Backward Peak Research Articles

The OZI rule does not apply to baryons

Determinations of the π-N σ-term and the EMC measurement of deep inelastic polarized μp scattering and various theoretical arguments indicate that baryons contain a significant number of strange quark-antiquark pairs. Their presence gives rise to additional connected diagrams which evade the Okubo-Zweig-Iizuka (OZI) rule for meson-baryon couplings, and explain the apparent violation of the OZI rule in the reaction p p→φπ +π − as well as the process pp→pp φ+pions, and the backward peak seen in p p→ K + K − . we catalogue predictions, based on moments of deep inelastic structure functions, for the OZI-evading couplings to baryons of 0 −+, 0 ++, and 2 ++ and other mesons. Processes where these predictions can be tested include backward meson production in π-N scattering as well as p p annihilation and pp scattering.

Inelastic scattering of antiprotons off12C at 180 and 46.8 MeV

The cross-sections for the reactions12C(\(\overline p \),\(\overline p \)′)12C* (2+, 4.44 MeV; 0+, 7.65 MeV; 3−, 9.64 MeV) are calculated in terms of the antiproton-nucleon scattering amplitude, the elastic-scattering amplitude of antiprotons on mass-11 nuclei and the inelastic-transition densities obtained by analysing inelastic electron scattering data. The results reproduce the available data at 180 and 46.8 MeV. The relation of the cross-sections for the inelastic- to the elastic-scattering amplitude is discussed. The cross-sections for inelastic scattering even at small angles serve to rule out such an optical potential that gives rise to the backward peak in the cross-sections for elastic scattering.

Crossed beam study of the reaction of van der Waals molecule O+(NO)2→NO*2+NO

The reaction O+(NO)2 was studied by use of a crossed-beam apparatus. An (NO)2 beam generated by the supersonic expansion crossed at right angles with a collimated effusive beam containing oxygen atoms which were formed by microwave discharge. The product NO*2 was detected by the chemiluminescence. The angular distribution of the product was measured by an angle-resolved emission detection technique. The distribution has forward and backward peaks with respect to the oxygen atom incidence and indicates the occurrence of an intermediate complex in the course of the reaction. The angular velocity distribution, as well as the onset of the chemiluminescence, indicates that the reaction exothermicity appears mostly as internal energy of NO*2 . The remaining energy flows into the product translation and rotation; the vibrational freedom of the third-body molecule is not effective as an energy absorber. The emission intensity was found to decrease with increasing relative collision energy. A sharp drop of the intensity was observed at 2 kcal/mol of collision energy, which is in good agreement with the bond energy of the NO dimer.

Reactive scattering of a supersonic fluorine atom beam: F + Cl2

Reactive scattering of F atoms with Cl2 molecules has been studied at an initial translational energy E ∼ 32 kJ mol-1, using a supersonic beam of F atoms seeded in He buffer gas. Laboratory angular and velocity distributions of FCl product have been measured which show scattering peaking sharply in the forward direction with a smaller backward peak of relative height ∼0·3 ± 0·1. The product translational energy for scattering in the forward and backward directions is greater than that for the sideways scattering by a factor ∼2. Reaction proceeds via a short-lived collision complex with a lifetime ∼0·5 rotational periods for complexes rotating in the plane of collision. Bent structures are proposed for the collision complex and the reactant transition state, which relate the observed scattering to the initial orientation of the reactant Cl2 molecule with respect to the incident F atom direction.

Effect of Surface Roughness on Remote Sensing of Snow Albedo

Narrow field-of-view sensors on satellites monitoring solar radiation measure the reflected radiance in a particular direction. For climatic studies of the Earth’s radiation budget, the albedo is needed, which is the integral of the upward radiance over all angles divided by the downward irradiance. In order to infer the albedo from a radiance measurement at only one angle, it is necessary to know a priori the distribution of reflected radiation with angle, i.e. the bi-directional reflectance-distribution function (BRDF). The BRDF is a function of four angles: solar zenith and azimuth, and satellite zenith and azimuth. For areal or temporal averages on many natural surfaces, only three angles are needed to describe the function, because only the difference between the two azimuths is important, not their individual values. This assumption was made when developing empirical BRDFs from Nimbus-satellite data for use in the Earth Radiation Budget Experiment (ERBE). However, in large areas of the polar regions, all four angles are needed, because the sastrugi are oriented parallel to a prevailing wind direction. The BRDF shows a forward peak when the solar beam is along the direction of the sastrugi, and an enhanced backward peak when it is perpendicular. Averaging over all solar azimuths (relative to the sastrugi azimuth) causes back-scattering to be averaged together with forward-scattering. The conclusion of the ERBE analysis, that snow is the most nearly isotropic of all Earth surfaces, is therefore at least partly a spurious result of this averaging.Measurements of the BRDF were carried out from a 23 m tower at the South Pole during January and February at 900 nm wavelength for varying azimuths between the Sun and the sastrugi fabric. The wavelength was selected near the midpoint of the solar-energy spectrum but where scattered sky radiation is negligible. Measurements were made with 10° field of view at 15° intervals in viewing zenith and azimuth angles throughout the day, at intervals of 1 h (15° of solar azimuth). For BRDF normalized such that its angular average is unity, the principal features of the results include a forward-scattering peak with a value of about five together with a side- and back-scattering lobe of 1.1 to 1.3. Variations in solar azimuth produced a skewness in BRDF which was approximately consistent with enhanced scattering at the specular angle with respect to the solar azimuth and the orientation of the principal fabric of the sastrugi pattern. The angularly averaged pattern was remarkably similar to the results of Taylor and Stowe even though their values were integrated over wavelength and were made through the atmosphere. Our studies thus suggest that, for mid- to late summer, the Taylor and Stowe results require only small corrections for sastrugi effects. This is not, however, expected to be true from sunrise through late November.Spectral albedos showed values at visible wavelengths of 0.97 to 0.99 which agree very well with the model calculations of Wiscombe and Warren using our observed mean snow grain-sizes. Albedos for wavelengths above 1400 nm were higher than model predictions, indicating that the depth dependence of grain-size must be included in the analysis.This research was supported by National Science Foundation grant DPP-83–16220.

Effect of Surface Roughness on Remote Sensing of Snow Albedo

Narrow field-of-view sensors on satellites monitoring solar radiation measure the reflected radiance in a particular direction. For climatic studies of the Earth’s radiation budget, the albedo is needed, which is the integral of the upward radiance over all angles divided by the downward irradiance. In order to infer the albedo from a radiance measurement at only one angle, it is necessary to know a priori the distribution of reflected radiation with angle, i.e. the bi-directional reflectance-distribution function (BRDF). The BRDF is a function of four angles: solar zenith and azimuth, and satellite zenith and azimuth. For areal or temporal averages on many natural surfaces, only three angles are needed to describe the function, because only the difference between the two azimuths is important, not their individual values. This assumption was made when developing empirical BRDFs from Nimbus-satellite data for use in the Earth Radiation Budget Experiment (ERBE). However, in large areas of the polar regions, all four angles are needed, because the sastrugi are oriented parallel to a prevailing wind direction. The BRDF shows a forward peak when the solar beam is along the direction of the sastrugi, and an enhanced backward peak when it is perpendicular. Averaging over all solar azimuths (relative to the sastrugi azimuth) causes back-scattering to be averaged together with forward-scattering. The conclusion of the ERBE analysis, that snow is the most nearly isotropic of all Earth surfaces, is therefore at least partly a spurious result of this averaging. Measurements of the BRDF were carried out from a 23 m tower at the South Pole during January and February at 900 nm wavelength for varying azimuths between the Sun and the sastrugi fabric. The wavelength was selected near the midpoint of the solar-energy spectrum but where scattered sky radiation is negligible. Measurements were made with 10° field of view at 15° intervals in viewing zenith and azimuth angles throughout the day, at intervals of 1 h (15° of solar azimuth). For BRDF normalized such that its angular average is unity, the principal features of the results include a forward-scattering peak with a value of about five together with a side- and back-scattering lobe of 1.1 to 1.3. Variations in solar azimuth produced a skewness in BRDF which was approximately consistent with enhanced scattering at the specular angle with respect to the solar azimuth and the orientation of the principal fabric of the sastrugi pattern. The angularly averaged pattern was remarkably similar to the results of Taylor and Stowe even though their values were integrated over wavelength and were made through the atmosphere. Our studies thus suggest that, for mid- to late summer, the Taylor and Stowe results require only small corrections for sastrugi effects. This is not, however, expected to be true from sunrise through late November. Spectral albedos showed values at visible wavelengths of 0.97 to 0.99 which agree very well with the model calculations of Wiscombe and Warren using our observed mean snow grain-sizes. Albedos for wavelengths above 1400 nm were higher than model predictions, indicating that the depth dependence of grain-size must be included in the analysis. This research was supported by National Science Foundation grant DPP-83–16220.

Molecular beam study of the radical group effect in the K + RI → KI + R(R = CH3, C2H5, nC3H7) reactive collisions

Differential reaction cross-sections for the K + RI → KI + R(R = CH3, C2H5, C3H7) systems have been measured as a function of the collision energy by using our molecular beam apparatus. The analysis of the centre-of-mass angular and recoil velocity distribution of the products indicated: (a) a backward peak character corresponding to a direct, rebound mechanism (b) that the average translational energy of the products increases approximately linearly with increasing collision energy, E T, as follows /kJ mol-1 = a /kJ mol-1 + b where (a, b) are (0·65, 66·5), (0·56, 58·4) and (0·28, 30·3) for the methyl, ethyl and propyl iodide reactions respectively. Whereas in the methyl and ethyl reactions the fraction of the available energy that appears in translation, f′T, is about 0·65–0·55 in the propyl case it falls to ca. 0·3. A comparison with photofragmentation studies for the alkyl iodides, RI, has shown similar dynamics involving a ‘quasidiatomic’ C-I excitation followed by recoil of a ‘soft’ ra...

Proton compton scattering at backward angles in the energy range from 400 MeV to 1050 MeV

Differential cross sections of proton Compton scattering have been measured in the energy range between 400 MeV and 1050 MeV at C.M.S. angles of 150° and 160°. The recoil proton was detected with a magnetic spectrometer using multi-wire proportional chambers and multi-wire spark chambers. The scattered photon was detected with a lead glass Čerenkov counter of the total absorptive type with two layers of multi-wire proportional chambers which measured the horizontal and vertical positions of the scattered photon. The proton Compton scattering was differentiated from the background of the π 0 photoproduction events with the use of angular correlations between the recoil proton and the scattered photon. The cross-section data show the clear second resonance peak at E γ = 750 MeV and a bump around E γ = 925 MeV at both angles. Also the angular distributions show the backward peak in the energy range between 700 MeV and 950 MeV. The data are compared with theoretical calculations based on an isobar model with some phases for the resonances. In this calculation, the proton Compton data were fitted varying the photocouplings of the nucleon resonances around the bump and the phases below the third resonances as free parameters. The calculation reproduced the angular distribution of differential cross sections well. However, it was inevitable that we use large photocouplings of P 33(1600) in order to fit the bump.

Crosssed beam study of the Na(3 2P [formula omitted] + N 2 quenching process: angular distributions with product state analysis

The transfer of electronic to vibrational rotational energy for Na(3 2P 3 2 ) + N 2(ν = 0 j) → Na(3 2S 1 2 ) + N 2(ν′, j′) is studied in an experiment with crossed supersonic Na and N 2 beams and single-mode cw dye laser excitation (relative kinetic energy 0.16 eV). At c.m. forward scattering the ν′ = 3 state is excited to more than 50%, accompanied by a noticeable rotational excitation amounting to over 0.1 eV. For backward scattering the vibrational levels ν′ = 2,3 and 4 are dominantly populated. The angular distributions show a pronounced narrow forward maximum and a smaller (8–30%) backward peak. The observations are rationalized in terms of the bond stretch attraction model.

Inelasticity corrections in the elastic proton-deuteron back-angle scattering at intermediate energies

The elastic proton-deuteron scattering cross sections at back angles have been calculated in the light of Kerman-Kisslinger model, using a generalised baryon transfer mechanism on the assumption that theN*'s exist (with a probability∼1 %) in the deuteron and that the backward peak is caused by their exchange. The effect of numerous competing open inelastic channels at intermediate energies on the elastic cross section is computed in a particularly simple model of Sopkovich. The resultant damping of the back scattering amplitude is expressed directly in terms of the forward angle elastic scattering data. The results are compared with the experimental cross sections in the energy range of 1.5–2.5 GeV.

Differential cross section and analyzing power for backward pions in [formula omitted

Cross sections and analyzing powers are presented for the reaction 2 H( p, π +) 3 H at 400, 425, 443 and 470 MeV, and laboratory pion angles of 120°, 130°, 140°, 150° and 160°. The cross sections have flat angular distributions, are in contradiction with an earlier experiment which indicated a backward peak at 470 MeV, but are in quantitative agreement with a calculation based on the two-nucleon model.

Exactly central heavy-ion collisions by nuclear hydrodynamics

We study the dynamics of heavy-ion collisions using the hydrodynamical description and focus our attention on the head-on collisions which provide the most favorable case for such a description. Angular distributions and energy distributions were obtained for various combinations of projectiles and targets of equal and unequal masses in the energy range from 50 to 400 MeV per projectile nucleon. It is found that regions of high density (the shock regions) are formed during the collisions and that the angular and energy distributions for many of these collisions have prominent features. In the collision of a small projectile with a heavy target, there is the forward angular peak of slow dissociated particles which represent much of the projectile nuclear matter stopped in the larger target nucleus, in addition to the nucleons from the expansions of the shock region. There is the side angular peak corresponding to the sidesplash of the target nuclear matter due to the impact of the projectile. There is also the backward angular peak due to the expansion of the shock region into the backward direction. In the collision of two equal nuclei, there are only the forward angular peak and the side angular peak. The effects of viscosity and thermal conductivity are investigated and found to affect the angular and energy distributions of the reaction products.NUCLEAR REACTIONS Heavy-ion reactions, nuclear hydrodynamics, $^{20}\mathrm{Ne}$ +$^{197}\mathrm{Au}$ and $^{208}\mathrm{Pb}$+$^{208}\mathrm{Pb}$ at 50, 100, 250, and 400 MeV per projectile nucleon. Nuclear viscosity and thermal conductivity.

Observation of the orbiting backward peak in the differential cross section for Na( 2P)-Hg collisions

A typical feature of collisions governed by attractive and repulsive forces is the orbiting phenomenon. Most clearly these collisions are visible as a backward peak in the differential cross section. In this work we report the first observation of this backward peak in the interaction of neutral atoms, specifically for Na( 2P interacting with Hg.

The reactions K − + p → pseudoscalar meson + Λ (1520) at 4.2 GeV/ c

The total and differential cross sections of the reactions K −p → π 0Λ (1520), ηΛ(1520) and η′ Λ(1520) have been measured. Prominent forward peaks are onserved in all three reactions. The first reaction shows also a backward peak. The spin density matrix elements of the Λ(1520) in this reaction are determined. For forward production the results show a remarkable alignment of the Λ(1520) corresponding to an M2 transition in the model of Stodolsky-Sakurai for 3 2 − baryon production.

Reactive scattering of a supersonic oxygen atom beam : O + Cl2

Reactive scattering of O atoms with Cl2 molecules has been studied at an initial translational energy E = 31 kJ mol-1 using a supersonic beam of O atoms seeded in He and at E = 13 kJ mol-1 using O atoms seeded in Ne. Velocity distributions of OCl product were measured by cross-correlation time-of-flight analysis. A full contour map of the differential reaction cross-section was obtained with O atoms seeded in He which peaks strongly in the forward direction with a smaller backward peak of relative height 0·30±0·1. For O atoms seeded in Ne, the relative height of the backward peak increases to 0·55±0·15. The product translational energy for scattering in the forward direction is higher than that for wide angle scattering by a factor of ∼3. Thus the O + Cl2 reaction proceeds via a short-lived collision complex where the lifetime of the complex depends upon the initial translational energy. However, all reactive collisions do not sample the most stable configuration of the complex to an equal extent. The obs...

Sharp Backward Peak inp-He4Elastic Scattering at 1.05 GeV

$p$-$^{4}\mathrm{He}$ elastic scattering has been measured at 1.05-GeV incident proton energy, close to 180\ifmmode^\circ\else\textdegree\fi{} in the center of mass. The steep backward peak observed at lower energies is still present, but its slope appears to decrease.

Large contribution of deep inelastic processes to reactions of40Ar and48Ca with238U

Differential recoil range distributions have been measured for heavy-reaction products ranging from Te(Z=52) to quasielastic transfer products near the charge and mass of the targets for the reactions of 276 MeV48Ca+238U, 237MeV and 250 MeV40Ar+238U, and 259 MeV40Ar+197Au. The measured recoil range distributions for the40Ar+197Au reaction agree with range distributions calculated from the known projectile-like fragment angular distributions for this reaction. The angular distributions of recoil products formed in the uranium target reactions are deduced and show that the products in the75Re to83Bi region have backward peaked angular distributions characteristic of deep inelastic reactions. The heavy product angular distributions smoothly vary from a (1/sinθ) shape to an exponential shaped backward peak as the atomic number of the product increases from 52 to 83. The trend in the deduced angular distributions for those elements for which recoil range distributions were determined in the40Ar+197Au reaction and the 250 MeV40Ar+238U reaction is similar, suggesting that just as for the Ar+Au system the composite system for the uranium target reaction is also not fully equilibrated along the mass asymmetry coordinate. These conclusions show that the fraction of the total reaction cross section resulting in complete fusion must be re-evaluated for the40Ar+238U reaction and similar heavy-target reactions.

Sommerfeld poles and backward peaks in elastic scattering

In this paper we propose a new use of the complex-angular-momentum representation of the scattering amplitude. In particular we show that it is not possible to connect a sequence of compound-state resonances with a pole trajectory. Furthermore the high-energy backward peaks in the elastic channel are analysed, and we propose a model of the mechanism responsible for these backward enhancements. The mathematical formalism of this model, which employs the poles of theS-matrix in the complex-angular-momentum plane, is investigated in detail. Finally, in order to test the theory, a phenomenological analysis is performed; the results that we obtain are in agreement with the theory.

Cross sections and polarizations in the reactionsπ−p→ΛK0andπ−p→ΛK*0(890)near the backward direction, from 3 to 6 GeV/c

We have measured the differential cross sections and $\ensuremath{\Lambda}$ polarizations in the reactions ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\Lambda}{K}^{0}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\Lambda}{K}^{*0} (890)$ near the backward direction, at 3, 4, 5, and 6 GeV/c. Data equal to several times the world's total sample above 2 GeV/c were recorded. Both reactions are characterized by cross sections falling rapidly with beam momentum, and by large positive $\ensuremath{\Lambda}$ polarizations for ${u}^{\ensuremath{'}}$ between 0.0 and 0.6 ${\mathrm{GeV}}^{2}$. Analysis of ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\Lambda}{K}^{0}$ yields an effective Regge trajectory consistent with antishrinkage of the backward peak. Separation into amplitudes of definite-parity-naturality exchange shows the reaction to be dominated by unnatural-parity exchange. The energy behavior of this exchange is, however, not consistent with a single linear baryon Regge trajectory or exchange-degenerate pair of trajectories. An apparent normalization discrepancy between data on ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\Lambda}{K}^{0}$ of a CERN-ETH group and other high-statistics data including that of this experiment is discussed.

Backward scattering of pions by nucleons

Backward elastic scattering of pions by nucleons is an elementary form of excitation with baryon exchange. The backward scattering cross section is very small and decreases rapidly with increasing energy. The cross section becomes maximal when the scattering angle approaches 180°, i.e., a peak is observed in the backward scattering. In contrast to forward scattering, in backward scattering the processes in which positive and negative pions participate are not similar. This is confirmed by the exchange character of the backward scattering. In the energy interval up to 5 GeV, backward scattering has an extremely pronounced resonant character, due to the influence of the s-channel baryon resonances. Experimental data on backward scattering in the intermediate energy region (up to 20 GeV) are satisfactorily described by the Regge theory of complex angular momenta. The energy dependence of the cross section agrees with the model with linear baryon trajectories. In the Serpukhov-accelerator energy range (20–40 GeV), however, a weakening of the energy dependence is observed in the backward π–n scattering. It is difficult to reconcile this behavior within the framework of the Regge phenomenology, with the linear form of the nucleon trajectory. A phenomenon that has a bearing on the observed behavior of the backward scattering at high energies was unexpectedly observed in an entirely different region. A phase-shift analysis of πN scattering at low energies (to 1 GeV) has shown that one of the partial waves (corresponding to the quantum numbers of the nucleon) experiences an appreciable rise when the energy approaches zero. It turns out that this singularity can be connected with the asymptotic behavior of the backward scattering. The two phenomena—the behavior of the backward scattering at high energies and the singularity of the partial wave near zero—indicate in a consistent manner that the effective spin of the nucleon reggeon greatly exceeds the value that follows from the linearity of the nucleon trajectory. In contrast to backward π–n scattering, the behavior of backward π–p scattering (pure Δ exchange) reveals no singularities whatever in the Serpukhov-accelerator energy interval and continues to have the same energy dependence as observed at lower energies. As to the angular distributions, a very narrow backward peak is observed in the π–p scattering, and has a slope comparable with the peak of the π–n(π+p) scattering. The closeness of the π±n angular distributions, which has been observed for the first time at high energies (25-40 GeV), suggests the possibility of a geometrical interpretation—scattering by an extended object. The analogy between backward scattering of pions by nucleons and glory—an optical effect observed when light is backscattered from a raindrop—is discussed. In conclusion, radiative corrections to backward scattering are considered.