Small Energy Transfer Research Articles

A new system of gravity spectrometer with fall focussing of ultra cold neutrons

A high resolution gravity spectrometer for ultra cold neutrons (UCN) and the UCN source of a supermirror turbine are described. The possibilities of the fall focussing of UCN emitted into the 4π or 2π directions to a localized point of a sample or of a detector are analysed, and as a result it is shown that a focussing mirror arranged in the form of a modified ellipsoid can be used both as a monochromator and as an analyser with the highest geometrical efficiency for UCN. Numerical calculations for a typical case of the proposed spectrometer with an equivalent radius of 50 cm gave an energy resolution of ∼2 x 10 8 eV in the optimized arrangement for a neutron velocity of 5 m/s. Thus, the proposed system can be used for high resolution experiments of incoherent scattering or low- q coherent scattering with small energy transfer of ε ≲ μeV.

Effects of electron-electron collisions with small energy transfers on quantum localisation

The effect of electron-electron collisions with small energy transfers on the quantum electron localisation has been studied. It is shown that in one and two dimensions such collisions determine the temperature dependence of the conductivity. In three dimensions the contribution of processes with small energy transfers is less than that of the usual electron-electron collisions, in which the energy transfer is of the order of the temperature T. The criterion for the quasiparticle description of electrons in metals in different dimensions is discussed. It is shown that for d>or=2 this description is valid, while for d=1 it is not correct. The effect of noise in the external circuit on quantum corrections to the conductivity is studied.

Neutron scattering from paramagnetic bccHe3

The dynamic form factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}},\ensuremath{\omega})$ of bcc solid $^{3}\mathrm{He}$ in the paramagnetic phase is calculated using the self-consistent-phonon (SCP) theory for comparison with proposed neutron scattering measurements. The magnitude of $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}},\ensuremath{\omega})$ is predicted to be 2-3 times smaller than that observed in liquid $^{3}\mathrm{He}$ at saturated vapor pressure but comparable with that expected in liquid $^{3}\mathrm{He}$ near the melting line. Longitudinal phonons should be observable at low scattering wave vectors $Q\ensuremath{\lesssim}0.8$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. Transverse phonons will be more difficult to observe since larger scattering wave vectors outside the first Brillouin zone are usually required to observe transverse phonons. At $Q\ensuremath{\gtrsim}2.5$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}},\ensuremath{\omega})$ is dominated by scattering from multiphonons and bcc $^{3}\mathrm{He}$ responds like a gas of weakly interacting particles. Collective spin excitations or critical scattering will be observable only at very small neutron energy transfers (\ensuremath{\sim} 0.1 \ensuremath{\mu}eV) and at temperatures near the spin-ordering temperature (\ensuremath{\sim}1 mK). Comparison with experiment will provide a test of the SCP theory and of the assumption used here to separate the nuclear and spin dynamics.

Intramolecular low-frequency vibrations in lysozyme by neutron time-of-flight spectroscopy.

AbstractHigh‐resolution neutron time‐of‐flight (TOF) spectra were measured for partly deuterated hen egg‐white lysozyme in solution with and without N‐acetyl‐glucosamine inhibitor bound to the cleft, and in polycrystalline form. Weak but reproducible bands occur at frequencies between 25 and 375 cm−1. The bands were tentatively assigned on the basis of previous results for homopolypeptides. At very small energy transfers (between about 1 cm−1 and 40 cm−1), the TOF spectra show a dependence both on inhibitor binding and crystalline environment. This is interpreted in terms of conformational flexibility.

Reactive scattering of a supersonic oxygen atom beam : O+C3F7I

Reactive scattering of O atoms with C3F7I molecules has been studied at an initial translational energy E = 28 kJ mol-1 using a supersonic beam of O atoms seeded in He buffer gas. Velocity distributions of OI product were measured by cross-correlation time-of-flight analysis. A full contour map was obtained for the differential reaction cross-section which shows essentially isotropic scattering. Only a single velocity scan in the direction of the laboratory centroid vector could be measured using O atoms seeded in Ne buffer gas at an initial translational energy E = 14·6 kJ mol-1 due to the low signal of OI reactive scattering. The product translational energy distributions for both sets of measurements were found to be skewed with respect to the initial translational energy distributions indicating significant energy transfer to internal modes of the reaction products. However the product translational energy distributions extend to much higher energies than those predicted for a long-lived collision complex. Comparison of these results with previous measurements on the O + CF3I, C2F5I reactions indicates increasing energy transfer from initial translational energy to vibrational and torsional modes of the perfluoroalkyl radical along the series CF3, C2F5, C3F7. However this appears to involve primarily bonds close to the ruptured C-I bond in the C3F7 radical. These results are in accord with a previously proposed mechanism involving hard sphere scattering at small impact parameters and energy transfer to low frequency modes of the perfluoroalkyl radical.

Low yield sputtering of monocrystalline metals

Sputtering of monocrystalline metals by light noble gas ions is studied experimentally and theoretically at low primary ion energy. Evidence is found for a multiple collision process in which surface atoms are sputtered by backscattered ions. The introduction of the maximum recoil energy E M in the sputtering yield relation enabled us to describe sputtering when small energy transfers are involved.

Many-body field theoretic framework for inelastic pion-nucleus scattering

We consider inelastic scattering of pions from nuclei using many-body quantum field theory methods. We find that, in an inelastic amplitude for small energy transfer, one can separate out effects of particle-hole correlations in the final nuclear state. The ratio of π + and π − inelastic cross sections can differ substantially from the analogous ratio for free πN scattering.

Diagrammatic approach to pair production in slowly varying and constant fields

We consider the problem of pair creation in slowly varying and essentially constant fields using directly momentum-space Feynman diagrams for the pair production amplitude. When the production occurs via many interactions with small energy transfer, the problem can be viewed as an integration on paths in energy space. An estimate via the integral over the optimal path given by Hamilton's principle, a fuller Lagrangian equation, is introduced and discussed. The existence of such a classical path reflects in an asymptotic behavior such as $n!{c}^{n}$ of high-order Feynman diagrams, which in a formal Borel-type summation yields the essentially singular tunneling behavior in constant fields.

Direct model fitting of uncorrected time-of-flight data from quasi-elastic neutron scattering experiments

A new approach to the analysis of quasi-elastic neutron scattering data from time-of-flight spectrometers is described. The uncorrected time-of-flight data are simulated directly by a model containing relatively few variable parameters. The time-of-flight model, the full derivation of which is given, provides a general representation of the composite scattered neutron profile in the quasi-elastic (small energy transfer) region, applicable to most types of microscopic diffusive motions having sufficiently short correlation times. Though the general model is not in all cases a directly physical description of the motion, it is frequently adequate to completely describe the data. Its parameters therefore contain all the available information, and moreover lend themselves readily to quantitative comparisons with more realistic models. The advantages of the direct fitting method over conventional analysis procedures [in which the data are transformed into S( Q, ω) or I( Q, t) forms] are that the correct statistical weight of each experimental point is preserved, and that any errors inherent in transforming the data are avoided. The accuracy of the information extracted using this technique (as a function of experimental resolution and counting statistics) is discussed. The results of tests on artificially generated spectra (with known parameters) are given.

Fragmentation of relativistic heavy ions

A simple explanation of the phenomena observed when relativistic heavy ions are fragmented upon colliding with a variety of target nuclei is developed. Explanations are provided for the approximately isotropic angular distribution of each fragment type, for the small momentum and energy transfer to the projectile nucleus, for the independence of the branching ratio with respect to the target nucleus and for the approximate energy independence.

Spin susceptibilities and the theory of itinerant-electron antiferromagnetism

Abstract This article investigates the equilibrium states of antiferromagnetic itinerant-electron systems in the Hartree-Fock approximation. As a result, the spin susceptibilities are determined in the random phase approximation. The lowlying collective excitations are then obtained by finding the poles of these susceptibilities. We start by giving a brief review of the Hartree-Fock procedure and by indicating how the susceptibilities are obtained. The density matrix approach, where the ground state is interpreted as that minimizing the energy, is used throughout. Using an effective Coulomb interaction of the Hubbard type we consider two distinct systems: a one-band system with an incommensurate spin density wave in its ground state, and a many-band simply commensurate model for f.c.c. manganese. The first of these is such that the band structure and resulting susceptibilities can be obtained explicitly. The spin-wave energies and wave-vectors are found by a careful, small energy and momentum transfer, ex...

Collisional-radiative transfer between Rydberg states of helium and electronic recombination ofHe+

We report detailed spectroscopic measurements of light emission and excited level populations in a pure-helium afterglow at a pressure of 2.03 Torr. The free-electron temperature could be varied by microwave heating. Electron density ${n}_{e}$ and temperature ${T}_{e}$ were measured by precision microwave interferometry and they range from 5 \ifmmode\times\else\texttimes\fi{} ${10}^{9}$ to 3 \ifmmode\times\else\texttimes\fi{} ${10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ for ${n}_{e}$ and from 300 to 600\ifmmode^\circ\else\textdegree\fi{}K for ${T}_{e}$. Rydberg states of neutral helium near the bottleneck for collisional-radiative (CR) recombination were perturbed in a well-controlled manner by photoionization with 10.6-\ensuremath{\mu}m photons. Our experimental data are consistent with a CR recombination scheme with simultaneous stabilization by collisions with free electrons and with neutral helium atoms. They establish the fact that the Gryzi\ifmmode \acute{n}\else \'{n}\fi{}ski formalism for electron-impact-induced transitions between bound rydberg states of high principal quantum number seriously overestimates the probability of collisions with small energy transfers. This study gives also experimental indications of what appears to be neutral-stabilized CR recombination of an atomic ion, ${\mathrm{He}}^{+}$. The experimental recombination rate coefficient is well represented over the range of parameters covered at 2.03 Torr by $\ensuremath{\alpha}({\mathrm{cm}}^{3} invsec)=3.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{T}_{e}^{\ensuremath{-}1.9}+6.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}{T}_{e}^{\ensuremath{-}2.18}{{n}_{e}}^{0.37}+3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}{T}_{e}^{\ensuremath{-}4.5}{n}_{e}$, in reasonable agreement with available theories.

Erratum: ’’Singlet–singlet electronic energy transfer: Dipole–dipole and exchange contributions’’

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Diffusion of hydrogen in the β-phase of pd-H studied by small energy transfer neutron scattering

The diffusion of hydrogen in β-PdH x has been studied by quasielastic neutron scattering. It is shown that the diffusion occurs through jumps between adjacent octahedral interstitial sites. The observed integrated quasielastic intensities cannot be described by a simple Debye-Waller factor. The phase transition from the β-phase to the α-phase has also been studied. No dramatic changes in the scattering patterns were observed. It is concluded that the diffusion mechanism is remarkably similar for the low concentration α-phase and the high concentration β-phase.

Quasiparticle scattering in Fermi fluids

The scattering of quasiparticles in a normal Fermi fluid is analyzed within the framework of Landau's kinetic theory, and a generalized Bethe-Salpeter equation for the scattering amplitude is derived. This integral equation accounts for both large and small momentum and energy transfers ; in the forward-scattering limit it reduces to Landau's well-known equation. An explicit expression for the scattering probability is also derived. An off-diagonal generalization of the quasiparticle interaction function f is introduced and its calculation from microscopic theory is discussed. The results are applied to an explicit calculation of the scattering amplitude in a dilute hard-sphere Fermi gas, to second order in the scattering-length parameter kFas, and the calculation is shown to be consistent with symmetry requirements for the scattering of fermions.

Momentum Distributions of Isotopes Produced by Fragmentation of RelativisticC12andO16Projectiles

The fragment momentum distributions in the projectile rest frame are, typically, Gaussian shaped, narrow, consistent with isotropy, depend on fragment and projectile, and have no significant correlation with target mass or beam energy. The nuclear temperature is inferred from the momentum distributions of the fragments and is approximately equal to the projectile nuclear binding energy, indicative of small energy transfer between target and fragment.

Diffusion of hydrogen in the β-phase of PdH studied by small energy transfer neutron scattering

Diffusion of hydrogen in the β-phase of PdH studied by small energy transfer neutron scattering

Generalized oscillator strengths for the ionization of helium by protons, calculated with the classical three-body collision theory

Differential cross sections and generalized oscillator strengths fE(q) for ionization of helium by 100 and 300 keV protons have been calculated, using a classical three-body collision theory, in which the momentum transfer to the atomic nucleus has been eliminated. Comparisons are made with the results of the scaled first Born approximation and the binary encounter theory. The calculated generalized oscillator strengths depend upon the energy of the incident proton. There is a marked difference between the present results and the other two theories for small energy transfers.

Design of Sensitive Photographic Materials for the High-Voltage Electron Microscope

Effective application of the high-voltage electron microscope to a wide variety of biological studies has been restricted by the radiation sensitivity of biological systems. The problem of radiation damage has been recognized as a serious factor influencing the amount of information attainable from biological specimens in electron microscopy at conventional voltages around 100 kV. The problem proves to be even more severe at higher voltages around 1 MV. In this range, the problem is the relatively low sensitivity of the existing recording media, which entails inordinately long exposures that give rise to severe radiation damage. This low sensitivity arises from the small linear energy transfer for fast electrons. Few developable grains are created in the emulsion per electron, while most of the energy of the electrons is wasted in the film base.

Model for grouping small energy transfers in electron transport theory

In an analysis of a “condensed-collision” scheme, in which all the interactions of an electron between two successive collisions involving the production of fast secondary particles are “condensed,” approximate analytic expressions are derived for the Green's function describing multiple scattering of electrons in remote collisions. Distributions required for simulating the changes in the electron parameters as a result of multiple scattering are given.