Total Momentum Transfer Research Articles

Electron scattering of electrons in helium

The authors report differential elastic cross section measurements for electron scattering in helium at incident electron energies of 7.5, 10.0, 12.5, 15.0 and 17.5 eV and at scattering angles of 0-130 degrees . The measurements were made using a new type of electron spectrometer employing co-axial cones to analyse the electrons. A phaseshift analysis is applied to the data and the results are compared with recent theoretical and experimental work. Total elastic and momentum transfer cross section values are also derived from the present measurements and compared with recent measurements and calculations.

The j-dependence of the ( 19F, 16O) reaction

The total angular momentum transfer ( j) dependence was studied for orbital angular momentum transfers l = 1, 2, and 3 in the ( 19F, 16O) reactions on 28, 30Si and 60Ni. In contrast to the strong j-dependence for the l = 2 transitions to 31, 33P states, no distinct j-dependence was found for the l = 1 and l = 3 transitions to 63Cu states. Previously reported results for the 28 Si( 19 F, 16O) 31 P reaction were re-analyzed using optical-potential sets which fit the elastic-scattering data for both the entrance and exit channels. Results of DWBA calculations without use of spin-orbit potentials were found to be out of phase with the data for all l-transfers and the j-dependence could not be reproduced. Both of these problems were alleviated by including spin-orbit forces in the optical potentials. However, a good fit to the 28Si( 19F, 16O) 31P data was obtained only if the optical potentials that fit the elastic scattering data were modified for the exit channel.

On the net forces produced by surface-mounted obstacles

Numerical calculations of the forces involved in Ekman layer flow past three-dimensional topography are presented. The forces are obtained from finite-difference solutions of the Navier-Stokes equations. The results confirm expectations from earlier two-dimensional work that many flows produce no significant change in total momentum transfer between the fluid and the surface. Only flows generating some form of trailing vortex system appear capable of changing the total force on the lower boundary. The effects of Ekman boundary layer instabilities, and their interaction with topography, are also discussed.

Complete fusion and transfer reactions induced by 273 MeV 40Ar on 159Tb

The nuclear reactions induced by 273 MeV 40Ar ions on a 159Tb target have been studied using recoil techniques and off-line X-ray spectrometry. The heavy products from fusionevaporation, fusion-fission, and transfer reactions can easily be separated on the basis of charge identification by X-ray spectrometry. The corresponding angular and range distributions are typical of each process. For each value of the atomic number, the average mass of the evaporation residues was determined with an uncertainty of ± 2 mass units (i.e.±1 %). The data were consistent with the assumption that 9±2 particles (nucleon and possibly some α-particles) were evaporated by the compound nucleus. The range measurements give results which agree with calculated values based on the total momentum transfer hypothesis within ± 8 %. The c.m. angular and energy distributions of transfer reaction products are typical of deep inelastic transfer reactions, with a contribution from partially damped events. The comparison of experimental data with the results of a calculation based on the model of Ngoˆand Hofmann in which statistical fluctuations are explicitly taken into account, indicates that the model reproduces correctly the position of the angular distribution maxima, for one- and two-charge transfer reactions, but underestimates the width of the angular distributions. Moreover, no transfer of more than two charges from the projectile to the target is predicted by this model while significant cross sections are observed experimentally.

Rate coefficients and inelastic momentum transfer cross sections for electronic excitation of N2 by electrons

Rate coefficients, as a function of the electron temperature, have been determined from the integral cross sections for excitation of the 19 singlet and triplet electronic states of N2 within 14.2 eV of the ground state. For electron temperatures less than 10 eV, the rates for excitation of the A 3Σ+u, B 3Πg, W 3Δu, and a 1Πg are all greater than that for excitation of the C 3Πu state. The differential cross sections for excitation of these same electronic states were also used to calculate the inelastic momentum transfer associated with the excitation of these states. The total momentum transfer cross section for electrons in N2, as a function of the electron energy, was obtained by adding the inelastic momentum transfer to that associated with elastic scattering. Inelastic momentum transfer accounts for about 25% of the total momentum transfer above 15 eV. Over the energy range 20–60 eV, inelastic scattering contributes 20–25% to the total N2 electron scattering cross section. The total scattering cross section obtained here is in good agreement with a recent direct measurement of this cross section.

A study of the [formula omitted] reaction at 20.7 and 29 MeV

Angular distributions of differential cross section and vector analyzing power of the 12 C( dα) 10 B reaction have been measured at bombarding energies of 20.7 and 29 MeV for excitation energies up to 5 MeV. The reaction was studied at scattering angles ranging from 17° to 140° c.m. The reaction exhibits differential cross sections of the order of 1 mb sr and vector analyzing powers A y approaching unity in some cases, thus making it attractive as a beam polarization monitor for polarization studies. Zero-range DWBA calculations were carried out using both cluster transfer and two-particle form factors. Fairly good description of the shapes of the cross-section angular distributions is obtained while the trends of the vector analyzing power angular distributions are correctly described only in some cases. In both the data and the calculations, A y ( θ) shows a stronger dependence upon the total angular momentum transfer J than does dσ(θ) dΩ .

Low energy dependence of momentum transfer rate constants of rare gas atomic ions in their parent gases: Evidence for the importance of a polarization potential at near thermal energies

The total momentum transfer rate constants k m for rare gas atomic ions in their parent gases have been measured versus ion energy from ∼0.3 eV to 1.1 eV(He +), 4.3 eV(Ne +), 1.5 eV(A +), 0.6 eV(Kr +) and 0.5 eV(Xe +). The measurements were made by an ion cyclotron resonance collisional line broadening method. For all the rare gases it was found that k m initially decreases with increasing ion energy, passes through a minimum near 0.5 eV and then increases with ion energy. From a consideration of the relation of the interaction potentials of ion—atom systems with the energy dependence of the total momentum transfer rate constant, we conclude that the initial decrease in k m with ion energy indicates the importance of a polarization potential coupled to a repulsive and/or a charge exchange potential.

Supernovae in close binaries

The impact of a supernova shell onto 2.82M⊙ and 20.0M⊙ main-sequence stars is investigated for various initial orbital separations, and various supernova shell masses and velocities. The inelastic collision between the star and the supernova shell, the shock propagation into the companion star, and other forms of momentum transfer such as the rocket effect are considered. The total momentum transfer due to the supernova is insufficient to eject the companion from the binary as long as the companion retains most of its mass, regardless of the initial orbital separation. Ejection of the companion may occur if the companion is nearly destroyed. Even in contact binaries destruction does not necessarily occur, and if the orbital separation exceeds 1012 cm, destruction of the companion becomes quite unlikely.

Longitudinal momentum transfers in the multiperipheral model

The inclusion of longitudinal momentum transfers in the multiperipheral model is investigated. As recently pointed out by Jadach and Turnau, these longitudinal momentum transfers, if present, have a very large effect on properties of the model. In this paper we find that data rules out such effects. Furthermore, if the longitudinal momentum effects were present, they would in no way solve the serious problem with the multiperipheral model, that average multiplicity and elastic slope ought to be proportional, but experimentally are not. A multiperipheral model using transverse momentum transfers has fewer phenomenological difficulties than one using total momentum transfer.

Elastic Scattering and Rotational Excitation of Molecular Hydrogen by Low Energy Positrons

The adiabatic nuclei approximation is used to study low energy positron collisions with hydrogen molecules. The interaction of the positrons with the hydrogen molecules is represented as a superposition of electrostatic and polarization potentials. Total and differential elastic and momentum transfer cross sections are calculated. The effect of small variations in the potentials, and the convergence of the partial wave expansion are discussed. The annihilation rate of the positrons is calculated with and without incorporating the effect of distortion of the electron cloud by the incoming positrons. Rotational excitation cross sections, both differential and total, are presented. The results are compared, where possible, to recent similar two-center calculations of Hara, and experimental results of Coleman et al.

Semi-classical interpretation of the vector analyzing power in sub-coulomb neutron-transfer reactions

Sub-Coulomb neutron-transfer reactions are considered in a classical model in which the incident and outgoing projectiles follow Coulomb scattering trajectories with coincident turning points. The dependence of the vector analyzing power on bombarding energy and Q-value, and the angular dependence of the cross section are explained. The sign of the analyzing power is related directly to the total angular momentum transfer. Predictions of the model for ( d , p ) and ( d , t ) reactions are compared with DWBA calculations employing only Coulomb distortions. Limitations of the model are discussed.

On the meaning of Goldstone’s theorem

It is shown that when a continuous symmetry is broken, a polar singularity arises in the vertex part at zero total energy and momentum transfer. Such singularity has as a consequence (and is in turn entirely predictable as a consequence of) the existence of a continuous manifold of degenerate ground states, and arises from the possibility of freely « rotating » the system among such states. Whether or not it is possible to infer the existence of a bosonlike excitation with frequencyΩ(q) such that\(\mathop {\lim }\limits_{q \to 0} \)Ω(q)=0 depends on the range of the forces.

Calculation of cross-sections for electron-helium collisions

The elastic scattering of electrons from helium is studied using analytic procedures for representing the electronic wavefunction. Total elastic and momentum transfer cross-sections are calculated and compared with experiment. The first scattering resonance in the elastic channel is examined.

Use of polarized deuterons to determine the total angular momentum transfer in stripping reactions

Polarized deuterons have been used to initiate stripping reactions to determine vector analysing powers for transitions for which the orbital angular momentum l and total angular momentum j of the captured neutron are known. Measurements have been performed at a deuteron energy of about 8 MeV for the target nuclei 9Be, 12C, 24Mg, 40Ca and 52Cr. For a given l, there is pronounced difference between the vector analysing powers for j = l+ 1 2 and j = l− 1 2 reactions. The measured vector analysing powers are compared with predictions based on the distorted-wave Born approximation. Effects of variations of optical parameters are discussed. If optical potentials which fit the elastic scattering data are used, the measured vector analysing powers are reproduced for the intermediate-weight nuclei.

Use of Polarized Deuterons to Determine the Total Angular Momentum Transfer in Stripping Reactions

Abstract Polarized deuterons have been used to initiate stripping reactions to determine vector analysing powers for transitions for which the orbital angular momentum l and total angular momentum j of the captured neutron are known. Measurements have been performed at a deuteron energy of about 8 MeV for the target nuclei 9 Be, 12 C, 24 Mg, 40 Ca and 52 Cr. For a given l , there is pronounced difference between the vector analysing powers for j = l+ 1 2 and j = l− 1 2 reactions. The measured vector analysing powers are compared with predictions based on the distorted-wave Born approximation. Effects of variations of optical parameters are discussed. If optical potentials which fit the elastic scattering data are used, the measured vector analysing powers are reproduced for the intermediate-weight nuclei.

Stopping of Energetic Copper Ions in Aluminum

By means of differential-range experiments, we have measured the average ranges and range straggling of 24-min ${\mathrm{Cu}}^{60}$ and 3.3-h ${\mathrm{Cu}}^{61}$ in Al. These species were produced with initial recoil energies from 3 to 18 MeV by bombardment of thin targets of ${\mathrm{Co}}^{59}$ and ${\mathrm{Mn}}^{55}$ with ${\mathrm{Li}}^{6}$, ${\mathrm{B}}^{10}$, and ${\mathrm{B}}^{11}$ heavy-ion beams. The average ranges increase smoothly with recoil energy and the distributions in range about the average values follow a Gaussian relationship. The experimental range-energy data are in good agreement with theoretical expectations, assuming total momentum transfer over the full energy region investigated. We conclude that the nuclear processes which produced the recoiling ions are pure compound-nucleus reactions. Although theory and experiment yield consistent average-range values, the stopping-theory predictions for range straggling are much smaller than experimental estimates of the straggling inherent in the stopping process. The source of the discrepancy is discussed in terms of the relative contributions of electronic and nuclear stopping.

Recoil Range Evidence for the Compound-Nucleus Mechanism in Reactions between Complex Nuclei

We have measured the recoil-range distributions of 4.1-h ${\mathrm{Tb}}^{149}$ produced in a variety of complex nuclear reactions. The targets were ${\mathrm{Pr}}^{141}$, ${\mathrm{Ce}}^{140}$, ${\mathrm{La}}^{139}$, and ${\mathrm{Ba}}^{138}$; projectiles were ${\mathrm{C}}^{12}$, ${\mathrm{N}}^{14}$, ${\mathrm{N}}^{15}$, ${\mathrm{O}}^{16}$, ${\mathrm{O}}^{18}$, ${\mathrm{F}}^{19}$, and ${\mathrm{Ne}}^{20}$. In every case the range distributions could be fitted to a Gaussian function. The average range values give evidence for total momentum transfer, and the range straggling is consistent with nuclear evaporation. We conclude that these reactions are pure compound-nucleus reactions. Excitation energies were approximately 50 to approximately 150 MeV, corresponding to incident energies of 5 to 10.4 MeV per nucleon.

Plasma Dynamics in Comets I. Plasma Instability.

view Abstract Citations (20) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Plasma Dynamics in Comets I. Plasma Instability. Hoyle, Fred ; Harwit, Martin Abstract Biermann has suggested that ionized gas clouds in comet tails are accelerated by collision with a stream of solar particles In Paper I we treat the field-free case, in order to establish conditions for which cometary plasma acceleration may be enhanced by plasma instability. We derive a general criterion for instability of plasmas of arbitrary ionic composition and velocity distribution. This result is applied to determine the stability of a number of different combinations of cometary gas densities and solar particle densities and temperatures Electron-ion instability is able to grow for a brief period if the solar electrons are cool enough. However, this is a transient effect. As soon as the electrons lose their translational velocity, their temperature becomes high enough to restore plasma stability, even for succeeding generations of inflowing electrons. The total momentum transfer is negligibly small compared with the observed momenta of cometarytail ions We conclude that plasma instability does not appreciably contribute to tail plasma acceleration. In Paper II we examine the effect of transverse magnetic fields carried by a solar stream. We find that many features of comets can be satisfactorily explained if magnetic fields are present Publication: The Astrophysical Journal Pub Date: May 1962 DOI: 10.1086/147330 Bibcode: 1962ApJ...135..867H full text sources ADS | Related Materials (1) Part 2: 1962ApJ...135..875H

Integral Representations of Two-Point Functions

An integral representation for a general matrix element of two field operators between eigenstates labelled by an arbitrary number of momenta is presented. This representation is conveniently parametrized over a set of invariants related to the total momentum and momentum transfer, and explicitly incorporates spectral conditions. Physically interesting dispersion relations for off-forward scattering cannot be obtained from this representation alone.

Momentum distribution of nucleons in the nuclear surface

The results of the 40 MeV (p, 2p) experiments of Griffiths and Eisberg are analysed on the basis of a model for the total momentum transfer. Assuming two-body collisions and the impulse approximation and representing the momentum distribution of bound protons by a Fermi distribution whose maximum momentum is p f , it is almost certain that 0.5 MeV < p f 2/2 m < 1.5 MeV. Assuming a semiclassical model for the reaction it is shown that the events observed in this experiment occur in the extreme nuclear surface. Thus the experiment is strong evidence in support of the Thomas-Fermi approximation for nucleons in a finite nucleus. Representing the main bulk of the nucleus by an absorbing sphere, it is shown that the observed ratio of (p, 2p) to (p, p′) events is consistent with the assumption that direct interactions all proceed from initial two-body collision.