. Of the two, the eikonal approximation provides the better description of the data. The full calculation, on the other hand, underestimates the cross sections at small angles and the cross section for the more tightly bound $s$-orbital relative to the small-angle $p$-orbital cross section. It also underestimates the ratio of the large- to small-angle peak heights in the $p$-orbital cross section. All three approximations improve as the energy is increased. The full calculation shows that the factorized distorted-wave impulse approximation cannot provide an adequate description of the reaction.

Factorized distorted-wave approximation for the (e, 2e) reaction on atoms: Noncoplanar symmetric

The coplanar symmetric (e,2e) cross section has been studied in the intermediate-energy region for the valence states of the inert gases He, Ar, and Ne. Experimental measurements at 200, 400, 800, and 1200 eV for He, and at 400, 800, and 1200 eV for Ne and Ar, are compared with calculations based on the factorized half-off-shell distorted-wave impulse approximation. Calculations are carried out using partial-wave-expanded optical-model wave functions which describe elastic scattering for the distorted waves, the eikonal approximation, and the plane-wave approximation. The latter two significantly overestimate the cross sections at small angles and the valence s-orbital cross section relative to the valence p-orbital one. They also predict the small-angle peak in the p-orbital cross section to be at an angle significantly smaller than is observed. Of the two, the eikonal approximation provides the better description of the data. The full calculation, on the other hand, underestimates the cross sections at small angles and the cross section for the more tightly bound s-orbital relative to the small-angle p-orbital cross section. It also underestimates the ratio of the large- to small-angle peak heights in the p-orbital cross section. All three approximations improve as the energy is increased. The full calculationmore » shows that the factorized distorted-wave impulse approximation cannot provide an adequate description of the reaction.« less

Saturation of high-energy forward elastic amplitudes with an infinite-resonance model

In this paper we discuss the possibility that the elastic amplitudes in the asymptotically large energy domain could be dominated by the exchange of an infinite set of resonances in the direct channel. A few examples are presented suggesting that this infinite-resonance model can very easily, but not uniquely, account in particular for the appearance of the small-angle diffraction peak or Regge-like behavior in the forward direction. Whereas this nonuniqueness of the solution is one shortcoming of the model, it permits sufficient flexibility so that one may perhaps be able to reproduce the forward high-energy angular distribution once sufficiently reliable functional dependences for the resonant parameters are found. The sufficiency conditions on the partial-wave amplitudes for the elastic amplitudes to be exponential functions oft over the whole angular domain are also derived under the rather restrictive conditions that, ass→∞, the elastic amplitudes become entire functions oft. Even in this restrictive case the infinite-resonance model does not seem to possess a unique solution, but presumably very detailed information on the behavior of the amplitude whens→∞ might make the solution unique.

Photoproduction of Charged Pion Pairs andN*(1238)++in Hydrogen from 0.9 to 1.3 GeV

The momentum spectrum of negative pions produced in the reaction $\ensuremath{\gamma}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}+{\ensuremath{\pi}}^{+}+p$ has been measured at eight photon laboratory energies from 0.9 to 1.3 GeV at c.m. angles from 7\ifmmode^\circ\else\textdegree\fi{} to 150\ifmmode^\circ\else\textdegree\fi{}. The reaction was produced in a liquid-hydrogen target illuminated by a bremsstrahlung beam from the Caltech synchrotron. The ${\ensuremath{\pi}}^{\ensuremath{-}}$ were detected and momentum analyzed with a magnetic spectrometer employing a combination of scintillation counters and Cherenkov counters. The incident photon energy was fixed by using the technique of bremsstrahlung subtraction. The cross section for the pseudo-two-body reaction $\ensuremath{\gamma}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}+{N}^{*}{(1238)}^{++}$ was obtained by fitting the ${\ensuremath{\pi}}^{\ensuremath{-}}$ momentum spectrum at each angle and energy with a linear combination of a resonance term and three-body phase space. The angular distribution of the ${\ensuremath{\pi}}^{\ensuremath{-}}$ in ${N}^{*}$ production shows the small-angle peak and decrease near 0\ifmmode^\circ\else\textdegree\fi{} predicted by the one-pion-exchange (OPE) model. Gauge-invariant models are in poorer agreement with the data. Moravcsik fits to the angular distributions are presented, and are extrapolated to obtain a value for the $\ensuremath{\pi}N{N}^{*}$ coupling constant of 23.1\ifmmode\pm\else\textpm\fi{}2.0 Ge${\mathrm{V}}^{\ensuremath{-}2}$, in fair agreement with the value obtained from the width of the ${N}^{*}(1238)$. The total cross section for pion pair production decreases smoothly from 78.9\ifmmode\pm\else\textpm\fi{}2.9 \ensuremath{\mu}b at 0.93 GeV to 59.1\ifmmode\pm\else\textpm\fi{}5.2 \ensuremath{\mu}b at 1.29 GeV, whereas the ${N}^{*}$ part of the cross section decreases from 45.0\ifmmode\pm\else\textpm\fi{}2.4 \ensuremath{\mu}b to 18.2\ifmmode\pm\else\textpm\fi{}3.5 \ensuremath{\mu}b over the same range. There is no strong evidence for formation of the ${N}^{*}(1688)$ as an intermediate state.