Minimum Momentum Transfer Research Articles

A comparison of different methods for improving flux and resolution on SANS instruments

Small-angle neutron scattering (SANS) is one of the most popular and oversubscribed techniques at every user facility for neutron scattering studies of condensed matter that offers it. The limiting features in SANS experiment design are the length of time required to make a measurement and the minimum momentum transfer Q that can be measured, and the resolution. In the traditional pinhole-camera geometry, these two constraints are inextricably linked, forcing tradeoffs. However, a number of methods have been developed for reducing this linkage, thus allowing higher throughput while retaining high resolution and a low minimum Q. These methods include using multiple confocal pinhole apertures, lenses, and focusing mirrors. We compare and contrast these options and discuss their suitability for use on instruments at pulsed neutron sources.

Possible application of compound Fresnel lens for neutron beam focusing

We have developed a Fresnel-type focusing device for cold neutrons fabricated using single crystals of magnesium fluoride. This stacked-lens device using 50 elements (with 50 beam–bending interfaces) demonstrated a focal length of 5 m with a good transmission of 0.829 for 1.14 nm neutrons. The focused beam was 5 times more intense than a beam of the same spot size with the same final flight path length produced with the traditional pinhole collimation. The background-scattering noise from lens was an order of magnitude larger than that of the traditional pinhole collimation in the momentum range of 0.01 –0.05 nm −1 , almost 10 −3 of focused direct beam at the lowest momentum transfers measurable. This device produced an intensity gain in measured SANS data of more than 10 times when compared with the conventional pinhole geometry with the same minimum momentum transfer.

Magnetoquantum oscillations of thermoelectric power in multisublevel quantum wires

The electron-diffusion and phonon-drag thermoelectric power (TEP) is investigated in a quantum wire as a function of the temperature, perpendicular magnetic field, and the electron density in the regime, where the conductivity is limited by elastic scattering. The wire is narrow in the growth direction with only the ground sublevel populated but is wide in the other confinement direction providing several occupied sublevels at zero field. Magnetic field causes depopulation of these sublevels, yielding quantum oscillations of the TEP and the conductance. An anomalous, large positive electron-diffusion TEP is obtained when the Fermi level lies slightly above a sublevel other than the ground sublevel due to the van Hove singularity at the subband edge. In contrast to the power-law temperature (T) dependence in higher dimensions, the phonon-drag TEP is proportional to $\mathrm{exp}(\ensuremath{-}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{F}}{/k}_{B}T)$ at low temperatures, where $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{F}}$ is the threshold phonon energy with a wave number ${q}_{\mathrm{F}}$ corresponding to the minimum momentum transfer for back scattering.

Exclusive semi-leptonic decays of bottom baryons

We calculate the exclusive semi-leptonic bottom baryon decays Λ b →Λ c +ℓ −+ v ℓ , Σ b → Σ c +ℓ −+ v ℓ and Σ b →Σ c ∗+ℓ −+ v ℓ in the spectator quark model. The helicity structure of the baryonic current transitions Λ b→ Λ c, Σ b →Σ c (Σ c ∗) is matched to the helicity structure of the free quark current transitions b → c at minimum momentum transfer q 2 = 0. The results are continued to q 2≠0 by pole dominated form factors. We obtain semi-leptonic baryonic decay rates which are close to the corresponding semi-leptonic mesonic decay rates.

Monte Carlo studies of high-transverse-energy hadronic interactions.

A four-jet Monte Carlo calculation has been used to simulate hadron-hadron interactions which deposit high transverse energy into a large-solid-angle calorimeter and limited solid-angle regions of the calorimeter. The calculation uses first-order QCD cross sections to generate two scattered jets and also produces beam and target jets. Field-Feynman fragmentation has been used in the hadronization. The sensitivity of the results to a few features of the Monte Carlo program has been studied. The results are found to be very sensitive to the method used to ensure overall energy conservation after the fragmentation of the four jets is complete. Results are also sensitive to the minimum momentum transfer in the QCD subprocesses and to the distribution of ${p}_{T}$ to the jet axis and the multiplicities in the fragmentation. With reasonable choices of these features of the Monte Carlo program, good agreement with data at Fermilab/CERN SPS energies is obtained, comparable to the agreement achieved with more sophisticated parton-shower models. With other choices, however, the calculation gives qualitatively different results which are in strong disagreement with the data. These results have important implications for extracting physics conclusions from Monte Carlo calculations. It is not possible to test the validity of a particular model or distinguish between different models unless the Monte Carlo results are unambiguous and different models exhibit clearly different behavior.

An optical scanning mechanism (OSMA) with minimum momentum transfer

The Development Model of an Optical Scanning Mechanism Assembly (OSMA) is described as being two equal inertial masses which collide with each other to minimize the momentum transfer to the satellite and other mounted instruments. The design criteria for the Mirror, the Compensating Inertia and other components are given. The details of the design are discussed and related test results are presented, which show the validity of the design concept for momentum compensation.

Electronic Relativistic Effect in Inner-Shell Ionization Cross Section and Electron Momentum Distribution

The inner-shell ionization cross section by charged-particle impact is expressed in the form of the momentum distribution of the target electron. Based on this approximation, the correction factor for the electronic relativistic effect is obtained as the ratio of the relativistic to nonrelativistic momentum distribution at the momentum corresponding to the minimum momentum transfer in the ionization process. It is found that for K -, L 1 - and L 3 -shell ionization cross sections the correction factor obtained from the momentum distribution is in good agreement with the exact relativistic calculation.

The lund monte carlo for e +e − jet physics

The lund monte carlo for e +e − jet physics

Screening and antiscreening by projectile electrons in high-velocity atomic collisions

The scattering amplitude for a projectile of nuclear charge ${Z}_{1}$ carrying $N$ electrons colliding with an atomic target with charge ${Z}_{2}$, evaluated in the first Born approximation using hydrogenic wave functions, is compared with recent experimental results. In the present approximation where the minimum momentum transfer ${t}_{min}$ is considered to be approximately independent of the final state of the projectile, the differential cross sections separate into a product of one term that depends only on the target times the square ${Z}_{1}^{2}(t)$ of an effective projectile charge. Here an analytic expression for ${Z}_{1}^{2}(t)$ is given for 2, 1, and 0 electrons. Some total ionization cross-section ratios are also given.

Empirical Coulomb Correction for K-Shell Ionization by Light Ions

Recent systematic comparisons of published K-shell ionization cross sections induced by protons or alpha particles show that the various data agree fairly well with each other and with the CPSSR theory by Brandt and Lapicki (1979), except at low energies. Assuming that the latter discrepancy is due to the Coulomb correction, we plot the experimental cross sections, divided by the theoretical PSSR cross sections, versus × = ?dqO?, where d is half the distance of closest approach (for a headon collision), hqo is the minimum momentum transfer for ionization, and ? is the binding/ polarization correction. If we approximate these empirical Coulomb corrections by exp(-?x), we find values ? between 1.4 and 1.7 (higher target atomic numbers Z2 corresponding to larger values); Brandt's correction CK(x) = exp(-x)/(1 + x/9) would, however, require ? = 1.11. The use of exact integration limits in the calculation of the theoretical cross section reduces ? by 0.1 but does not remove the discrepancy. Kocbach's calculation for Au targets describes the heavy target data well.

Coulomb deflection in ion-atom collisions

The Coulomb-deflection factor, defined as the ratio of the Coulomb to plane-wave Born cross sections, is derived for slow but classically moving ions, and found to be in agreement with the data for $K$-shell ionization. When the half distance of closest approach in a head-on collision, $d$, is comparable to the important impact parameters ($\ensuremath{\sim}\frac{1}{{q}_{0}}$, where ${q}_{0}$ is the minimum momentum transfer), this factor simplifies to $\mathrm{exp}(\ensuremath{-}\ensuremath{\pi}d{q}_{0})$ as it has been employed in the inner-shell-ionization theory. When the impact parameters are small on the scale of the projectile de Broglie wavelength, as they are in nuclear phenomena, the Coulomb-deflection factor tends to $\mathrm{exp}(\ensuremath{-}2\ensuremath{\pi}d{q}_{0})$. An extension of our results to screened Coulomb repulsion gives good agreement with the semiclassical calculations and the data for $K$-shell excitation in ${\mathrm{Ne}}^{+}$-Ne collisions.

Elastic π0 electroproduction above the resonance region

We report on the measurement of the process e + p → e + p + π 0 at energies above the resonance region. The pions are predominantly produced perpendicular to the electron scattering plane. The cross section shows a dip at the minimum momentum transfer. Both features are expected from comparison with photoproduction.

Relationship between the triple-Pomeranchukon coupling and the Pomeranchukon slope at minimum momentum transfer

A relationship is given that shows the proportionality of an integral involving the triple-Pomeranchukon coupling ${g}_{P}(t)$, where $t$ is the momentum transfer, to the Pomeranchukon slope ${\ensuremath{\alpha}}_{P}^{\ensuremath{'}}$. This relation involves the measurable total $\mathrm{pp}$ cross section and also a quantity determined from the elastic $\mathrm{pp}$ cross section. It is found that ${g}_{P}({t}_{0})$ may vanish, where ${t}_{0}$ is the minimum momentum transfer.

Confirmation of the A 2 splitting near threshold

The shape of the A 2 resonance has been measured in πp → pA 2 at 2.6 GeV/ c, i.e. near threshold, with A 2 produced at minimum momentum transfer. The results confirm, with a new method and instrument, the A 2 splitting found previously with the Jacobian-peak method.

Kinematics of momentum transfers in many-body final states

The kinematics of momentum transfers in many-body final states exhibit some surprising features. For example, the minimum momentum transfer from the beam to a final-state particle does not necessarily occur when the final-state particle travels forwards with maximum momentum. Some implications of these properties relevant to reaction mechanisms are discussed.

Production of heavy hypernuclei and scattering of argon ions in photographic emulsion

Scattering of argon ions in photographic emulsion was examined in order to learn what is the minimum transfer of momentum to a heavy emulsion nucleus (bromine or silver) that is necessary for it to record a visible track in emulsion. The results indicate that this minimum momentum transfer is about 400 MeV/ c. Since the average mass of the heavy spallation hypernuclei produced in the interactions of K − mesons of 800 MeV/ c momentum is not much different from the masses of the heavy emulsion nuclei, a similar momentum cut-off should be applicable to the reactions in which such hypernuclei originate.

Radiative Corrections to High-Energy Scattering Processes

A unified treatment of radiative corrections to a class of scattering experiments is presented. The experiments considered are those in which either (but not both) the scattered or recoil particle is detected. The recoil kinematics are properly treated and the calculation is simplified by retaining only terms of logarithmic order. The general results are applied to specific practical examples in which radiative corrections are likely to be important. Except possibly for the case of Compton scattering with nearly maximum or nearly minimum momentum transfer, the errors are estimated to be less than 2% of the cross section.

High-Energy Interference Effect of Bremsstrahlung and Pair Production in Crystals

With the use of monocrystalline targets for bremsstrahlung and pair production experiments, interference phenomena are expected to occur which will markedly change the $\ensuremath{\gamma}$-ray spectrum as well as the pair energy distribution, for certain angles giving enhancement of radiation and pairs. The effect increases with energy; it sets in at $\ensuremath{\delta}\ensuremath{\lesssim}{n}_{0}(\frac{2\ensuremath{\pi}}{a})$, where $\ensuremath{\delta}$ is the minimum momentum transfer to the target atoms, $a$ the lattice constant, and ${n}_{0}$ a number of the order 2 or 3. This corresponds to \ensuremath{\sim}200-Mev primary energy for bremsstrahlung, \ensuremath{\sim}1 Bev for pair production. The effect is confined to angles between the primary beam and a line of atoms, of order $\ensuremath{\theta}\ensuremath{\lesssim}(\frac{{a}_{\mathrm{screen}}}{{\ensuremath{\lambda}}_{C}})(\frac{m{c}^{2}}{E})$. The temperature motion of the lattice reduces the interference effect to some extent. The Born approximation was used for the quantitative analysis of the problem.