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 .     

New investigation of the decay of the high-spin isomer in 151Er

The decay of the T _1/2 = 420 ns isomer in ¹⁵¹Er has been reinvestigated. The multipolarities of the decaying transitions have been established by measuring the electron conversion coefficients. An I ^π = 67/2⁻ assignment is proposed for this isomer with a π[h ₁₁^2/4 d ₃^2/1 d ₅^2/−1]⊗ν[f _7/2 h _9/2 h ₁₁^2/−1] configuration.     

On the Bose-Einstein condensation of free relativistic bosons with or without mass

The Bose-Einstein condensation of free relativistic particles [=(M ² c ⁴ +c ² p ² ) ^1/2 –Mc ² ] is studied rigorously. For massless bosons (=cp), the condensation transition of third (second) order occurs in2 (3) dimensions (D). The molar heat capacity follows the T ² (T ³ ) law below the condensation temperature T_c [k ^B T_c=(2 ² c ² n/1.645) ^1/2 [( ^{2 3} c ³ n/1.202) ^1/3 ], reaches4.38 (10.8) R at T=T_c, and approaches the high-temperature-limit value2 (3) R with no jump (a jump equal to6.75R) in2 (3)D. For finite-mass (M) bosons, the phase transition occurs only in3D with the condensation temperature T_c always smaller than that of the corresponding nonrelativistic bosons [=(2M) ^–1 p ² ]. If the mass M is reduced to zero, the condensation temperature T_c grows monotonically and reaches eventually that of massless relativistic bosons. This mass-dependence of T_c is therefore distinct from the case of nonrelativistic bosons, where T_c grows to infinity as M 0. A brief discussion is given for a possible connection with the normal-to-super transition of the independently moving Cooper pairs (bosons).     

Predissociation and photodissociation of IBr

The observed predominance of excited Br(² P _1/2) atoms in the nearultra-violet photodissociation products of IBr is shown to be quantitatively consistent with an intermediate coupling regime in the visible absorption region, which invalidates the traditional interpretation of the B′(O ⁺) state as a new Born-Oppenheimer state arising from a strongly avoided potential curve crossing. A general theory of predissociation at intermediate coupling, covering the positions, intensities and widths of the spectral lines, shows that both diabatic and adiabatic characteristics must be taken into account. The presence of a sharp level is predicted at any coincidence between an adiabatic and a diabatic term value with the same J value, and the spacing between neighbouring lines is shown to depend on an average between the diabatic and adiabatic rotational constants. The theory is successfully applied to the B(³Π _{o ⁺} ) and B′(O ⁺) states of IBr, and potential curves for the two states are reported. The analysis is consistent with the following curve crossing parameters r_x = 3·220 Å, E_x = 16 915 cm^-1, V ₁₂ = 170 cm^-1, and ΔF = 9178 cm^-1 Å^-1, and with the following spectroscopic constants for the B′(O ⁺) state of IBr⁷⁹:

     

Blistering of rhenium irradiated with 21keV helium ions

This paper describes blistering of rhenium following 21 keV He⁺-ion irradiation at temperatures between 300 K and 1200 K. Blistering starts at 300 K at a dose of 3×10¹⁷ ions/cm². The most probable blister diameter varies from 4400 ? at 300 K to 10100 ? at 1200 K. The blister depth τ _bl , the blister diameter φ _bl and the blister heighth _bi show a distribution. From the observations one could derive the following relationships:h _bl = 0.35φ _bl ; τ _bl =3.43φ _bl ^2/3 . The erosion yieldE _y due to blistering is function of doseE _y =0.51 atoms/ion at 3×10¹⁷ ions/cm²,E _y =0.56 atoms/ion at 6×10¹⁷ ions/cm² andE _y =0.14 atoms/ion at 3×10¹⁸ ions/cm². The sputtering yieldS (21 keV) is estimated to be ∼0.1 atom/ion. The corresponding surface regression is 44? at 3×10¹⁷ ions/cm² and 1323 ? at 9×10¹⁸ ions/cm². Surface regression has therefore little influence on the observations at low doses. Work performed at the Mathematicals Science Department of S.C.K./C.E.N. at Mol (Belgium)     

() reaction studies of Dy and Hf

Angular distributions for the ¹⁶³Dy(t,p) and ¹⁷⁷Hf(t,p) reactions were measured using 17 MeV tritons from the McMaster University Tandem Van de Graaff accelerator. Reaction products were analyzed with a magnetic spectrograph and detected with photographic emulsions. Favored L=0 transitions confirmed assignments of the 5/2⁻[523] band in ¹⁶⁵Dy and 7/2⁻[514] band in ¹⁷⁹Hf. Additional L=0 transitions in each nuclide identified previously unknown 5/2⁻ levels in ¹⁶⁵Dy and 7/2⁻ ones in ¹⁷⁹Hf. Overall trends of L=0 strengths support the existence of subshell closures at neutron numbers 98 and 108. On the basis of a relatively strong L=2 transition, the K^π=11/2⁻ γ-vibration based on the 7/2⁻[514] state is identified at 1689 keV in ¹⁷⁹Hf, about 440 keV above its previously-assigned K^π=3/2⁻ partner.     

低温下Er3+/Yb3+共掺碲酸盐玻璃的发光特性研究

研究了在8—300K温度范围中, Er³⁺/Yb³⁺共掺碲酸盐玻璃的15μm荧光光谱、上转换光谱与温度的关系. Er³⁺:⁴I_13/2→⁴I_15/2跃迁发射光谱通过高斯拟合和简单的四能级系统估计了Er³⁺离子⁴I_13/2和⁴ 关键词： 碲酸盐玻璃 上转换发光 低温 荧光特性     

Pulsed-laser photolysis of Mn2(CO)10: A time-resolved fluorescence study

Mn₂(CO)₁₀ was photolysed in the gas phase by the XeCl-excimer laser with fluence in the range 25–300 mJ/cm² and a dye laser. The UV/VIS emission of the products was probed on a nanosecond time scale. The emission from excited states of metal atoms was detected only. The Mn atoms are predominantly formed in their ground statea ⁶ S _{2 1/2}. The absorption of one photon and the subsequent relaxation process leads to the formation ofz ⁶ P _J ⁰ (J = 11/2, 21/2, 31/2) states and emission of photons at a wavelength of 403 nm. The formation of the excited statese ⁸ D _{5 1/2},z ⁶ F _{4 1/2} ⁰ ande ⁶ D _{4 1/2} and the subsequent emission observed at wavelengths of 357, 383 and 446 nm requires the absorption of two photons by the ground-state Mn atoms. In addition, transition from thea ⁶ D _j (J = 11/2, 21/2) lower states were observed in the wavelength-resolved Laser-Induced Fluorescence (LIF) spectra.     

Self-pulsing dynamics of ytterbium-doped fiber laser with pump-bypassed cavity

In addition to efficient continuous wave laser action at 1.06 μm (⁴ F _3/2→⁴ I _11/2 transition), with a slope efficiency 30% and 30 mW pump power threshold, this work presents a throughout study of the spectroscopic, and thermo-optical properties of a 2.0 mol % Nd³⁺ doped fluoroindogallate glass. The characterization of the sample using the pump probe experimental technique indicated the presence of two broad excited state absorption bands from 0.94 to 1.05 μm (⁴ F _3/2→² D _3/2, ² G _9/2, ⁴ G _11/2, ² K _15/2) and from 1.16 to 1.42 μm (⁴ F _3/2→⁴ G _9/2, ⁴ G _7/2, ² K _13/2), found not to interfere with the stimulated emission at 1.06 μm, with a peak cross section value σ_SE = 2.55×10^-21 cm² and a full width at half maximum of 22 nm. Thermal lens measurements were performed to quantify the Auger upconversion parameter (γ=(1.26±0.09)×10^-16 cm³/s) and evaluate the thermal loading in the sample in comparison to other commercial glasses. PACS 181.05.Kf; 78.45.+h; 42.70.Hj     

黏滞等离子体中双撕裂模不稳定性的数值模拟研究

本文采用磁流体力学模型,数值研究了平板位形下双撕裂模线性增长率关于等离子体电阻η和黏滞v的定标关系.结果表明,对于有理面间距较大的情况,线性增长率关于电阻和黏滞的指数定标率随着黏滞的增加逐渐由γ∝ η3/5v0的定标变化到γ∝η5/6v-1/6的定标;而对于有理面间距较小的情况,其指数定标率随着黏性的增加从γ∝η 1/3 v0的定标逐渐变化到γ∝η2/3v-1/3的定标.本文还给出了初始阶段对称的双撕裂模的非线性演化,发现在非线性阶段对称的双撕裂模将转化为反对称的双撕裂模,并解释了相应的物理机理.     

Enhanced isospin dependence of the empirical particle-hole effective interaction

The separation betweenT=0 andT=1 centroids of the empirical effective interaction is fairly large for the (d ₃ ^2/−1 f _7/2)JT particle-hole interaction as compared to nearby (f _7/2)² JT and (d _5/2)² JT particle-particle interactions. This interesting feature of the empirical effective interaction is shown to arise as a consequence of renormalization of the effective interaction as one truncates the configuration space from (s−d)⁻¹(f−p)¹ to (d ₃ ^2/−1 f _7/2) and from (f−p)² and (s−d)² configurations to (f _7/2)² and (d _5/2)² respectively.     

Ricci collineations of the Bianchi type II,VIII, and IX space-times

Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of ^a (x ^b ) is different from zero and (ii) two components of ^a (x ^b ) are different from zero, fora, b=1, 2, 3, 4, are presented. In subcase (i.b), which is ^a = (0, ¹(x ^a ),0,0), some known solutions are found, and in subcase (i.d), which is ^a =(0, 0, 0, ⁴(x ^a )), choosingS(t) = const.×R(t), the Bianchi type II, VIII, and IX spacetime is reduced to the Robertson-Walker metric.     

Investigation of the intershell higher order resonant recombination and polarization of X-ray emission of B-like silicon ions

K-shell dielectronic, trielectronic, and quadruelectronic recombination and polarization of X-ray emission have been studied for the highly charged Si⁹⁺ ions in the initial ground state ²P_1/2 and the metastable state ²P_3/2 using the Flexible Atomic Code. It is found that the resonant recombination cross section from the long-lived metastable state is comparable in magnitude with that of the ground state, so it is important for plasma diagnostics. For Si⁹⁺(²P_1/2), trielectronic recombination contributions of nearly 25% to the total resonant recombination strength are predicted, which is less than previous calculations. We compare the degree of linear polarization for the eleven dominant resonant recombination satellite lines from the initial parent Si⁹⁺(²P_1/2) and Si⁹⁺(²P_3/2) ions. For the same X-ray lines, large variations of polarization are found between ²P_1/2 and ²P_3/2, which can be employed to diagnose formation mechanisms of intermediate resonance states and corresponding X-ray lines.     

High-spin states in 160Lu

High-spin states of ¹⁶⁰Lu have been studied through the ¹⁴⁴Sm( ¹⁹F, 3n) reaction. The previously known πh _11/2⊗υi _13/2 yrast band is extended from I ^π = 21^- to 25^- and a four quasiparticle band with configuration πh _11/2[523]7/2 ^-⊗υh _9/2[521]3/2 ^-⊗ (υi _13/2)² is reported. Received: 21 May 2001 / Accepted: 19 July 2001     

The kinetic limitation of anti-stokes luminescence of Er3+ and Yb3+ doped infrared upconversion materials

Infrared-to-visible wave-length conversion in the Yb³⁺−Er³⁺ doped phosphors system has been described by a simple three level model based on two ions mechanism. The excitation in the range of 900–1000 nm of an IR-photon is first absorbed by Yb³⁺ ion as a sensitizer attributed to the resonant energy transition in Er³⁺ ion from ⁴ I _3/2 → ⁴ S _15/2 and ¹ F _9/2 → ⁴ I _15/2, respectively for green and red emission. The essential energy transfer processes in this system i.e. upconversion from ⁴ I _11/2 and ¹ I _13/2, cross-relaxation from ⁴ S _3/2 and ¹ F _9/2 are taken into account. The limitations of the rate-equation approach are examined with a focus on the underlying dynamics of this rare-earth system.     

Diffusion by Turbulence

The turbulent diffusivity K of the atmosphere has first been studied by Richardson 1926 who empirically found that K depends on the scale l, K = Al^α, with α = 4/3 and A = 0.6 cm^2/3 s^?1. This empirical scaling law is derived here from a unified theory (based on the Navier-Stokes equation) together with an explicit result for the prefactor, A = 2.4 ?^1/3. The mean atmospheric dissipation rate compatible with this is ? = 0.016 cm² s^?3. For windtunnels with typical dissipation rates ? ? 1 m² s^?3 the turbulent diffusion coefficient should be K/cm² s^?1 = 52 (l/cm)^4/3.     

Investigation into the rotational bands of 185Pt with the particle-rotor model

Theoretical calculations have been performed for the ν9/2⁺[624](i _13/2) and ν7/2⁻[503]( f _7/2) bands of ¹⁸⁵Pt in the framework of particle-rotor model. The band properties of signature splitting and configuration mixing have been analyzed. The level energy and signature splitting before the band crossing can be well interpreted by introducing triaxiality. The positive-parity yrast band is proposed to be dominated by the ν9/2⁺[624](i _13/2) component, while the negative-parity band shows strong mixing of ν7/2⁻[503](f _7/2) and ν9/2⁻[505](h _9/2) configurations.

     

Laser-induced fluorescence line narrowing in cobalt I

Laser-Induced Fluorescence Line Narrowing (LIFLN) measurements of hyperfine structure splittings performed on the cobalt I transition sequence3d ⁸4s a ² P _1/23d ⁷4s4p z ²4D _3/2 ⁰ 3d ⁸4s b ⁴ F _3/2are presented. The hyperfine coupling constants of theb ⁴ F _3/2 level were determined to beA = 302.8(1.9) MHz andB = – 81.6(18.2) MHz and are compared with results of both experimental and theoretical studies reported by other authors.     

Er3+：GdVO4中Er3+离子的光谱参数计算和晶场中能级分裂的讨论

对Er³⁺：GdVO₄样品的光谱参数以及Er³⁺在晶场中能级的分裂情况进行了研究. 首先对样品进行了吸收光谱的测量，接着用Judd-Ofelt理论拟合出了Er³⁺在GdVO₄晶体中的强度参量Ω_t，并由此计算了跃迁的振子强度、自发辐射跃迁速率、荧光分支比和积分发射截面. 通过计算结果可以发现有较多能级之间的跃迁都有大于10^-6的振子强度和大于10^-18cm的积分发射截面，并且具有较高的荧光分支比，特别是²H_11/2→⁴I_15/2，⁴S_3/2→⁴I_15/2，⁴F_9/2→⁴I_15/2和⁴I_13/2→⁴I_15/2等几个强发光能级除了具有较大的振子强度和积分发射截面外还有很好的应用前景，因此也更加值得关注. 最后还利用群论讨论了Er³⁺离子在GdVO₄晶场中各能级的分裂情况并对各Stark子能级的J_z混杂情况进行了分析.