Azimuthal Angular Distribution Research Articles

Scattering angle dependence of double-collision processes

In solid targets projectile and target K vacancies or 1sσ molecular orbital (MO) X-rays may be created by a double-collision process where a projectile L or K vacancy is formed in one-collision then transfer to the K shell or radiates a MO X-ray in a second collision. The scattering-angle dependence of the probability for this process to occur is calculated. The projectile scattering in the first collision can influence the observed scattering-angle dependence in several ways: (1) the MO X-ray production probability falls off faster with decreasing angle, (2) the azimuthal angular distribution of MO X-ray emission is smeared out, and (3) predicted oscillations in the MO X ray spectrum for fixed impact parameter in the second collision are probably not observable in solid targets.

Measurements on anisotropy of angular distribution for the backscattering electron emission on copper monocrystals

AbstractDuring the perpendicular bombardment with 25 keV primary electrons the azimuthal and polar angular distribution are measured of those backscattered electrons which escape from the low index surfaces of a copper monocrystal. A movable electron spectrometer operates as a detector with the energy resolution of ΔE/E ≈ 10−3 and the angular resolution of Δθ = 0.5°. The observed angular distribution proves congruously with large angle Kikuchi reflection diagrams, the representation of which at metallic surfaces was successful as yet only for oblique incidence. The connection between escape direction and energy loss and also the influence of covering layers are investigated.

Angular distribution of dileptons in hadronic collisions

The polar and azimuthal angular distributions of the lepton pair produced in hadron-hadron collisions are studied. For large Q T these are calculated from lowest-order QCD diagrams. For low Q T we present simple expressions which take into account the effect of primordial quark transverse momentum on the angular distributions.

The estimation of asymmetries from incomplete azimuthal angular distributions

The problem of estimating the parameters of an angular distribution in scattering experiments is discussed. The context is an experimental situation that artificially restricts the available angular range in a manner that differs from one scattering event to the next. The formal solution, which is non-linear in the parameters, is presented, and its implementation in a particular case is described.

Experimental study of hadrons produced in high-energy charged-current neutrino-proton interactions

We analyze a sample of about 2000 charged-current neutrino-proton interactions with neutrino energy greater than 10 GeV produced in the 15-ft hydrogen bubble chamber at Fermilab using a broad-band neutrino beam. We study the details of the hadrons produced and find generally good agreement with the quark-parton model and present parametrizations of quark fragmentation ($D$) functions. The $D$ functions are found to be independent of ${Q}^{2}$ and $W$ (total hadronic mass) for $Wg4$ GeV, in agreement with the model. The height of the rapidity plateau in the quark (current) fragmentation region is compared to that of the diquark (target) fragmentation region and the two are found to agree. Detailed charge-correlation data are presented and compared to the Field-Feynman model of the $D$ functions, and also to a longitudinal-phase-space model, and are found to disagree with both. The mean transverse momentum ${P}_{T}$ of the hadrons is studied for its ${Q}^{2}$ and Feynman-$X$ dependence. We find a sizeable increase of $〈{{P}_{T}}^{2}〉$ with Feynman $X$ which agrees, however, with our longitudinal-phase-space model. We find no statistically significant dependence of $〈{{P}_{T}}^{2}〉$ on ${Q}^{2}$, up to ${Q}^{2}=64$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, although the highest-momentum hadrons are consistent with a mild ${Q}^{2}$ dependence. The azimuthal angular distribution of the highest-momentum hadrons in high-${Q}^{2}$ events is examined for evidence of anisotropy of the type that has been predicted for effects of gluon radiation.

Charged-particle multiplicities associated with large-transverse-momentum photons

We have measured the charged-particle multiplicities of events containing a large-transverse-momentum (p/sub perpendicular/) photon produced near center-of-mass polar angles (theta) of 90 degree, 17.5degree, and 8degree in proton-proton collisions. The data were obtained at the CERN Intersecting Storage Rings at center-of-mass energies of 23, 31, 45, 53, and 62 GeV and for the transverse-momentum range 0 < or = p/sub perpendicular/ < or = 4.5 GeV/c. When the photons are detected near theta = 90degree, the associated multiplicity in the hemisphere away from the observed photon is found to increase with increasing photon transverse momentum. In the hemisphere containing the photon, the associated multiplicity decreases at the lowest energy and is approximately constant at the highest energies. The data at theta = 17.5 degree and 8degree are similar, with the exception that the particle multiplicities near the detected photon are found to decrease with increasing photon p/sub perpendicular/ at all energies. No strong back-to-back structure is observed in the data; however, as the photon emission angle is changed, some shift of the multiplicity distributions in the direction opposite the photon is observed. The data at all three polar angles show a broad peak in the azimuthal angular distributions at phimore » = 180degree (opposite the detected photon). Finally, the data are compared to a simplified picture for particle production in high-p/sub perpendicular/ events, and to the various classes of high-p/sub perpendicular/ models that have been proposed. (AIP)« less

Production and decay of the π−π−π+ system in the reaction π−d → d π−π−π+ at 9 GeV/ c

In this paper we present a study of the reaction π −d → π − π − π +d at 9 GeV/ c. The mass spectra are in fair agreement with the predictions of a reggeized pion-exchange Deck model. However, the s-channel azimuthal angular distribution indicates a ϱ-exchange Deck contribution. The results of the partial-wave analysis of the (3 π) − system are compared with those obtained in a hydrogen target: the J P = 2 + contribution is very small (at most 1.5 ± 1.2)% in our data, which are dominated by J P = 1 + for low mass, whereas the J P = 0 −, 1 +, 2 − have comparable importance in the higher mass region.

Coincidence Electroproduction and Scaling in the Regge Region

We consider the coincidence electroproduction process $l+p\ensuremath{\rightarrow}{l}^{\ensuremath{'}}+{p}^{\ensuremath{'}}+\mathrm{anything}$. With the momentum transfer between $p$ and ${p}^{\ensuremath{'}}$ held fixed, a single trajectory in the $p{\overline{p}}^{\ensuremath{'}}$ channel dominates as the laboratory energy of the virtual photon becomes large. (It is known that the onset of single-trajectory dominance may be ascertained by observing the azimuthal angular distribution of the detected hadron.) In the region of large virtual photon mass and missing mass (with their ratio fixed) the process may be picturesquely described as deep-inelastic scattering of a lepton on a Reggeon target. We implement the assumed Regge behavior in the language of van Hove. The scaling behavior of the various structure functions is then determined by the canonical light-cone commutator (taken between spin-$J$ states), if certain smoothness assumptions are granted. Relations of the Callan-Gross type are also derived. The experimental features corresponding to our results are relatively easy to observe. The kinematics of coincidence electroproduction (with a polarized beam) is discussed in some detail.

On the azimuthal effects of two prong πN and three prong DD events produced by 17.2 GeV/c π− mesons

A deviation from isotropy in the azimuthal angular distribution of secondary particles of two and three prong pion-nucleon interactions is observed in emulsion at 17.2 GeV/c. Attempts are made using Monte Carlo calculations to interpret these azimuthal effects on the basis of (i) the kinematics of reactions π− p→pπ− (k π0) and π− p→nπ+π− (k′ π0) and (ii) the diffraction dissociation of pions on nuclei. A new method is given for the selection of the contribution of DD interactions from three prong events. Using this method λDD=(1065±288)m and λDD=(113±13)m are obtained for the mean free path of the diffraction dissociation in emulsion at ∼7 and 17.2 GeV/c, respectively. The possible influence of theDeck effect in the case of three prong events is also investigat

Azimuthal Angular Distribution ofC12(γ, p0)

The azimuthal angular distribution of the photoprotons produced in the reaction $^{12}\mathrm{C}(\ensuremath{\gamma}, {p}_{0})^{11}\mathrm{C}$ by monochromatic polarized gamma rays from $^{3}\mathrm{T}(p, \ensuremath{\gamma})^{4}\mathrm{He}$ was measured for gamma-ray energies of 21.3 and 21.6 MeV. The ratio $R$ of the number of photoprotons with directions between 0\ifmmode^\circ\else\textdegree\fi{} and 45\ifmmode^\circ\else\textdegree\fi{} (with respect to the gamma-ray polarization) to the number between 45\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} was determined. The average observed ratio for $R$, 2.8\ifmmode\pm\else\textpm\fi{}0.7, is larger than but not inconsistent with that calculated for pure electric-dipole photon absorption, 2.08\ifmmode\pm\else\textpm\fi{}0.1.

Remarks on the phenomenological analysis of resonances

Some remarks are made concerning various aspects of the analysis of resonances produced in multi-particle final states resulting from high-energy collisions. The shape and position of a resonance are discussed by means of the connection between production cross-sections for stable and unstable particles, and a numerical example ofN* as seen in KN → KN* at different energies is given. The relation between the present description of the resonant effects and others (Watson’s finalstate interaction formula and the one-meson-exchange model of Chew and Low) is examined. Off-the-mass-shell corrections to the one-meson-exchange model are obtained in a relatively simple way. The bearing of the decay angular correlations on the production mechanism is explored ; co-ordinate axes appropriate for the peripheral model are specified; the equivalence of the azimuthal angular distribution and the Treiman-Yang distribution is established. Angular correlations are given for the decay of boson resonances (J=l, 2) resulting from definite spin and parity states in thet-channel. Some remarks are made about the inclusion of nonresonant contributions when there is a mixture of pseudoscalar and vector exchange.

Scattering of neutrons by α-particles at 14.1 MeV

The angular distribution of 14.1 MeV neutrons elastically scattered by α-particles has been measured by observing the α recoils in a helium-filled cloud chamber. The results are in satisfactory agreement with those previously obtained by other authors. Inspection of the smallangle region of the measured distribution shows that phase shifts of orbital angular momentum higher than L=1 are not negligible, although, according to the present experiment, quantitative information on D-waves turns out to be somewhat elusive. The azimuthal angular distribution agrees well with the value P = 0.02 of the neutron beam polarization, as measured by Perkins.

Investigation of azimuthai effects at multiple particle production

The azimuthal angular distribution of the secondary particles produced at p-N collisions of 9 GeV energy and nuclear interactions of single charged cosmic ray particles in the photoemulsion have been investigated by the suggested method. The influence of the energymomentum conservation law was estimated. The experimental results were compared with some theories and models of nuclear interactions produced by high energy nucleons.

Reaction O16(γ, p)N15 20.5 MeV Polarized Bremsstrahlung

D 2 O soaked, H 2 O soaked and unsoaked emulsions were irradiated simultaneously at the characteristic angle the 20.5 MeV polarized brems-strahlung from a thin Al target in a betatron. The linear polarization of the gamma rays from 4 MeV to 6 MeV was estimated to be 31.7±5.0% observing the azimuthal angular distribution of photoprotons from deuterons. The H 2 O soaked emulsion and unsoaked one were used to study O 16 (γ, p ) reaction. The proton energy spectrum shows a structure which agrees with the earlier results except a peak at 1.1 MeV of proton energy. This peak which has never been found corresponds to the well-known resonance in N 15 ( p , γ)O 16 at 1.05 MeV of proton energy. The azimuthal angular distributions of photoprotons caused several photon energy regions were observed. From these angular distributions it is shown that a resonance at a photon energy of 17.3 MeV is E 1 transition, and the corresponding level of O 16 is considered to have J =1 - , T =1, which is in good agreement with the theoretical calculation in the intermediate coupling.

Plane Polarization of 8.5 MeV Bremsstrahlung

The polarization of bremsstrahlung produced by 8.5 MeV electrons incident on thin Al, Ag, Au and U targets in a betatron was studied with D 2 O-loaded nuclear emulsions. The Polarization was measured at the characteristic emission angle \(\varTheta{=}mc^{2}/E_{0}\) by observing the azimuthal angular distribution of photoprotons from deuterons. The results show different energy dependence of polarization for different elements. For low Z targets the polarization is positive and large in the lower energy part of bremsstrahlung spectrum, in qualitative agreement with the theoretical calculations. For high Z targets the polarization is negative in the higher energy range and positive in the lower energy range. This reversal of the sign of polarization occurs at much lower energies than those expected from the theory.

Effects of photon polarization on the azimuthal angular distribution in (γ, N) reactions

The purpose of this note is to point out some simple features in the azimuthal angular distribution in photonuclear reactions induced by a partially plane polarized photon beam. The use of such a beam can be made of special interest as a check to the electric dipole character of the photon absorption in the giant resonance region.

Plane Polarization of 15.1-Mev Bremsstrahlung from 25-Mev Electrons

Linearly polarized gamma rays were produced with the aid of a special betatron doughnut which made it possible to limit the effective thickness of the bremsstrahlungproducing Al and Pt targets. The linear polarization of 15.1-Mev bremsstrahlung gamma rays was detected by measuring the azimuthal angular distribution of gamma rays which were scattered elastically from the wellknown nuclear level in C/sup 12/. For the particular effective thickness of Al that was used, the maximum polarization of 15.1-Mev gamma rays in the bremsstrahlung of 25-Mev electrons was 1.53 plus or minus 0.05, (This corresponds to 21% in the more conventional polarization notation.) Both this observed maximum (which occurred at an angle of 1.4 ction prod- ) and the polarization measured at four other angles confirm theoretical predictions. With the platinum target that was used, the observed polarization of 1.28 plus or minus 0.04 was about 10% lower than the value predicted by theoretical calculations which use the Born approximation and neglect screening. Available screening and Coulomb corrections bring the theoretical predictions into essential agreement with the experimental values. Since the elastic scattering pattern of gamma rays shows unambiguously that the strong photon scattering level at 11.1 Mev in C/sup 12/ is excitedmore » by magnetic dipole radiation, this level has spin 1 and even parity. (auth)« less

Geomagnetic Measurements on Heavy Primary Cosmic Radiation near the Equator

The azimuthal angular distribution of primary cosmic radiation with charges $Z\ensuremath{\ge}6$ has been measured near the geomagnetic equator (at Guam) in horizontal emulsions with known orientation relative to the earth. The observed distribution is well described by using the centered-dipole approximation to the earth's surface magnetic field (north pole at 79\ifmmode^\circ\else\textdegree\fi{}N and 70\ifmmode^\circ\else\textdegree\fi{}W) if the effect of the solid earth is included by assuming that the main cone is the allowed cone. This verifies the prediction that the penumbra becomes forbidden near the geomagnetic equator. The main-cone equatorial cutoffs were applied to an assumed integral energy spectrum which is inversely proportional to the $\ensuremath{\alpha}$ power of the total energy per nucleon. The exponent $\ensuremath{\alpha}$ was found to be at least 1.82\ifmmode\pm\else\textpm\fi{}0.19.

Geomagnetic Effects on Heavy Primary Cosmic Radiation at 42°N

The zenith and azimuthal angular distribution of primary cosmic rays with charges $Z\ensuremath{\ge}5$ has been measured at Texas using horizontal emulsions with known orientation relative to the earth. The magnitude of the azimuthal asymmetry is consistent with St\ormer theory down to a zenith angle of about 65\ifmmode^\circ\else\textdegree\fi{} while for larger zenith angles the effect of the solid earth (shadow cone) is observed. The direction of the asymmetry seems to be consistent with the centered dipole approximation of the earth's magnetic field (north pole at 79\ifmmode^\circ\else\textdegree\fi{}N and 70\ifmmode^\circ\else\textdegree\fi{}W). The flux at the top of the atmosphere is 1.6\ifmmode\pm\else\textpm\fi{}0.3 particles/${\mathrm{m}}^{2}$ sec sterad for nuclei with $Z\ensuremath{\ge}10$ and 4.8\ifmmode\pm\else\textpm\fi{}1.0 particles/${\mathrm{m}}^{2}$ sec sterad for CNOF nuclei.

Heavy Primary Cosmic Radiation at the Equator

The zenith and azimuthal angular distribution of primary cosmic rays with charges \ensuremath{\geqq} 6 has been measured at the equator using oriented nuclear emulsions. The magnitude of the azimuthal asymmetry is consistent with an integral power law spectrum which falls off inversely as the 2.0 power of the total energy per nucleon. However, the maximum intensity comes from the southwest rather than the west. This is consistent with the recently proposed shift of the earth's effective magnetic field for cosmic rays.The flux at the top of the atmosphere is 0.68 particle ${\mathrm{m}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ${\mathrm{sterad}}^{\ensuremath{-}1}$ for CNOF (carbon, nitrogen, oxygen, fluorine) nuclei and 0.21 particle ${\mathrm{m}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ${\mathrm{sterad}}^{\ensuremath{-}1}$ for nuclei with $Z\ensuremath{\geqq}10$.