The electronic structures of Mg,Al and Si in octahedral coordination with oxygen from SCF Xα MO calculations

Molecular orbital calculations performed using the SCF Xα Scattered Wave Cluster method are presented for the octahedral oxyanions MgO₆^?10, AlO₆^?9 and SiO₆^?8. The AlO₆^?9 results are used to assign and interpret the X-ray photoelectron spectra (XPS), X-ray emission (XES) and u.v. spectra of Al₂O₃. Agreement between calculation and experiment is good for valence band and fair for conduction band orbitais. The SCF Xα results for MgO₆^?10 are also in good agreement with observed valence band energies in MgO, but in this case the lowest energy features in the u.v. spectrum are not assignable in terms of either the calculations or the X-ray spectral results. The substantial increase in covalency expected between the Mg and Si oxides is evidenced in the calculations by an increase in valence region width from 2.6 to 5.3 eV and an increase in valence-conduction band separation from 5.2 to 10.0 eV. The calculated trends are in reasonable agreement with u.v. spectral data and with absolute valence orbital binding energies derived from X-ray spectra. A comparison of the SiO₆^?8 calculation with the analogous tetrahedral SiO₄^?4 calculation shows the valence band in the octahedral oxyanion to be much simpler in structure and somewhat narrower than that in the tetrahedral oxyanion. Using the orbital structure calculated for the valence bands of tetrahedral and octahedral oxides, a method is presented for calculating atomization energies directly from X-ray spectral data for SiO₂, Al₂O₃ and MgO. Results are in good agreement with experiment but the method involves an empirical parameter which is not presently understood in detail. Studies of trends in p-type bonding orbital binding energies derived from experimental data provide a qualitative explanation for the preferred coordination numbers in the Mg, Al and Si oxides.     

Hyperspherical Three-Body Calculation for Exotic Atoms

Ground state energies of atomic three-body systems like negatively charged hydrogen, normal helium, positively charged-lithium, beryllium, carbon, oxygen, neon and negatively charged exotic- muonium and positronium atoms have been calculated adopting hyperspherical harmonics expansion method. Calculation of matrix elements of two body interactions needed in the hyperspherical harmonics expansion method for a three body system is greatly simplified by expanding the bra- and ket-vector states in the hyperspherical harmonics (HH) basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal–Revai coefficients (RRC), which are the transformation coefficients between the HH bases corresponding to the two partitions. Use of RRC become particularly essential for the numerical solution of three-body Schr?dinger equation where the two-body potentials are other than Coulomb or harmonic. However in the present work the technique is used for two electron atoms ¹H^?(p ⁺ e ^? e ^?), D^?(d ⁺ e ^? e ^?), Mu^?(μ ⁺ e ^? e ^?),⁴He(⁴ He ²⁺ e ^? e ^?),⁶Li(⁶ Li ³⁺ e ^? e ^?),¹⁰Be(¹⁰ Be ⁴⁺ e ^? e ^?),¹²C(¹² C ⁶⁺ e ^? e ^?),¹⁶O(¹⁶ O ⁸⁺ e ^? e ^?) etc. and the exotic positronium negative ion Ps ^?(e ⁺ e ^? e ^?) where the interactions are purely Coulomb. The relative convergence in ground state binding energy with increasing K _max for ²⁰Ne has been demonstrated as a representative case. The calculated energies at K _max ?=?28 using RRC’s have been compared with those obtained by a straight forward manner in some representative cases to demonstrate the appropriateness of the use of RRC. The extrapolated energies have also been compared with those found in the literature. The calculated binding energies agree within the computational error.     

Investigation of the 6Li(d, α)4He reaction between 1.5 and 11.5 MeV

The differential cross section σ₀(θ) and the analysing powers T₁₁(θ), T₂₀(θ), T₂₁(θ) and T₂₂(θ) of the reaction ⁶Li(d, α)⁴He have been measured for twelve energies between 1.5 and 11.5 MeV at c.m. angles between 3.5° and 90°. The results were fitted with Legendre polynomials. The energy dependence of the resulting coefficients indicates resonance-like behaviour at several energies corresponding to excitation between 22 and 32 MeV in ⁸Be. The reaction ⁶Li(d, α)⁴He shows excellent features as an analyser for deuteron vector and tensor polarization over the whole energy range investigated.     

A precise determination of the τ-mass

The energy dependence of the cross sections for e⁺e^? → e^±(μ^±) + 1 charged track has been measured for centre of mass energies between 3.60 and 4.40 GeV. The pair production of the τ-lepton is observed at all energies and the τ-mass is determined to be 1.787_?0.018^+0.010 GeV from a fit to the energy dependence of the cross section.     

Collective and two-quasiparticle states in 158Gd observed through study of radiative neutron capture in 157Gd

The level structure of ¹⁵⁸Gd has been studied using the prompt γ-rays and conversion electrons emitted following neutron capture in ¹⁵⁷Gd. The γ-ray energy and intensity measurements were made using both Ge(Li) detectors and a curved-crystal spectrometer. Conversion-electron energy and intensity measurements were made using two separate magnetic spectrometers: one to measure the primary electron spectrum and the other to measure the lower energy secondary electron spectrum. Some γ-γ coincidence measurements were also made among the secondary γ-rays. From these data, a neutron separation energy of 7937.1 ± 0.5 keV has been determined for ¹⁵⁸Gd. A level scheme containing 59 excited states with energies < 2.25 MeV, for which de-excitation modes have been identified, is proposed for ¹⁵⁸Gd. Many of these states have been grouped into rotational bands. A total of thirteen excited rotational bands with band-head energies below 2.0 MeV are contained in the level scheme. Features of the proposed level scheme include: the K^π = 0^?, 1^? and 2^? octupole-vibrational bands with band-head energies of 1263, 977 and 1793 keV, respectively; the γ-vibrational band at 1187 keV; three excited K^π = 0⁺ bands with band-head energies of 1196, 1452 and 1743 keV; several two-quasiparticle bands with band-head energies in keV (and K^π assignments) of 1380 (4⁺), 1636 (4^?), 1847 (1⁺), 1856 (1^?), 1920 (4⁺) and 1930 (1⁺). An analysis of (d, p) reaction data is presented which permits definite two-quasiparticle configuration assignments to be made to most of these latter bands. Evidence is presented which suggests strong mixing of some two-neutron and two-proton bands. A phenomenological four-band mixing analysis is made of the energy and E2 transition-probability data for the ground-state band and the three lowest-lying excited collective positive-parity bands. Good agreement with experiment is obtained. A Coriolis-mixing analysis of the octupole bands has been carried out and good agreement with the data on level energies and E1 transition probabilities to the ground-state band has been achieved. Values of Z, the ratio of the E1 transition matrix element with ΔK = 1 to that with ΔK = 0, involving the octupole bands and the first four 0⁺ bands are derived. For three of these 0⁺ bands, absolute values of these matrix elements are deduced. An interesting alternation in the sign of Z is observed for these four 0⁺ bands.     

A study of 75Se by neutron capture and the SU(3)-SU(5) transition in the quadrupole-phonon representation

The γ and e^? spectra following thermal neutron capture in ⁷⁴Se were studied with curved-crystal, β, and pair spectrometers. Precise energies have been obtained for the transitions and levels at low energies. Two primary E2 transitions were found. The neutron separation energy for ⁷⁵Se was determined as 8027.6 keV. Precise γ-energies following the electron capture decay of ⁷⁵Se were also measured, resulting in precise level energies in ⁷⁵As. The calculation of the energy levels in ⁷⁵Se has been performed in the SU(6) particle-vibrational model (PTQM) and 27 theoretical states have been tentatively assigned to the experimental levels. The spectrum of the core nucleus ⁷⁴Se has been calculated in the SU(6) quadrupolephonon model (TQM). The structure of theoretical states, the relation to SU(3) and SU(5) limits, and potential energy surface are discussed. The E2, M1 and E1 transitions have been calculated in PTQM and compared to the experiment. Also, an overview is presented of theoretical explanations of the I = j, j?1, j?2 anomalous triplet emphasizing the rule with shell-model classification corrected for quadrupole phonons.     

High-spin states in26Mg

Theγ-decays of levels in²⁶Mg have been investigated up to 12.5 MeV excitation energy by proton-γ-ray coincidence measurements in the²³Na(α, pγ) reaction at 14.2 and 16 MeV bombarding energy. Lifetime-measurements, made with the Doppler-shift attenuation method, and proton-γ-ray angular-correlation measurements were performed at E_α=14.2 MeV. Many high-spin states were observed, among them levels at 6,978 (5⁺), 7,283(4^?), 7,395(5⁺), 7,953(5^?), 8,202(6⁺), 8,472(6⁺), 9,065(5), 9,112(6⁺), 9,169(6^?), 9,383 (6⁺), 9,542(5), 9,829(7⁺), 9,989(6⁺) and 12,479(8⁺, 7^?) keV excitation energy. The spectrum of positive-parity states and their electromagnetic properties are reproduced with good accuracy by shell-model calculations which employ a unifieds-d shell Hamiltonian and the unrestricted configuration space of the 0d _5/2 1s _1/2 0d _3/2 shell. Members of five inferred rotational bands, withK ^π=0⁺, 2⁺, 3⁺, 0⁺ and 3^? have been observed up to at leastI=6. TheK ^π=2⁺ band shows strong anomalies of excitation energies andE2 transition rates near theI=6 state. The static intrinsic quadrupole moments calculated from the shell model wave functions indicate transitions from prolate to oblate deformation within theK ^π=2⁺ band and also the ground state band. The lowest lyingI ^π=4⁺ state appears to be “spherical” and cannot be associated with a rotational band.     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

Energy level scheme and the effect of magnetic order on the optical transitions in europium chalcogenides

The optical constants of Eu-chalcogenide single crystals have been determined at room temperature for photon energies from 1 to 6 eV. In the same energy range the transmission of thin evaporated films (except for EuO) has been measured with polarized light above and below the magnetic ordering temperature. The observed polarization-dependent splittings of the two main absorption maxima in the region of magnetic order suggest transitions from the 4f⁷-level into the crystal field split 5dt_2g- and 5de_g-states. An attempt has been made to relate the maxima of the absorption coefficient to interband transitions and transitions from the localized 4f-states. With this assumption we derived a consistent energy level scheme of the four Eu-chalcogenides. From the scheme we gained useful information about the width of the 5d-states, the crystal field splitting and the possible type of conductivity. Finally we tried to explain theoretically the splittings observed in the region of magnetic order. For this purpose a one-particle model has been used to calculate the transition probabilities for the 4f⁷?4f⁶(⁷F _J ) 5dt_2g and the 4f⁷?4f⁶(⁷F _J ) 5de_g transition, taking into account an exchange interaction as well as a spin-orbit coupling. Although this simple model can explain the splittings of the excited 4f⁶(⁷F _J ) 5de_g-state, a complete explanation of the effect of magnetic order on the 4f⁶(⁷F _J ) 5dt_2g-state fails up to now.     

Effect of temperature on the fluorescence emission of 2H-chromen-2-one derivative in non-polar and polar solvents

The effect of temperature (293-333 K) on the fluorescence emission of 4-(5-methyl-3-phenyl-benzofuran-2-yl)-6-chloro-2H-chromen-2-one (MPBClC) is recorded in non-polar (1,4-dioxane, and toluene), and polar (butanol and DMSO) solvents. It is found that there is no shift in the position of fluorescence maxima, but the intensity decreases with increase in temperature, which depends on the polarity of the solvent. A mechanism of fluorescence quenching with rise in temperature is discussed in terms of the relative location of lowest ¹(ππ^?) and ³(nπ^?) states, and the energy difference between them. The change in temperature brings about a change in the probabilities of radiative and non-radiative transition. The radiationless deactivation of excited-state in the absence of quencher is temperature-dependent and its thermal activation energy has been determined.     

Higher overtones of the bending vibrations of the ground states of 12CS2 and 13CS2

Large numbers of ‘hot’ bands in the first electronic absorption systems of ¹²CS₂ and ¹³CS₂ have been analyzed from plates taken at high dispersion, and accurate rotational constants have been obtained for the overtones of the ground state bending vibration up to v₂ = 6 and l = 3 for ¹²CS₂ and v₂ = 4, l = 2 for ¹³CS₂. The energy differences between the various levels with the same l value have been determined to an accuracy of about ±0.006 cm^?1, but (because of the parallel polarization of the electronic transition) the absolute energies of levels with l > 0 cannot be obtained.     

The isoscalar strength distribution in 24, 26Mg, 28Si and 40Ca obtained from inelastic alpha scattering at 120 Mev

The inelastic α-scattering reaction at E_α = 120 MeV with an energy resolution of 90–150 keV has been used to investigate isoscalar strength distributions in ^{24, 26}Mg, ²⁸Si and ⁴⁰Ca. For ^{24, 26}Mg and ²⁸Si the E2 strength between E_x = 14 and 27 MeV is strongly fragmented. In ⁴⁰Ca the E2 strength is mainly concentrated near $\text{E}{}_{\mathrm{<mtext>x</mtext>}}\text{~ 65 A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ MeV, although here the onset of fragmentation can be observed. The sum rule strength for the different multipolarities was obtained by applying for each nucleus an L-dependent normalization procedure. In this way we observed in total in ^{24, 26}Mg, ²⁸Si and ⁴⁰Ca for excitation energies up to 27 MeV an amount of (61⁺⁸_?6), (50⁺⁹_?8), (38⁺⁸_?6) and (94 ± 14)%, respectively, of the isoscalar E2 energy weighted sum rule (EWSR) of which (36⁺⁷_?5), (28⁺⁸_?7), (24⁺⁷_?5) and (74 ± 12)% was found between E_x = 14 and 27 MeV. In addition isoscalar E0, E3 and E4 strength was observed in this excitation energy region. A detailed comparison has been made between the isoscalar quadrupole strength distribution observed in the ^{24, 26}Mg(α, α') reaction and the E2 strength excitation function obtained from radiative α-capture measurements. In the low excitation energy region coupled channel effects have been observed, especially for the excitation of the 3⁺ states. Moreover, a considerable percentage of the 1?ω isoscalar dipole and octupole strength has been observed for excitations below 14 MeV.     

On the energy of the 8<Stack><Subscript>2</Subscript><Superscript>−</Superscript></Stack> 1479-keV level in <Superscript>178</Superscript>Hf

The difference in the 332-and 326-keV transition energies from ¹⁷⁸Ta decay is measured with a magnetic β spectrometer and a γ spectrometer. The energy of the 332-keV transition (E(332) = 331 607 ± 4 eV) and the energy of the 8 ₂ ^? 1479-keV level in ¹⁷⁸Hf (E(1479) = 1479001 ± 6 eV) are determined with high accuracy.     

Resonant two-photon absorption in the Cr2O3 antiferromagnet

Two-photon absorption (TPA) spectra of the Cr₂O₃ model antiferromagnet have been studied for two polarization configurations at energies ranging from 2.5 to 3.55 eV. Several strong TPA peaks with the maximum coefficient β ～ 0.08 cm/MW are observed in the 2.7–3.1-eV range characterized by the ⁴ A ₂(F) → ⁴ T ₁(F) d-d one-photon transition of the Cr³⁺ ion. An analysis of the results obtained suggests that the general form of the TPA spectrum in this range is primarily determined by the resonance at the ² E(G) and ² T ₁(G) intermediate levels. At energies above 3.44 eV, the TPA coefficient sharply increases up to β ～ 0.1 cm/MW due to transitions between the valence and conduction bands.     

The analysing powers iT11, T20, T21 and T22 in deuteron-deuteron elastic scattering between 6 and 11.5 MeV

The angular distributions of the analysing powers iT₁₁(θ), T₂₀(θ), T₂₁(θ) and T₂₂(θ) of the elastic scattering of polarized deuterons on deuterons have been measured at deuteron energies of 6.0, 8.0, 10.0 and 11.5 MeV. The vector component has small but non-zero values which change sign between 6.0 and 10.0 MeV. The tensor components have increasing values with increasing energy. The results are discussed in respect of resonances in ⁴He and a term scheme is proposed for a complete phase-shift analysis.     

Energetics of “double” charge transfer and two-to-one charge-transfer adducts

Second-order perturbation theory and Hückel approximation are used to estimate the charge-transfer stabilization energy due to the mixing-in of the following dative configurations into the neutral donor (D) and acceptor (A) systems, (1) A^?D²⁺A^?, (2) D⁺A^2?D⁺, (3) D²⁺A^2?, and (4) D⁺A^?. $\text{General}$ parametric energy formulas are derived in terms of orbital overlap (S_DA), one- and two-electron electron affinities (E_A⁽¹⁾ and E_A⁽²⁾), and Coulomb energy differences (σU_c). These parametric formulas will help the assessment of the occurence and relative importance of the “defect” dative structures necessary for conduction. The specific case of the BZ-I₂ complexes studied show that (1), (2) and (3) exist with stabilization energies of less than 1% of that of (4). (4) is the conventionally known contributor to the usual “single” charge-transfer state.     

Recoil distance lifetime measurements in82Kr

The lifetimes τ=124±12, 6 _?2 ⁺⁴ and 380±100 ps of theE _x (I ^π )=3.46(8⁺), 2.92(6⁺) and 3.04(6^?) MeV states, respectively, populated by the reaction⁷⁶Ge(¹²C,α2n) were measured with the recoil distance method. In addition upper lifetime limits were obtained for nine states. The measured lifetimes and energies indicate a band crossing at aboutI ^π =8⁺, probably arising from the alignment of twog _9/2 neutrons. For the 3.04 MeV 6^? state as a second member of a band built on the 2.65 MeV 4^? state the measured lifetime points to a two-quasiparticle configuration. The positive-parity states have been discussed in the frame of the interacting boson approximation, nuclear field theory and the cranked shell model.     

Measurement of the longitudinal structure function and the smallx gluon density of the proton

At HERA energies the smallx region (x?10^?2) can be explored atQ ² values large enough that leading twist QCD calculations are valid. We show how measurement of the longitudinal structure function,F _L (x,Q ²), can lead to accurate measurement of the gluon structure function at such smallx values. Experimental systematic errors are discussed fully and requirements for the measurement outlined. We conclude that it should be possible to distinguish between the widely varying gluon distributions which are currently allowed.     

Electronic structure of PbI2 from photoelectron spectra and the exciton problem

The valence band density of states for PbI₂ is determined from X-ray and u.v. induced photoelectron spectra. It is shown that the band derived from Pb 6s states is at 8 eV binding energy and not at the top of the valence bands as suggested by band structure and charge density calculations. A rigid shift in the predominantly iodine 5p derived bands to lower binding energy brings the band structure calculations into essential agreement with experiment. Pb 5d core level binding energies determined here are used to derive core level exciton energies of 0.7 eV from published reflectivity spectra.     

Partial cross sections for Rb− photodetachment in the region of the Rb(5p 2 P 1/2 3/2) thresholds and their analysis by multichannel quantum defect theory

A crossed ion-laser beam apparatus has been used to measure accurate relative total and partial cross sections for photodetachment from Rb^? ions with high photon energy resolution (0.1–0.6 cm^?1) in the region of the Rb(5p ² P _1/2,3/2) thresholds (photon energy range 16,350–16,820 cm^?1). Satisfactory fits to these data by multichannel quantum defect theory (MQDT) have been obtained, resulting in a reliable set of seven MQDT parameters. The electron angular distribution parameter for the Rb(5_s) channel was found to beβ(5s)=2, independent of photon energy. MQDT predicts a sharp, window-type variation of?(5s) around the minimum of the 5s-cross section below the Rb(5p ² P _1/2) threshold (where an accurate experimental measurement ofβ(5s) was not possible) and a similar behaviour ofβ(6s) in the case of Cs^?photodetachment below the Cs(6p ² P _1/2) threshold.