Rare earth hyperfine interactions studied by perturbed angular correlations

This paper reviews the application of the perturbed angular correlation (PAC/D) technique to studies of rare earth hyperfine interactions. First, PAC/D measurements of the interaction of rare-earth nuclei with the large hyperfine fields of their own partially filled 4f electronic shell are discussed. It is shown that PAC/D spectroscopy is particularly useful for the investigation of 4f spin relaxation in liquid and solid environments, and for the study of the formation and stability of 4f magnetic moments in metallic hosts. The second part of the paper deals with the static hyperfine interaction of non-rare-earth impurity nuclei in the hexagonal, magnetically ordered rare-earth metals. The PAC/D contributions to the systematic investigation of impurity electric field gradients and magnetic hyperfine fields in rare earths are discussed. The importance of PAC/D as the main source of information on the temperature dependence of impurity hyperfine interactions in rare earths is stressed. The trends of the electric field gradients are compared to the behaviour of simpler non-cubic metal systems. The magnetic fields are discussed in the context of current theories.     

Dynamical correlations in the one-dimensional electron gas with short-range interactions

We study the dynamical correlation effects in a one-dimensional Fermion gas with repulsive delta-function interaction within the quantum version of the self-consistent field approximation of Singwi, Tosi, Land, and Sj?lander [Phys. Rev. 176, 589 (1968)]. The dynamic correlation effects are described by a frequency dependent local-field correction . There is a corresponding local-field factor for the spin-density correlations. We investigate the structure factors, spin-dependent pair-correlation functions, the frequency dependences of and , and the plasmon dispersion relation within this formalism. We compare our results with other theoretical approaches, in particular the static version of the self-consistent field approximation to highlight the importance of dynamical correlations. Received 11 December 1998 and Received in final form 25 April 1999     

The influence of short-range correlations on nucleon emission in electron scattering by nuclei

The nucleon emission induced by high-energy electrons is analysed in three experimental situations: electron-proton coincedence and single detection of electron or proton. The coincidence and proton detection experiments are recommended as sensible tools for studying the nuclear correlations.     

Saturation of nuclear matter and short-range correlations

A fully self-consistent treatment of short-range correlations in nuclear matter is presented. Different implementations of the determination of the nucleon spectral functions for different interactions are shown to be consistent with each other. The resulting saturation densities are closer to the empirical result when compared with (continuous choice) Brueckner-Hartree-Fock values. Arguments for the dominance of short-range correlations in determining the nuclear matter saturation density are presented. A further survey of the role of long-range correlations suggests that the inclusion of pionic contributions to ring diagrams in nuclear matter leads to higher saturation densities than empirically observed. A possible resolution of the nuclear matter saturation problem is suggested.     

Level crossing in hyperfine interactions studied by perturbed γ-γ angular correlations

The technique of differential γ-γ angular correlation measurements has been applied to an investigation of the hyperfine interactions in the 482 keV level of¹⁸¹Ta. The activity was embedded in the lattice of a hafnium single crystal. The investigation of the quadrupole interaction gave for the electric interaction frequencyω ₀=(313±4) MHz. The electric field gradient was found to be axially symmetric, the asymmetry parameter beingη<0.1. Furthermore the combined collinear magnetic dipole and electric quadrupole interaction was studied. The angular correlation was investigated as a function of the strength of the external magnetic field by integral as well as time differential measurements. The integral anisotropy as function of the magnetic field has the shape of a resonance curve. The maximum was observed at a magnetic field ofB _res=(24.2±0.5)kG.     

Proton-proton and deuteron-deuteron correlations in interactions of relativistic helium nuclei with protons

The reactions⁴Hep pp+X,³Hep pp+X and⁴Hep ddp have been investigated and the correlation function has been measured for protons and deuterons with small relative momenta. Strong positive correlation has been observed for protons related mainly to the final state interactions in¹S₀ state. The root mean square radius of the proton source calculated from the correlation function has been found to be equal to (1.7±0.3) fm and (2.1±0.3) fm for⁴He and³He respectively. It agrees with the known radii of these nuclei.We would like to thank Dr R. Lednicky for discussion, helpful suggestions and for making available the computer program that calculates the theoreticalpp correlation function. The authors also thank Dr D.H. Boal for providing the results of the two-deuteron correlation function calculations.     

Beta decay and hyperfine interactions

Experimental searches for the second-class currents and the soft pion effects in the nuclear weak axial currents are discussed. Also discussed are the hyperfine interactions of light interstitial impurities in ferromagnetic Fe and Ni, as well as in fcc and bcc non-magnetic metals. For these spin-ray correlation experiments, it is emphasized that the technical developments and improvements of the nuclear spin control by NMR and the production of polarization in the short-lived nuclear states are vital necessities.     

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

Relying upon our previous treatment of the density matrices for nuclei (in general, nonrelativistic self-bound finite systems) we are studying a combined effect of center-of-mass motion and short-range nucleon-nucleon correlations on the nucleon density and momentum distributions in light nuclei (⁴He and ¹⁶O). Their intrinsic ground-state wave functions are constructed in the so-called fixed center-of-mass approximation, starting with mean-field Slater determinants modified by some correlator (e.g., after Jastrow or Villars). We develop the formalism based upon the Cartesian or boson representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators for oscillatory quanta in the three different space directions, and get the own “Tassie-Barker” factors for each distribution and point out other model-independent results. After this separation of the center-of-mass motion effects we propose additional analytic means in order to simplify the subsequent calculations (e.g., within the Jastrow approach or the unitary correlation operator method). The charge form factors, densities and momentum distributions of ⁴He and ¹⁶O evaluated by using the well-known cluster expansions are compared with data, our exact (numerical) results and microscopic calculations.     

Theoretical aspects of hyperfine interactions

This work reviews the basics of the theoretical determination of the hyperfine interactions. Starting from the Dirac equation the relevant expressions for the isomer shift, the hyperfine field and the electric field gradient are derived. In the second part examples from band structure calculations are given for Fe₄N as a prototypical system where all features of the pressure dependence of the hyperfine interactions can be demonstrated. This revised version was published online in July 2006 with corrections to the Cover Date.     

The short-range correlations of a doped Mott insulator

This paper presents numerical studies of the single hole model that address the interplay between the kinetic energy of itinerant electrons and the exchange energy of local moments as of interest to doped Mott insulators. Due to this interplay, two different spin correlations coexist around a mobile vacancy. These local correlations provide an effective two-band picture that explains the two-band structure observed in various theoretical and experimental studies, the doping dependence of the momentum space anisotropic pseudogap phenomena and the asymmetry between hole and electron doped cuprates.     

Identification of short-range nuclei with low atomic numbers

The problems of identification of slow nucleus with small atomic numbers in photographic emulsion are discussed. We proposed to measure the distance between track edge and track axis and to search the atomic numbers by minimizing the square differences between the theoretical and experimental values of these distances.     

Brownian particles with long- and short-range interactions

We develop the kinetic theory of Brownian particles with long- and short-range interactions. Since the particles are in contact with a thermal bath fixing the temperature T, they are described by the canonical ensemble. We consider both overdamped and inertial models. In the overdamped limit, the evolution of the spatial density is governed by the generalized mean field Smoluchowski equation including a mean field potential due to long-range interactions and a generically nonlinear barotropic pressure due to short-range interactions. This equation describes various physical systems such as self-gravitating Brownian particles (Smoluchowski-Poisson system), bacterial populations experiencing chemotaxis (Keller-Segel model) and colloidal particles with capillary interactions. We also take into account the inertia of the particles and derive corresponding kinetic and hydrodynamic equations generalizing the usual Kramers, Jeans, Euler and Cattaneo equations. For each model, we provide the corresponding form of free energy and establish the H-theorem and the virial theorem. Finally, we show that the same hydrodynamic equations are obtained in the context of nonlinear mean field Fokker-Planck equations associated with generalized thermodynamics. However, in that case, the nonlinear pressure is due to the bias in the transition probabilities from one state to the other leading to non-Boltzmannian distributions while in the former case the distribution is Boltzmannian but the nonlinear pressure arises from the two-body correlation function induced by the short-range potential of interaction. As a whole, our paper develops connections between the topics of long-range interactions, short-range interactions, nonlinear mean field Fokker-Planck equations and generalized thermodynamics. It also justifies from a kinetic theory based on microscopic processes, the basic equations that were introduced phenomenologically to describe self-gravitating Brownian particles, chemotaxis and colloidal suspensions with attractive interactions.     

Study of combined magnetic and electric hyperfine interactions for cadmium in Dysprosium by time differential perturbed angular correlations

The combined magnetic and electric hyperfine interaction at the site of a¹¹¹Cd impurity in magnetically ordered Dysprosium has been investigated as a function of temperature by time differential perturbed angular correlation measurements. Three different phases have been found in metallic Dy with transition temperatures of 85 and 179 °K in agreement with the results of bulk material measurements. In the paramagnetic phase above 179 °K a pure electric quadrupole interaction has been observed. The various contributions to the electric fieldgradient are analyzed and it is shown, that the dominant contribution comes from the conduction electrons. In the ferromagnetic phase which extends from 0 to 85 °K the magnetic hyperfine field at the site of¹¹¹Cd has the same temperature dependence as the spontaneous magnetization. The value of the hyperfine field at 4.2 °K is ¦H _eff¦=(221 ± 4) kG. At 85 °K a transition to the antiferromagnetic phase of Dy occurs, which shows a hysteresis of the transition temperature. In the antiferromagnetic phase the temperature dependence of the hyperfine field deviates considerably from the magnetization curve. It is suggested that this deviation might be due to a temperature dependence of thes-f exchange interaction.     

Co-existence of long- and short-range magnetic correlations in holmium-erbium superlattices

The effect of competing crystal-field anisotropies on magnetic order has been investigated in a series of Ho/Er superlattices using a combination of x-ray and neutron scattering techniques. For temperatures in the interval T_N(Er)≤T≤T_N(Ho) the Ho basal-plane order propagates coherently through the paramagnetic Er over a typical length scale of 1000 Å. At low temperatures the Ho moments retain their bulk-like helical configuration, whereas the magnetic structure in the Er blocks has both basal-plane and c-axis components. Below T_N(Er), the coherence length of the basal-plane order decreases on cooling, while the longitudinal component of the Er moments fails to order across the Ho block. It is argued that these results require an extension of current models of indirect exchange in superlattices to explicitly include the superlattice band structure.     

Measurement of two- and three-nucleon short-range correlation probabilities in nuclei

The ratios of inclusive electron scattering cross sections of 4He, 12C, and 56Fe to 3He have been measured at 1 < xB <. At Q2 > 1.4 GeV2, the ratios exhibit two separate plateaus, at 1.5 < xB < 2 and at xB > 2.25. This pattern is predicted by models that include 2- and 3-nucleon short-range correlations (SRC). Relative to A = 3, the per-nucleon probabilities of 3-nucleon SRC are 2.3, 3.1, and 4.4 times larger for A = 4, 12, and 56. This is the first measurement of 3-nucleon SRC probabilities in nuclei.     

New measurements of high-momentum nucleons and short-range structures in nuclei

We present new measurements of electron scattering from high-momentum nucleons in nuclei. These data allow an improved determination of the strength of two-nucleon correlations for several nuclei, including light nuclei where clustering effects can, for the first time, be examined. The data also include the kinematic region where three-nucleon correlations are expected to dominate.     

Stroboscopic observation of quadrupole hyperfine interactions

A stroboscopic technique for the observation of quadrupole hyperfine interactions of isomeric nuclear states has been successfully developed. The inherent precision and resolution of this technique have been demonstrated by measuring the quadrupole hyperfine frequency for ${}^{69}\text{Ge(}\text{9}\text{2}{}^{\mathrm{+}}{}_1\text{, τ = 4.0μ)}$ in Zn metal at several temperatures; ω₀ = [19.67 ± 0.06] × 10⁶s^?1 (at 623 ± 3 K).