The deformation producing tendency of (d 3/2−f 7/2) empirical effective interaction

The effective matrix elements in (d _3/2−f _7/2)² configuration have been recently defined by Erskineet al. and Sherret al. assuming shell clcsures for S³² and Ca⁴⁰. We have attempted to verify whether this empirically deduced (d _3/2−f _7/2)² interaction permits thed _3/2 shell to remain closed when nucleons are added to Ca⁴⁰. It is found that the Erskine interaction gives rise to ground states of thef _7/2 shell nuclei in which thed _3/2 orbit is completely filled. However that interaction over-binds Ca⁴⁰. If the centroid of the (d _3/2)² interaction is modified to fit the Ca⁴⁰ binding energy, the ground states of Cr⁴⁸ and Fe⁵² become deformed and thed _3/2 orbit is not completely filled.     

Theory of Raman scattering and infrared absorption by interacting phonon-magnon states in FeF2

It is shown theoretically that, in the presence of a strong magnetic field, effects due to the interaction betweenB _1g ,E _g,TA phonons and magnons should be important in the Raman and infrared absorption spectrum of FeF₂. As a result the two magnon line should split. A microscopic Hamiltonian for the interactions has been derived. The calculated values of theE _g phonon-one magnon interaction, 9.9 cm^–1, and of theB _1g phonon-two magnon coupling, 6.3 cm^–1, are comparable to those in FeCl₂2H₂O metamagnet, in which C phonon-magnon hybrydization has been observed [1]. It is shown that hybridization between two magnon andB _1g orTA phonon can occur in FeF₂ if the magnon energy approaches the phonon energy due to increasing magnetic field or increasing temperature.On the leave from Technical University, Pozna, Institute of Physics, Pozna 61–138 Piotrowo 3, Poland     

Overlap contribution to57Fe3+ isomer shifts in fluorides and oxides

We have calculated the overlap contribution to the contact charge density at the⁵⁷Fe³⁺ site in fluoride and oxide lattices, FeF₃, CaFe₂O₄, CaBaFe₄O₈ and KFeO₂. The trend in isomer shifts in going from one lattice to another is explained in terms of the overlap effects. The experimental values of the change in isomer shift from lattice to lattice is used to obtain the change in nuclear size. The values of r/r _N are found to lie between –0.81×10^–4 and –1.56×10^–4.     

Three-body calculation of neutron-deuteron elastic scattering in the energy region from 2.5 MeV up to 50 MeV

The three-body Faddeev equations for neutron-deuteron scattering are solved in the energy region from 2.5 MeV to 50 MeV of the incident neutron energy with small energy steps. Higher-rank separable potentials are used in the¹ s ₀ wave and in the³ s ₁—³ d ₁ waves, while rank-1 separable potentials are used in¹ p ₁,³ p _0,1,2 ¹ d ₂ ³ d _2,3 waves. The calculation is compared with experiments for the total cross section, the total break-up cross section, the differential cross section and the analyzing power of neutron-deuteron scattering. The improvements in the agreement as compared to previous calculations are impressive in many cases. Especially, the calculated total cross section agrees with the experiment below 30 MeV within the error bars, which are as small as 1%. A discussion on the numerical accuracy is given. General aspects of the calculated cross section are discussed. It is pointed out that thes-wave asymptotic normalization of the deuteron wave function (A _s ) is important.     

Effective action in higher derivative (Super)gravities

'The one-loop effective action (EA) with an accuracy up to linear curvature terms ind=4R ²-gravity, conformal gravity, andN=1,d=4 conformal supergravity on the backgroundR ₄×T_4–k,k=1, 2, 3 is calculated. (Here,R _k is thek-dimensional curved space, T_n is then-dimensional torus). The one-loop EA in multidimensionalR ²-gravity and ind=10 conformal supergravity on the backgroundR ₄ ×T _d–4 is also obtained. The mechanism of inducing the Einstein gravity from the EA of considered theories of higher derivative (super)gravity is presented.We are grateful to I. L. Bukhbinder for the numerous discussions of considered questions.     

Transient optically detected ESR in the excited state of ruby

The dynamics of the(² E) state of Cr³⁺ in Al₂O₃ have been investigated. After excitation by a short laser pulse (<10ns) the relative intensity of the optically detected ESR signal (ODMR) as a function of the delay timet _d after the excitation is measured. A remarkable increase was found upon lengtheningt _d, while the line width remained constant. This increasing population difference of the Zeeman levels of(² E) can be explained by different resonant-reabsorption induced effective lifetimes. The experimental data could be reproduced by use of a phenomenological model.     

Fourier Transform Infrared Emission Spectroscopy of thebΠ–aΣSystem of BN

The emission spectrum of BN has been investigated in the 1800–9000 cm⁻¹region using a Fourier transform spectrometer. BN was formed in a microwave discharge of He with a trace of BCl₃and N₂. The bands observed in the 3000–7800 cm⁻¹interval have been assigned as theb¹Π–a¹Σ⁺transition, with the 0–0 band at 3513.99040(43) cm⁻¹. This transition is analogous to theA¹Π_u–X¹Σ⁺_g(Phillips) system of the isoelectronic C₂molecule. The rotational analysis of the 0–0, 1–1, 1–0, 2–1, 3–2, 2–0, 3–1, 4–2, and 4–1 bands has been obtained and the molecular constants for theb¹Π anda¹Σ⁺states have been determined. A local perturbation has been observed in thev= 1 vibrational level of theb¹Π state nearJ= 18 caused by the interaction with thev= 3 vibrational level of thea¹Σ⁺state. The principal equilibrium constants for thea¹Σ⁺state are: ω_e= 1705.4032(11) cm⁻¹, ω_ex_e= 10.55338(52) cm⁻¹,B_e= 1.683771(10), α_e= 0.013857(16) cm⁻¹, andr_e= 1.2745081(37) Å. Although theb¹Π–a¹Σ⁺transition has recently been seen in emission from boron nitride trapped in solid neon matrices [J. Chem. Phys.104,3143–3146 (1996)], our work represents the first observation of this transition of BN in the gas phase.     

Final-state interactions and quasi-free mechanism in the3He(d,3Hp)p reaction

A measurement of absolute differential cross sections of the³He(d,³Hp)p reaction atE _d=23.083 MeV shows the importance of the quasi-free reaction (QFR) mechanism. The observation of a prominent QFR peak indicates that complicated multiple-scattering processes may not be so important as to prevent a simple phenomenological analysis based on two-body interactions. In this respect we isolate final-state-interaction (FSI) effects related toS andP wave³H-p interactions. In particular, the FSI, associated with the⁴He level at 25.5 MeV of excitation energy, plays a dominant role.     

Strong spin-dependent absorption at theL 2,-edges of 5d-impurities in iron

Large spin-dependent absorption effects have been observed with circularly polarized photons of energies between 10.8 keV and 13.8 keV at theL _2,3-edges of Os, Ir, Pt, and Au impurities (3 at.%) in iron. The largest value of the spin-dependent absorption coefficient (µ _c /µ _o +0.22) is found at the PtL ₂-edge. From the energy dependence of the spin-dependent absorption at theL ₂- andL ₃-edges the spin-density profiles of thed _3/2-andd _5/2-projected states populated in the absorption process are derived. Thed _5/2-spin densities deduced from theL ₃ spin-dependent absorption spectra agree well with spin-polarized band-structure calculations for the ferromagnetic ground state. A comparison of thed _3/2- andd _5/2-spin densities shows a strong contribution of the spin-orbit effects to the exchange splitting in Os, whereas only small spin-orbit effects are indicated for Ir, Pt and Au impurities.     

Study of EPR parameters and defect structure for two tetragonal impurity centers in MgO:Cr<Superscript>3+</Superscript> and MgO:Mn<Superscript>4+</Superscript> crystals

The electron paramagnetic resonance (EPR) parameters (g-factors g _‖, g _⊥ and zero-field splitting D) of two tetragonal 3d³ impurity centers M_3d-V_Mg and M_3d-Li⁺ (where M_3d = Cr³⁺ or Mn⁴⁺, V_Mg is the Mg²⁺ vacancy) in M_3d-doped MgO crystals are calculated from the high-order perturbation formulas including both the crystal-field (CF) and the charge-transfer (CT) mechanisms for 3d³ ions in the tetragonal symmetry. The calculated results are in reasonable agreement with the experimental values. From the calculations, it can be found that the relative importance of the CT mechanism for EPR parameters increases with increasing valence state of the 3d³ ion. So, for the high-valence 3d ⁿ ions in crystals, a reasonable explanation of EPR parameters should take into account both CF and CT mechanisms. The defect structures (characterized by the displacement ΔR of O²⁻ in the intervening M_3d and V_Mg or Li⁺ at the Mg²⁺ site) for these tetragonal impurity centers are obtained from the calculations. The results are consistent with the expectations based on the electrostatic interactions.     

Spectroscopic properties of Fe ions at tetragonal sites—Crystal field effects and microscopic modeling of spin Hamiltonian parameters for Fe (S=2) ions in K2FeF4 and K2ZnF4

Magnetic and spectroscopic properties of the planar antiferromagnet K₂FeF₄ are determined by the Fe²⁺ ions at tetragonal sites. The two-dimensional easy-plane anisotropy exhibited by K₂FeF₄ is due to the zero field splitting (ZFS) terms arising from the orbital singlet ground state of Fe²⁺ ions with the spin S=2. To provide insight into the single-ion magnetic anisotropy of K₂FeF₄, the crystal field theory and the microscopic spin Hamiltonian (MSH) approach based on the tensor method is adopted. Survey of available experimental data on the crystal field energy levels and free-ion parameters for Fe²⁺ ions in K₂FeF₄ and related compounds is carried out to provide input for microscopic modeling of the ZFS parameters and the Zeeman electronic ones. The ZFS parameters are expressed in the extended Stevens notation and include contributions up to the fourth-order using as perturbation the spin-orbit and electronic spin-spin couplings within the tetragonal crystal field states of the ground ⁵D multiplet. Modeling of the ZFS parameters and the Zeeman electronic ones is carried out. Variation of these parameters is studied taking into account reasonable ranges of the microscopic ones, i.e. the spin-orbit and spin-spin coupling constants, and the energy level splittings, suitable for Fe²⁺ ions in K₂FeF₄ and Fe²⁺:K₂ZnF₄. Conversions between the ZFS parameters in the extended Stevens notation and the conventional ones are considered to enable comparison with the data of others. Comparative analysis of the MSH formulas derived earlier and our more complete ones indicates the importance of terms omitted earlier as well as the fourth-order ZFS parameters and the spin-spin coupling related contributions. The results may be useful also for Fe²⁺ ions at axial symmetry sites in related systems, i.e. Fe:K₂MnF₄, Rb₂Co_1−xFe_xF₄, Fe²⁺:Rb₂CrCl₄, and Fe²⁺:Rb₂ZnCl₄.     

Z 3-Graded exterior differential calculus and gauge theories of higher order

We present a possible generalization of the exterior differential calculus, based on the operator d such that d³=0, but d²0. The entities dx ⁱ and d² x ^k generate an associative algebra; we shall suppose that the products dx ⁱ dx ^k are independent of dx ^k dx ⁱ , while theternary products will satisfy the relation: dx ⁱ dx ^k dx ^m =jdx ^k dx ^m dx ⁱ =j ²dx ^m dx ^m dx ⁱ dx ^k , complemented by the relation dx ⁱ d² x ^k =jd² x ^k dx ⁱ , withj:=e^2i/3.We shall attribute grade 1 to the differentials dx ⁱ and grade 2 to the second differentials d² x ^k ; under the associative multiplication law the grades add up modulo 3.We show how the notion ofcovariant derivation can be generalized with a 1-formA so thatD:=d+A, and we give the expression in local coordinates of thecurvature 3-form defined as :=d² A+d(A ²)+AdA+A ³.Finally, the introduction of notions of a scalar product and integration of theZ ₃-graded exterior forms enables us to define the variational principle and to derive the differential equations satisfied by the 3-form . The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensorF _ik and its covariant derivativesD _i F _km .     

Additional symmetry for the electronic shell in its ground state and many-electron effects

The additional symmetry for the properties related to the ground state of the atom is considered taking into account many-electron effects. Calculations of the I _4f, I _3d,I _2p,I _3p binding energies, 4f ^N-15d - 4f^N system differences and 2p, 3p electron affinities in the second order of perturbation theory and in the configuration interaction approximation have been performed for the ground configurations with one open shell. The analysis of separate many-electron corrections for these quantities and their variation along the sequences of atoms and ions shows that the main corrections maintain the considered symmetry. Received 18 January 1999 and Received in final form 17 July 1999     

Vibrational Population of Hydrogen Molecules Excited by an RF Discharge in an Expanding Thermal Arc Plasma as Determined by Emission Spectroscopy

This work is devoted to the determination of the vibrational population of hydrogen molecules in the ground and excited electronic states from the analysis of visible spectra of the H₂ molecules excited by an RF discharge in an expanding thermal arc plasma. Comparison of the experimental results on relative electron-impact excitation cross sections for the transition H₂(X¹Σ, υ⁰ = 0)→ H₂(d³II_u, υ′) with other experiments, and with calculations based on the Franck-Condon principle, shows good agreement. This means, that for plasma under investigation: 1) in the ground electronic state H₂(d³II_u,υ′), only the lowest vibrational level with υ⁰ = 0 is significantly populated, and 2) direct electron exictation of H₂(d³II_u, υ′, υ′) state from the ground state H₂(X¹Σ, υ⁰ = 0) dominates.     

Magnetic excitations in the two dimensional planar antiferromagnets K2FeF4 and Rb2FeF4

The magnetic excitation spectrum of K₂FeF₄ and Rb₂FeF₄, two K₂NiF₄-structure planar antiferromagnets with rather large anisotropy and spins perpendicular to the c-axis, has been measured by Raman and FIR-spectroscopy. One of the two predicted one-magnon transitions and the two-magnon mode have been observed in K₂FeF₄ (Rb₂FeF₄) at 48.5 cm^-1 (37.6 cm^-1) and 182.0 cm^-1 (160.5 cm^-1) respectively. The magnetic field and temperature dependence of the spectra are reported too. The data are discussed on the basis of an easy plane spin model Hamiltonian. In K₂FeF₄: Mn²⁺ a low lying magnetic impurity mode is observed at 40.5 cm^-1.     

Dipole magnetic anisotropy fields in rhombohedral antiferromagnetic materials

Results of calculations of the contribution of magnetic dipole interactions to the effective uniaxial anisotropy fields of antiferro- and ferromagnetism vectors in rhombohedral antiferromagnetic materials with theS ions are given as functions of the ratio of the hexagonal crystal cell parameters c_H/a_H. There is a strong dependence of the calculated curves on the lattice parameters of real compounds. From the dependences obtained the effective anisotropy fields are calculated for FeF₃, FeBO₃, and MnCO₃. L. V. Kirenskii Institute of Physics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 82–86, May, 1999.     

Spin-dependent photoabsorption at theL-edges of ferromagnetic Gd and Tb metal

The spin-dependent absorption of circularly polarized x-rays is studied at theL-edges of ferromagnetic Gd and Tb metal. At theL ₁-edge a spin-dependent part of the absorption coefficient of 10^–3–10^–2 is observed. Strong resonance absorption known as white line occurs at theL ₂- andL ₃-absorption onset. Correlated with it one finds large spin-dependent absorption effects with amplitudes of a few percent. The spin-dependent absorption spectra reflect the profiles of the spin densities of the states populated in the absorption process. Thep-states show spin densities correlated with the first two flat bands above the Fermi level. The spin density of thed-like states is concentrated in the energy range of the white line. In Gd a splitting of (0.5–0.6) eV of the unoccupied 5d spin up and spin down bands is indicated for both spin-orbit partners. In Tb a large dependence of the 5d spin density on the spin-orbit configuration is observed. The experimental results on the spin densities in Gd are compared with band structure calculations for the ferromagnetic ground-state. The theoretical and experimental spin density profiles agree well for thep-states but not for thed-states. The discrepancy concerning thed-states may be attributed to core-hole polarization effects in the absorption process.     

Mössbauer study of an amorphous iron III flouride: FeF3, xHF (0 ⩽ x ⩽ 1)

A ferric amorphous flouride FeF₃, xHF with 0 ⩽ x ⩽ 1 synthesized by a soft chemistry reaction was studied by Mössbauer spectroscopy. The hyperfine characteristics are very close to those of deposited variety previously published: they show that the Fe³⁺ ions are surrounded by weakly distorted octahedra of flourine atoms. The study under external magnetic field indicates that the spins are randomly distributed: FeF₃, xHF has a speromagnetic behaviour like deposited amorphous FeF₃. Elsewhere the similarity between the two amorphous forms is confirmed by susceptibility measurements.     

Magnetic insulator glasses

An outline is given of the use of Mössbauer spectroscopy as a probe of the amorphous structure and magnetic coordination in magnetic insulator glasses. Using the⁵⁷Fe Mössbauer resonance as an example in the context of amorphous ferric oxides and fluorides, the manner in which both paramagnetic and hyperfine-field-split spectra can be analyzed is presented. Emphasis is given to the information contained in Mössbauer lineshapes and linewidths in addition to the more obvious line-position data. A number of general findings are set out for ferric speromagnetics with particular references to Mössbauer studies of amorphous Fe₂O₃, Y₃Fe₅O₁₂ (YIG), FeF₃ and NaFeF₄.     

Low-spin states of odd-mass xenon isotopes

In this work, we analyse the positive parity of states of odd-mass nucleus within the framework of interacting boson-fermion model. The result of an IBFM-1 multilevel calculation with the 2d_5/2, 1g_7/2, 3s_1/2, 2d_3/2 and 1h_11/2, single particle orbits is reported for the positive parity states of the odd-mass nucleus ^125–129Xe. Also, an IBM-1 calculation is presented for the low-lying states in the even-even ^124–128Xe core nucleus. The energy levels and B(E2) transition probabilities were calculated and compared with the experimental data. It was found that the calculated positive parity low-spin state energy spectra of the odd-mass ^125–129Xe isotopes agree quite well with the experimental data.