Scattering response of a phonon damped harmonic oscillator

We calculate the response for scattering off a particle bound by an isotropic harmonic force and damped through hybridization with a phonon bath. An exact expression for the scattering response is studied numerically to provide a detailed picture of its dependence on wave vector, frequency, temperature and phonon hybridization strength.     

Neutron excitation of landau and collective modes in a magnetized plasma

Summary The response function for magnetic neutron scattering off electrons forming a one-component plasma, or jellium model, subject to a steady magnetic field, is calculated in the semi-classical limit in which Boltzmann statistics apply to the electron states. A complete expression for the response of an ideal plasma is given in a compact, closed form, amenable to numerical investigation, and including the dependence on electron parameters such as effective mass and gyromagnetic ratio. Effects due to the Coulomb interaction are discussed within the limitations of the random phase approximation. The theoretical results are used to predict the conditions that must obtain for the observation of neutron excitation of Landau and collective modes.

---

Riassunto La funzione di risposta per lo scattering magnetico dei neutroni dagli elettroni che forma un plasma ad un componente, o modello di jellio, soggetto ad un campo magnetico fisso, è calcolata nel limite semiclassico nel quale la statistica di Boltzmann si applichi agli stati elettronici. Si dà un’espressione completa per la risposta di un plasma ideale in una forma compatta e chiusa adatta alla ricerca numerica e che include la dipendenza dai parametri elettronici come la massa efficace ed il rapporto giromagnetico. Si discutono gli effetti dovuti all’interazione di Coulomb entro i limiti dell’approssimazione di fase random. I risultati teorici sono usati per prevedere le condizioni che devono essere ottenute dall’osservazione dell’eccitazione dei neutroni di Landau e dei modi collettivi.

     

Linear spin dynamics of incommensurably modulated magnets

The linear spin dynamics of an incommensurably modulated Heisenberg magnet, with a single-Q structure, is studied using an analytic technique designed to calculate the transverse spin response observed in neutron scattering. Results are presented for a specialQ and also special scattering wave vectors. An approximate expression is proposed that is fully determined by the exchange and anisotropy parameters. The spin response is studied as a function ofQ and shown to be distinctly different from the case in which it is exhausted by a single collective spin oscillation.     

Electron excitation in atoms and molecules by neutron-nucleus scattering

The quantum theory of electron stimulated desorption developed in two preceding papers is presented in a WKB like form and is applied to the desorption of hydrogen and oxygen from tungsten. Retunnelling processes are taken into account and manifest themselves in an imaginary part in the potential of the desorbing particles. This imaginary part together with a non zero width of the wavepacket leads to quantum effects in the motion of the desorbing particles modifying the corresponding classical results of the reduction factor and of the energy conservation. The modifications turn out to be quite large for hydrogen as well as for oxygen increasing the reduction factor by several orders of magnitude. The isotope effect also is changed appreciable. The parameters of the model are determined from corresponding experimental data such as vibrational levels of the adsorbates, the energy distribution of the desorbing particles and the reduction factor.     

Scaling properties of models of nonequilibrium phenomena

The renormalization group method proposed by 't Hooft is developed for the study of scaling properties of some models of nonequilibrium phenomena. For one of two models studied in detail, the Langevin equation for the random variables contains a bilinear streaming velocity and the stationary probability distribution is Gaussian. The time-dependent Ginzburg-Landau model is chosen as a second example because it illustrates the advantage of the 't Hooft method of not having to specify a particular renormalization point. The scaling exponents for a model of the liquid-gas phase transition are calculated in lowest order to illustrate application of the method to a multifield system.     

Neutron-photon studies of condensed matter

A theory of simultaneous photon absorption and inelastic neutron scattering is developed by treating the photon and neutron-matter interactions perturbatively. The leading-order mixing between the interactions shows that the neutron scattering cross-section is proportional to the dynamic structure factor (or Van Hove function) evaluated at an energy that is enhanced by the photon energy. The photon induced modification of the scattering vector is negligible. Thus, the proposed technique affords the possibility of measuring the dynamic structure factor at large energies and modest wavevectors which is a domain that is usually difficult to access because of kinematic constraints. The theory is developed in detail for some models of nuclear and magnetic systems. The results show that, in most cases, the experiments are likely to demand the use of very high intensity light sources. A particularly promising application appears to be in the study of electron plasmas since, using readily available pulsed lasers, the neutron cross-section is comparable with that for pure magnetic scattering.     

Electricity and Magnetism,Volume 1: Third Edition,Electricity and Magnetism,Volume 2: Third Edition,by B.I. Bleaney and B. Bleaney

During the last decade the term ‘spin glass’ has become prominent in the literature on magnetism. It refers to magnetic alloys where the spins on the impurities become locked or frozen into random orientations below a characteristic temperature T ₀. In this article the properties of spin glasses are described with particular reference to the two archetypal examples AuFe and CuMn. Interest in spin glasses was mainly stimulated by some a.c. susceptibility measurements which showed sharp, cusp-like peaks, accurately defining T ₀ and suggesting that some type of phase transition was occurring. The Mossbauer effect and the anomalous Hall effect also showed clear features at T ₀ supporting this viewpoint. But measurements of the electrical resistivity and ‘specific heat’, here usually meaning the molar heat capacity, also the remanence, magnetic hysteresis and time-dependent effects observed in spin glasses were difficult to reconcile with a phase transition approach. This article discusses the results obtained from the very wide variety of experimental techniques which have been used to investigate spin glasses, and also deals with some of the important theoretical concepts which have arisen out of these studies. Then follows a short account of the many systems which have been found to exhibit spin glass behaviour and which suggest that it is a widespread magnetic state of matter. Lastly, an example is given which shows that some of the ideas of spin glasses are applicable to problems outside the sphere of magnetic alloys.     

The theory of neutron scattering from mixed harmonic solids

In the intermediate valent cerium alloys Ce_1–xY_xPd₃, Ce(Pd_1–xRh_x)₃ and Ce(Pd_1–xAg_x)₃ the Gd³⁺-ESR shows a non-linear increase of the linewidth H(T) in the temperature range 4.2KT300K. The deviation from the linear Korringa law can be described by a reduced conduction electron density of states at the Gd site (which is a Ce lattice site) in the energy range E _4f (=width of the Ce 4f states). This supposition allows a determination of E _4f from the H(T)-data. For CePd₃:Gd³⁺ we find E _4f=(650±100) K. E _4f increases with Y- and Rh-concentration and decreases with Ag-concentration.     

Magnetic neutron-electron scattering; use of thef-sum rule to assess the effect of electron correlations,lattice interaction and magnetic field

We have calculated thef-sum rule for magnetic neutron scattering off electrons. Correlations alter the cross-section significantly at intermediate scattering vectors. Field induced effects are most significant at small scattering vectors, and the sum rule diverges in the limit of zero scattering vector. This feature is attributed to the field induced coupling of neutrons to the lowest energy Landau level and the collective density oscillation (hybrid mode). Our interpretation is based on an RPA calculation of the response function for neutron scattering from a magnetized plasma. The contribution to the cross-section from the electron-phonon interaction is also assessed, and it is found to increase with decreasing scattering vector.