MAPW calculation of the anisotropic positron annihilation in copper

The wave function ψ_? of a positron in Cu is calculated using the MAPW (modified augmented plane wave) method. This method, taking into account the correct symmetry of ψ_? inside the atomic polyhedron and yielding the appropriate behaviour near the nucleus, leads to rapidly converging results. The Hartree potential seen by the positron is constructed from the electronic wave functions determined by the MAPW method. It is found that the lowest eigenstate of the positron is a Γ₁ state. In a provisional calculation, the matrix elements describing the two-quantum angular distribution of positron annihilation radiation are computed using recent MAPW electron wave functions. Good agreement with the measured anisotropic positron annihilation is found.     

Brillouin scattering in KH3 (SeO3)2 above the transition temperature

The Brillouin scattering measurement in KH₃(SeO₃)₂ above the transition temperature shows a large anomaly in hypersonic velocity of the transverse wave with the wave vector q = [010] and the polarization ξ = [001], which indicates acoustic phonon softening.     

The hydrostatic pressure derivatives of the elastic constants of indium and an indium cadmium alloy

The hydrostatic pressure derivatives of the elastic stiffness constants of indium and indium-3.4 at.% cadmium alloy single crystals have been obtained from pulse echo overlap measurements of the dependence of ultrasonic wave velocities upon pressure. The softest zone centre acoustic phonon mode in indium is a shear mode propagating k along the [101] direction rather than that (k[110], e[11?0]) which drives the ferroelastic phase transition in the indium-cadmium alloys. The derivative δ((C₁₁ – C₁₂)/2)/δP is positive, accounting for the stability of the fct structure of indium under high pressure. Using the quasiharmonic, anisotropic continuum model the acoustic mode Grüneisen parameters have been calculated and are discussed in terms of mode softening. The high temperature limiting value$\text{\$}\text{?}$γ_H (= 2.56) of the mean acoustic mode Grüneisen parameter is found to be close to the thermodynamic Grüneisen parameter γ^th (=2.5).     

Specific features of magnetic phase diagram of an MnSi helimagnet

Magnetization curves of MnSi single crystals have been measured in a range of temperatures T = 5.5–35 K and magnetic field strengths H ≤ 11 kOe for H ∥ [1 1 1], [0 0 1], and [1 1 0]. Special attention has been paid to the temperature interval near T _N = 28.8 K, where MnSi exhibits a transition to the state with a long-period helical magnetic structure. Some new features in the magnetic behavior of MnSi have been found. In particular, in an intermediate temperature region above the transition (28.8 K = T _N ≤ T < 31.5 K), the dM(H)/dH curves exhibit anomalies that are not characteristic of the typical paramagnetic state. It is established that the line of the characteristic field H*(T) of this anomaly is a natural extrapolation of the temperature dependence of the field of the transition from a conical phase to an induced ferromagnetic phase observed at T < T _N. It is concluded that the properties of MnSi in the indicated intermediate region are related to and governed by those of the conical phase (rather than of the A phase). Based on these data, magnetic phase diagrams of MnSi for H ∥ [1 1 1], [0 0 1], and [1 1 0] are plotted and compared to diagrams obtained earlier by other methods.     

Representations of the infinite direct product of universal coverings of isometry groups of the complex ball

In this paper we consider the group G?_M consisting of measurable functions on the set M with values in the group G? which is the universal covering of the group G of isometries of the n-dimensional complex ball. We construct a family of irreducible unitary representations of this group. The main elements of the construction are irreducible representations of the group G? obtained by interpolation from the representations of the discrete series of the group G.Suppose G? is a group, M a set with measure. Denote by G?_M the group of G?-valued functions on M. (The group G?_M does not necessarily contain all the functions). It is natural to consider the group G?_M as the direct product of ? copies of the group G?, where ? is the cardinality of the set M. In the case where the set M has no points of non-zero measure, it is natural to call G?_M the continuous tensor product of ? copies of G?. In the case where G? is the Heisenberg–Weyl group $\text{1}\text{a}\text{c}\text{0}\text{1}\text{b}\text{0}\text{0}\text{1}$ the group G?_M has been known since the end of the 1920, in view of the fact that the Lie algebra of this group is the Lie algebra of the Bose commutation relations.¹ The case where the group G? is semi-simple apparently first occurred in the theory ofcalibrated fields. A number of physical and mathematical papers (see [1], [2], [8]–[11]) are concerned with the groups G?_M and their linear representations. The present paper deals with the case where the group G? is the universal covering of the isometry group G of the complex ball (i.e. the domain in Cⁿ determined by the inequality ∑ z_kz?_k < 1). No conditions are imposed on the set M. By comparison with the papers [1], [2], [8]–[10], the explicit construction of the representations, copying the Fock representation, is new, as well as the proof of their irreducibility.The construction proposed below may be generalized to the case where G is the isometry group of any homogeneous domain Ω in Cⁿ, G? is the one-dimensional central extension of G. However, if Ω is a classical symmetrical domain (which is not a ball) and the set M contains no points of non-zero measure, it follows from [6] that the representation thus obtained is unitary in the indefinite sense. In the case where Ω = Cⁿ and G is the group of parallel translations G?—the Heisenberg-Weyl group, the proposed construction becomes the Fock construction of the representation of commutation relations. The other cases have not been studied yet. The main results of this paper have been (briefly) published in [4].     

Description of radiative strength functions in deformed nuclei

Radiative strength functions ofE1- andM1-transitions from ground states of doubly even deformed nuclei to states near the neutron binding energyB _n are calculated within the quasiparticle-phonon nuclear model. The wave functions of excited states include one- and two-phonon components. The calculations were made with the Pauli principle being or not included in the two-phonon components of the wave functions. It is shown that the radiativeE1- andM1-strength functions as well as the widths of giant dipole resonances in deformed nuclei are slightly influenced by the two-phonon components of the wave functions and they can be calculated in the RPA. Thek _E1- andk _M1-values are calculated for some deformed nuclei of the rare-earth and actinide region. The calculated values ofk _E1 are 1.5–2 times larger and the values ofk _M1 are somewhat less than the average values obtained in [14] from the analysis of available experimental data.     

Oxidation and thermal reduction of the Cu(1 0 0) surface as studied using positron annihilation induced Auger electron spectroscopy (PAES)

Changes in the surface of an oxidized Cu(1 0 0) single crystal resulting from vacuum annealing have been investigated using positron annihilation induced Auger electron spectroscopy (PAES). PAES measurements show a large increase in the intensity of the annihilation induced Cu M_2,3VV Auger peak as the sample is subjected to a series of isochronal anneals in vacuum up to annealing temperature 300 °C. The intensity then decreases monotonically as the annealing temperature is increased to ∼600 °C. Experimental probabilities of annihilation of surface-trapped positrons with Cu 3p and O 1s core-level electrons are estimated from the measured intensities of the positron annihilation induced Cu M_2,3VV and O KLL Auger transitions. Experimental PAES results are analyzed by performing calculations of positron surface states and annihilation probabilities of surface-trapped positrons with relevant core electrons taking into account the charge redistribution at the surface, surface reconstructions, and electron-positron correlations effects. The effects of oxygen adsorption on localization of positron surface state wave function and annihilation characteristics are also analyzed. Possible explanation is proposed for the observed behavior of the intensity of positron annihilation induced Cu M_2,3VV and O KLL Auger peaks and probabilities of annihilation of surface-trapped positrons with Cu 3p and O 1s core-level electrons with changes of the annealing temperature.     

The elastic behaviour of In-Tl alloys in the vicinity of the martensitic transition

To test further the prediction of collapse of the [110], q|| [11&#x0304;0] acoustic mode at the martensitic phase transition, pulse superposition measurements of ultrasonic wave velocities have been made in indium-thallium alloys containing 25 and 27 at. % thallium. These alloys are f.c.c. at room temperature and transform on cooling to the f.c.t. phase at 196 ± 2°K and 127 ± 2°K, respectively. Results show that $\text{1}\text{2}$(C₁₁ ? C₁₂) goes to zero within experimental error at the transition temperature. The room temperature elastic constants of the tetragonal 11.5 and 15 at. % thallium alloys are also reported.     

Positron and electron energy bands in several ionic crystals using restricted Hartree-Fock method

Using a restricted Hartree-Fock formalism and suitably localized and symmetrized wave functions, both the positron and electron energy bands were calculated for NaF, MgO and NiO. The lowest positron state at Γ₁ lies above the vacuum level and negative work functions are predicted. Positron annihilation rates were calculated and found to be in good agreement with measured lifetimes.     

The contribution of 5d electrons to the saturation magnetic moments and magnetic hyperfine fields in the heavy rare earth metals

The main results of a model for 5d electrons in the heavy rare earth metals are presented. The model involves the use of wave functions based on published analyses for 4fⁿ5d6s² atomic configurations, and the spreading of each of these energy levels uniformly over a band of width W in the metals. Excess saturation magnetic moments above those of the tripositive ions can be explained by the model with W in the range 0.84±0.16eV in the five metals Gd, Tb, Dy, Er and Tm. The magnetic hyperfine fields in the metals include negative contributions from the 5d electrons which have been shown to amount to about ?250koe in Gd, Er and Tm.     

On the positron in a metal

The self-consistent calculations of the spatial distributions of electrons and potentials in vacancies of metals with a localized positron, the spatial distributions of positrons localized in surface states, and the binding energies of positrons and their lifetimes have been performed in terms of the Kohn-Sham method and the stabilized jellium model. The presence of a localized positron in a vacancy leads to the effect that the vacancy is weakly distinguishable for electron waves: the positron weakens the potential field in the vicinity of the vacancy and leads to a phase shift of the scattering electron wave functions. The calculation of the phase shifts of the wave functions for quasi-free positrons scattered by unperturbed vacancies and the representation of a system of vacancies as a “superlattice” in a metal have made it possible to find the shift of the positron work function and the vacancy contribution to the positron effective mass.     

Momentum dependency of the volume plasmon damping in metals

The wave vector dependency of the damping of volume plasma oscillation has been studied on the metals Al, Ga and Sn by measuring the half-width ΔE _1/2 of the volume plasma loss of 51 kev electrons as a function of their scattering angle ?. We observed an interesting structure in the continuously increasing half width ΔE _1/2(?) which indicates resonance like processes at certain values of the plasmon wave vector.     

Evaluation of the formation entropy of a single vacancy by means of positron annihilation

Analyzing positron annihilation data it was found that the formation energy of a single vacancy is proportional to the characteristic temperature T_c in f.c.c. metals. Assuming that the equilibrium fractional concentrations of single vacancies at T_c are constant, one finds that the formation entropy of a single vacancy is (1.6 ± 0.1)k for all f.c.c. metals. For zinc and cadmium, the formation entropies are 2.5k and 3.3k respectively.     

Anisotropy in the angular correlation curves of NiO

The positron angular correlation curves were measured along the [100], [110] and [111] directions of NiO single crystals. A simple calculation based on the localized ion model shows that the measured anisotropy is ascribed to the uncompleted 3d orbitals of Ni with a slight covalent mixing of oxygen 2p orbitals.     

Longitudinal relaxation of Fe nuclei in Yb-doped YIG

Measurements of T₁ for ⁵⁷Fe nuclei in Yb-doped YIG are reported for the temperature range 0·7–140 K, with the magnetization along the [111], [100], [110], and [112] crystallographic directions respectively. The dependence of T₁ on Yb concentration and on the magnitude of the applied field was also studied. These results are interpreted in terms of the ‘slow relaxation theory’, and are correlated with the ferrimagnetic resonance work of Clarke, Tweedale, and Teale, whose data have been reanalyzed by us. Both sets of data can be represented fairly well by the theory, with a consistent set of relevant parameters. However, the tensor G which describes the splitting of the Yb ground-state doublet must be modified somewhat from that deduced by Clarke et al., the new principal values being G₁ = 29·0 cm⁻¹, G₂ = 20·4 cm⁻¹ and G₃ = 8·5 cm⁻¹ respectively. Below approximately 10 K, when the magnetization is in the [110] or [112] direction, the nuclear relaxation rate is higher than predicted. These anomalies correspond to those observed in ferrimagnetic resonance line width, which have been attributed to Yb ions on the octahedral lattice sites normally occupied by iron. Anomalously large values of T⁻¹₁ are also observed below approximately 4 K in the [111] and [100] directions, and these remain to be accounted for.     

Electronic g factors eleven atomic states of Zr

The g_j for eleven low-lying levels of Zr I have been measured with the atomic-beam magnetic resonance method. The agreement between the experimental g_J values and theoretical predictions deduced from intermediate coupling wave functions is better than 0.1%.     

Forming abilities of monatomic chains of several fcc and bcc metals in different crystallographic orientations

The forming abilities of monatomic chains (MC) of several fcc and bcc metals stretched in three principal crystallographic orientations of [1 1 1], [1 0 0] and [1 1 0] are analyzed in terms of a ratio between Peierls stress of a bulk crystal with dislocations (τ_p) and theoretical shear stress of a monatomic chain (τ_m). It is found that the structure and orientation dependent τ_m/τ_p values are proportional to the forming abilities of MC while τ_m/τ_p is a function of Possion's ratio ν. The above considerations are in agreement with known experimental and simulation results of Au. In addition, Nb as a candidate for MC formation is suggested.     

Shell-model calculations with an adjusted surface-delta interaction (I) application to spectroscopic factors inA=24–28 nuclei

Shell-model calculations have been performed for positive-parity levels of theA=24–28,T≦3/2 nuclei in a 1d _5/22s _1/21d _3/2 configuration space. The space, for each (A, J, T) set, was restricted such that only mixing of less than about 300 low-lying pure configurations was allowed. An effective interaction (MSDI) was used of which the parameters have been determined by a fit of the calculated energies to the experimental values. This resulted in an averaged deviation of 0.52 MeV for 67 fitted levels. Spectroscopic factors have been calculated with the derived wave functions. In order to obtain better agreement for the energies, all of the 63 two-body matrix elements and three single-particle energies were adjusted systematically. The wave functions derived from this adjusted set of matrix elements denoted by ASDI yield considerably better spectroscopic factors. For comparison, the spectroscopic factors have also been calculated in a 1d _5/22s _1/2 model space. The omission of the 1d _3/2 subshell was found to result in a substantially poorer agreement for the spectroscopic factors for 1d _5/2 and 2s _1/2 transfer.