Overall values of conventional discrepancy indices for crystals with heavy atoms. Part II. Results for monoclinic and orthorhombic crystals when the heavy-atom part alone constitutes the model

Theoretical expressions of 〈y _N〉, 〈|y _N − σ₁ y _P ^c |〉 and 〈|y _N ² −σ ₁ ² (y _P ^c )²|〉 (wherey _N andy _P ^c are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom contributionσ ₁ ² for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained for both the related and unrelated cases. The local values of 〈y _N〉 and 〈|y _N ⁿ − σ ₁ ⁿ (y _P ^c ) ⁿ |〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located in the structure. Contribution No. 550     

Theoretical optimization of metalp–n silicon Schottky barrier solar cell

The theoretical optimization of the design parametersN _A ,N _D andW _P has been done for efficient operation of Au-p-n Si solar cell including thermionic field emission, dependence of lifetime and mobility on impurity concentrations, dependence of absorption coefficient on wavelength, variation of barrier height and hence the optimum thickness ofp region with illumination. The optimized design parametersN _D =5×10²⁰ m⁻³,N _A =3×10²⁴ m⁻³ andW _P =11.8 nm yield efficiencyη=17.1% (AM0) andη=19.6% (AM1). These are reduced to 14.9% and 17.1% respectively if the metal layer series resistance and transmittance with ZnS antireflection coating are included. A practical value ofW _P =97.0 nm gives an efficiency of 12.2% (AM1).     

Electron paramagnetic resonance of NH 3 + radical in potassium sulphate

Room temperature EPR spectra of (NH₄)₂SO₄ doped K₂SO₄ monocrystals irradiated with x-rays show the presence of NH₃ ⁺ radicals. The EPR parameters areg ‖=2.0037 andg ⊥ = 2.0068;¹⁴NA _XX=13.75;A _YY=24.5;A _ZZ=25.5 gauss;¹HA _XX=A _YY=22 andA _ZZ=25 gauss. From the¹⁴N and¹H coupling constants it has been inferred that at room temperature the planar NH₃ ⁺ radical undergoes rotation about theC ₃ axis which corroborates with the equivalence of the protons, but the radical itself is in an asymmetric crystal field environment. The 77K spectra indicate a considerable reduction in the motion of the radical with the free motion almost completely stopped. Part of Ph.D. work of the second author     

Optically active Er3+ centers in Si/Si1 ? x Ge x structures under optical pumping

The Si/Si_{1 − x} Ge _x :Er/Si heterostructures, which are of interest for laser applications, have been investigated. The types of optically active Er³⁺ centers making a dominant contribution to the photoluminescence response of the structures studied are analyzed and their relationship with the parameters of the Si_{1 − x} Ge _x :Er heterolayer and the post-growth annealing conditions is shown. On the basis of the PL kinetic analysis of the structures with an isolated type of optically active Er³⁺ centers, it is concluded that population inversion of Er³⁺ ion states can be obtained under optical pumping and the effect of nonradiative recombination channels in Si_{1 − x} Ge _x :Er heterolayers on the excitation efficiency of Er centers and the conditions for population inversion is shown. Original Russian Text ? L.V. Krasilnikova, N.A. Baidakova, M.V. Stepikhova, Z.F. Krasilnik, V.Yu. Chalkov, V.G. Shengurov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 1, pp. 103–108.     

Analytic solution of the BCS gap equation inD dimensions (D=1, 2, 3), at finite temperatures

The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically in one, two and three dimensions, for temperatures close to zero andT _c. We work in the weak coupling limit, but allow the interaction widthν≡ħω _m/E _F to lie in the interval (0, ∞) Here,ħω _m is the maximum energy of a force-mediating boson, andE _F denotes the Fermi energy. We obtain expressions forT _c and ΔC, the jump in the electronic specific heat acrossT=T _c, in the limitsν≪1 (the usual phonon pairing) andν>1 (non-phononic pairing). This enables us to see howT _c scales with the mediating boson cut off. Our results predict a larger jump in the specific heat for the caseν>1, compared toν≪1. We also briefly touch upon the role of a van Hove singularity in the density of states.     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.     

Hard tissue ablation with a free running Er:YAG and a Q-switched CO2 laser: a comparative study

The Er:YAG and the CO₂ laser are competitors in the field of hard tissue ablation. The use of Er:YAG lasers (2.94 μm, pulse length _L of 100 to 200 μs) show smaller areas of thermal defects then ‘‘superpulsed’’ CO₂ lasers with pulse lengths of approximately 100 μs. Only the development of a Q-switched CO₂ laser (9.6 μm, τ_L=250 ns) allowed for similar results. In this paper new results for the Er:YAG and the Q-switched CO₂ laser under the influence of water spray will be presented. Several parameters are of special interest for these investigations: the specific ablation energy, which shows a minimum for the CO₂ laser at an energy density of 9 J/cm ² and a broad shallow minimum in the range of 10 to 70 J/cm² for the Er:YAG laser, and comparison of the cut-shape and depth. Surface effects and cutting velocity are discussed based on SEM pictures. Received: 19 July 2000 / Revised version: 1 November 2000 / Published online: 30 November 2000     

Low-temperature specific heats of lanthanum and yttrium phosphate glasses

Summary The specific heats of (R₂O₃) _x (P₂O₅)_1−x glasses containing high concentrations of La³⁺ and Y³⁺ ions have been measured between 1.5K and 30K. It is shown that, in addition to the usual Debye contribution, there is an excess specific heat arising from localized vibrational states which has been discussed in terms of two distinct models. The first predicts a maximum in the temperature dependence of the excess specific heat associated with the crossover frequency from phonon to fracton behaviour. The phonon-fracton density of states used to fit the excess specific heat gives rise to model parameters having the same magnitudes as those found previously for other glasses including samarium phosphates. The second model, formulated on the basis of soft vibrations in glasses, predicts a minimum in the excess specific heat, which is also observed. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Capanello, Italy, July 4–8, 1994.     

Optical absorption spectrum of Cr3+ in natural ruby

Two sharp line-like bands calledN andR lines on the red side, a close doublet (B lines) on the violet side and two broad bands are observed for natural ruby. At liquid air temperature the splitting ofR line was found and also three sharp-bands calledR, R′ andB lines are identified with spin-forbidden transitions of² E,² T ₁ and² T ₂. The two broad bands calledU band andY band are assigned accordingly to the spin-allowed transitions⁴ T ₂ and⁴ T ₁ respectively. The observed bands of natural ruby have been attributed to Cr³⁺ ion in an octahedral environment with trigonal distortion. The crystal field parameters which gave a good fit to the observed band positions areB=732 cm⁻¹,C=4.25B,Dq=1830 cm⁻¹,V=−1996 cm⁻¹ andλ=34 cm⁻¹.     

Carbon phosphide (B2 Σ + — A2 Π i) band system: RKR Franck-Condon factors andr-centroids

Franck-Condon factors andr-centroids based on Rydberg-Klein-Rees potential have been computed for the CP (B ² Σ ⁺ —A ² Π _i) band system. These results are compared with the Morse values and discussed.     

Paramagnetic relaxation of Er in an Er single crystal

The paramagnetic relaxation of Er in an Er single crystal was measured atT≫T _N and compared to the relaxation of Er ions in a polycrystalline Pb host. The results indicate an enhancement of at most 50% of the f-conduction electron exchange interaction in Er, as expected for highly ionic f-orbitals. The ratio of the quadrupole moments of the¹⁵⁴ Er(I ^π=11⁻) and the¹⁵⁵ Er(I ^π=13/2⁺) isomers was measured to be 1.18(3) indicating onset of nuclear deformation at N=87. Deceased May, 1986     

Analysis of the excitation functions of (α, xnyp) reactions on natural copper

Excitation functions of the reactions⁶³Cu[(α, n), (α, 2n)+(α, pn)] and⁶⁵Cu[(α, n), (α, 2n), (α, 3n), (α, 4n)+(α, p3n)] were investigated up to 50 MeV using stacked foil activation technique and Ge(Li) gamma ray spectroscopy method. Since natural copper used as the target has two odd-mass stable isotopes of abundance,⁶³Cu(69.17%) and⁶⁵Cu(30.83%), their activation in some cases, gives the same residual nucleus through different reaction channels but with very different threshold energies. In such cases, the individual reaction cross sections are separated with the ratio of theoretical cross sections. The experimental results were compared with the predictions of preequilibrium hybrid model of Blann. A general agreement was found in all reactions using initial exciton numbern ₀=4(4p0h) and also preequilibrium fraction depends on the incident particle energy.     

Intersectingp — p′ branes inpp-wave background

Several supergravity solutions corresponding to bothDp, as well asDp—Dp′ systems, inNS-NS andR-R pp-wave background originating fromAdS ₃ xS ³ xR ⁴ are presented. The supersymmetry properties of these solutions are analysed along with a brief outline of the world sheet construction for thep — p′ branes.     

Coexistence curve and rectilinear diameter in the critical liquid system carbon disulphide+nitromethane

The phase boundary of the binary liquid system CS₂+CH₃NO₂ is studied over nearly six decades in reduced temperature 3×10⁻⁶<ε=(T _C−T)/T _C<2×10⁻¹ and over the composition range 8-98 mole % of CS₂. The critical parameters areT _C=335.13₂K andx _C=57.3₄ mole % of CS₂. A single critical exponentβ=0.315±0.004 fits the observations over the entire range with no indication ofβ increasing to the classical value of 1/2 far away fromT _C. The diameter of the coexistence curve shows a rectilinear behaviour only far away fromT _C. NearT _C, the deviation ΔX from the rectilinear law seems to fit a curve of the form ΔX=fε^7/8 exp (−gε ^h), the derivative of which has a singularity like that of specific heat. An ambiguity in the analysis of the data in terms of mole fractions and volume fractions is pointed out. It is also suggested that the curvature of the diameter may be much weaker in a liquid-gas system and hence might have escaped detection.     

Conservation laws for classical and relativistic collisions. II

On the basis of elementary symmetry arguments it is shown that (1) if in classical mechanics there exists a quantity λ+Σ_iμ_iυ_i+1/2νυ ² that is conserved, where λ,μ _i, andν are particle parameters, then theμ _i andν are all proportional to a single parameterμ and the quantityAμ+Σ_iB_iμυ_i+C(λ+ 1/2Dμυ ²), whereD ≡ν/μ, is conserved for all values ofA, B _i, andC; (2) if in relativistic mechanics there exists a quantity λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc[1−(υ ²/c ²)]^−1/2 that is conserved, then theμ _i andν are all proportional to a single parameterμ and the quantityAλ+Σ_iB_iμν_i[1−(υ ²/c ²)]^−1/2+Cμc [1−(υ ²/c ²)]^−1/2 is conserved for all values ofA, B _i, andC.     

Harmonically trapped ideal quantum gases

We solve the problem of a Bose or Fermi gas in d-dimensions trapped by δ ⩽ d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature T _c if and only if d + δ > 2, along with a jump in the specific heat at T _c if and only if d + δ > 4. Specific heats for both gas types precisely coincide as functions of temperature when d + δ = 2. The trapped system behaves like an ideal free quantum gas in d + δ dimensions. For δ = 0 we recover all known thermodynamic properties of ideal quantum gases in d dimensions, while in 3D for δ = 1, 2 and 3 one simulates behavior reminiscent of quantum wells, wires anddots, respectively. Good agreement is found between experimental critical temperatures for the trapped boson gases ₃₇ ⁸⁷Rb, ₃ ⁷Li, ₃₇ ⁸⁵Rb, ₂ ⁴He, ₁₉ ⁴¹K and the known theoretical expression which is a special case for d = δ = 3, but only moderate agreement for ₁₁ ²⁷Na and ₁ ¹H. Received 17 July 2002 / Received in final form 14 October 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: mdgg@hp.fciencias.unam.mx     

Hadron production near threshold

Final state interaction effects inpp→ pΛK ⁺ andpd →³Heη reactions are explored near threshold to study the sensitivity of the cross-sections to thepΛ potential and theηN scattering matrix. The final state scattering wave functions between Λ andp andη and³He are described rigorously. The Λ production is described by the exchange of one pion and aK-meson between two protons in the incident channel. Theη production is described by a two-step model, where in the first step a pion is produced. This pion then produces anη by interacting with another nucleon     

Exciton transitions in photoluminescence spectra of AIAs/GaAs superlattices

Conclusions The studies performed here have shown that the superlattice samples studied exhibit photoluminescence spectra which agree with the Kronig-Penney model, although in calculating the energies of the radiative transitions it is necessary to take into account the binding energy of the excitons,E _B. Due to the exciton—phonon interaction, the 1HH peak breaks up on the long wavelength side into a Poisson distribution. The energy of the LO phonon so determined is 34 meV. Bands due toD ⁰-A ⁰ andD ⁰X transitions, caused by remaining low-level impurities in the GaAs crystals are also observed. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 61, Nos. 3–4, pp. 241–245, September–October, 1994.     

Beta-gamma-gamma directional correlation in103Rh

β-γ-γ directional correlation studies for the cascades (i)β-rays ofE _max=0.12 MeV,γ-rays of 557 keV andγ-rays of 53 keV and (ii)β-rays ofE _max=0.21 MeV,γ-rays of 444 keV andγ-rays of 53 keV have been made. The triple correlation functionsW(θ) were obtained to beW(θ)=1+(−0.153±0.031)P ₂(cosθ)+(0.004±0.035)P ₄(cosθ) forβ-rays ofE _max 0.12 MeV→557→53 keV cascade andW(θ)=1+(0.163±0.042)P ₂(cosθ)+(−0.035±0.058)P ₄(cosθ) forβ rays ofE _max=0.21 MeV→444 keV→53 keV cascade. Spins and parities of the 650, 537 and 93 keV levels of¹⁰³Rh are deduced by triple angular correlation and the internal conversion coefficient studies. Multipolarities of the transitions are also determined.     

Magnetic circular dichroism in the absorption of theF A centre in KCl doped with Li and Na

Summary The spin-orbit structure ofF _A centres in KCl:Li and KCl:Na have been studied by means of the magnetic circular dichroism. Due to theirC _4V symmetry theF _A centres have two different spin-orbit parameters, Δ^‖ and Δ^⊥, which only in the KCl:Li case follow the relation: Δ^‖ < Δ_F < Δ^⊥ as expected from the theory. For a close comparison we have also reported our measurement of the spin-orbit coupling ofF centre in KCl. The spin-orbit parameters of theF andF _A centres have been determined using the method of moment.