On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r ₁₂, r ₁₃, r ₁₄, r ₂₃, r ₂₄, r ₃₄) and ten (r ₁₂, r ₁₃, r ₁₄, r ₁₅, r ₂₃, r ₂₄, r ₂₅, r ₃₄, r ₃₅ and r ₄₅) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial wave functions for the ¹ S states in four-electron atomic systems include the two independent spin functions χ₁ = αβαβ + βαβα − βααβ − αββα and χ₂ = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited 2³ S states in four- electron atomic systems.     

Description of α-decay half-lives of heaviest nuclei

The accuracy in describing α-decay half-lives T _α of heavy and superheavy nuclei is studied. A simple five-parameter phenomenological formula, expressing T _α as a function of the α-decay energy Q _α, is considered. It is found that such a formula can describe measured values of T _α within a factor of 1.3 for even-even, 2.1 for odd-even, 3.2 for even-odd, and 4.0 for odd-odd nuclei when measured values of Q _α are taken. This accuracy is decreased by a factor of about 4 when theoretical values of Q _α are used. The latter are obtained within a macroscopic-microscopic approach and reproduce the experimental values of Q _α of the same nuclei with an average accuracy of about 190 keV for even-even, 270 keV for odd-even, 260 keV for even-odd, and 330 keV for odd-odd nuclei. In the analysis, 201 nuclei with proton number Z = 84–111 and neutron number N = 128–161, with measured values of both Q _α and T _α, are taken. The text was submitted by the authors in English.     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

Alpha decay of the new isotopes 188,189Po

New neutron-deficient isotopes ^188,189Po have been produced in the complete fusion reaction of ⁵²Cr ions with a ¹⁴²Nd target at the velocity filter SHIP. The evaporation residues were separated in-flight and subsequently identified on the basis of α-γ and α-conversion electron coincidence measurements and of α-α position and time correlations. In ¹⁸⁹Po a ground state to ground state α decay with E_α1= 7540(20) keV, T_1/2= 5(1) ms and two fine structure α-decays at E_α2= 7264(15) keV and E_α3= 7316(15) keV have been observed. In ¹⁸⁸Po (T_1/2= 400⁺²⁰⁰ ₋₁₅₀μs) a ground state to ground state α decay at E_α= 7915(25) keV and a fine structure α decay at E_α= 7350(40) keV have been found. Improved data on the α-decay of ¹⁸⁹Bi were obtained. Received: 15 October 1999     

Influence of Thomson effect on the resultant local Seebeck coefficient in thermoelectric composite materials

The resultant local Seebeck coefficient α _R (=α _S−α _T) at the interface of a thermoelement has not yet been measured, although it is an important factor governing the thermoelectric efficiency, where α _S is the local Seebeck coefficient and α _T is the one caused by the Thomson effect. It is shown in this paper that α _S, α _T, and α _R of the p- and n-type Cu/Bi–Te/Cu composites are obtained analytically and experimentally on the assumption that the local temperature of the composite on which the temperature difference ΔT is imposed varies linearly with changes in position along the composite. They were indeed estimated as a function of position from the local experimental data of R,ΔI,ΔT, and V generated by applying an additional current of ±I to the composite, where R is the electrical resistance and ΔI is a current generated by the composite. As a result, it was found that the absolute values of α _S at the hot interface of the p- and n-type composites are approximately 1.5 and 1.4 times higher than their lowest values in the middle region of the composite, respectively, while those of α _T are less than 8% of α _S all over the composite and are so small that the relation α _R≈α _S can be held. We thus succeeded in measuring α _R at the interfaces of the composite.     

Glassy behavior and jamming of a random walk process for sequentially satisfying a constraint satisfaction formula

Random K-satisfiability (K-SAT) is a model system for studying typical-case complexity of combinatorial optimization. Recent theoretical and simulation work revealed that the solution space of a random K-SAT formula has very rich structures, including the emergence of solution communities within single solution clusters. In this paper we investigate the influence of the solution space landscape to a simple stochastic local search process SEQSAT, which satisfies a K-SAT formula in a sequential manner. Before satisfying each newly added clause, SEQSAT walk randomly by single-spin flips in a solution cluster of the old subformula. This search process is efficient when the constraint density α of the satisfied subformula is less than certain value α_cm; however it slows down considerably as α> α_cm and finally reaches a jammed state at α≈α_j. The glassy dynamical behavior of SEQSAT for α≥α_cm probably is due to the entropic trapping of various communities in the solution cluster of the satisfied subformula. For random 3-SAT, the jamming transition point α_j is larger than the solution space clustering transition point α_d, and its value can be predicted by a long-range frustration mean-field theory. For random K-SAT with K ≥ 4, however, our simulation results indicate that α_j = α_d. The relevance of this work for understanding the dynamic properties of glassy systems is also discussed.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Dynamics of α-clusters in N = Z nuclei

The systematics for binding energies per α-particle in N = Z nuclei, E _Bα/N _α, are studied up to ¹⁶⁴Pb. It is shown that, although a geometrical model can be used to explain the systematics for light nuclei, the binding energy per α-particle exhibits structures which are due to the well-known shells of the mean field of nucleons in nuclei. The overall dependence of E _Bα/N _α on N _α in N = Z nuclei (for the ground-state masses) can be described in a liquid-drop model of α-particles. Conditions for a phase change with the formation of an α-particle condensate, a dilute Bose gas in excited compound nuclei are discussed for E _Bα/N _α = 0, at the thresholds. This is achieved when the binding energy per nucleon in nuclei is equal to or smaller than in the α-cluster. At somewhat smaller excitation energies the appearance of a Bose gas with a closed-shell core (N = Z, e.g. of ⁴⁰Ca) is proposed within the same concept. The experimental observation of the decay of such condensed α-particle states is proposed with the coherent emission of several correlated α-particles not described by the Hauser-Feshbach approach for compound-nucleus decay. This decay will be observed by the emission of unbound resonances in the form of ⁸Be and ¹²C ^* (0⁺ ₂) clusters.     

Cluster model of s- and p-shell ΛΛ hypernuclei

The ΛΛ binding energy (B _ΛΛ) of the s- and p-shell hypernuclei are calculated variationally in the cluster model and multidimensional integrations are performed using Monte Carlo. A variety of phenomenological Λ-core potentials consistent with the Λ-core energies and a wide range of simulated s-state ΛΛ potentials are taken as input. The B _ΛΛ of _ΛΛ⁶He is explained and _ΛΛ⁵He and _ΛΛ⁵H are predicted to be particle stable in the ΛΛ-core model. The results for s-shell hypernuclei are in excellent agreement with those of non-VMC calculations. The _ΛΛ¹⁰Be in ΛΛαα model is overbound for combinations of ΛΛ and Λα potentials. A phenomenological dispersive three-body force, V _Λαα, consistent with the B _Λ of _Λ⁹Be in the Λαα model underbinds _ΛΛ¹⁰Be. The incremental ΔB _ΛΛ values for the s- and p-shell cannot be reconciled, consistent with the finding of earlier analyses.      

Focal switch of cosine-Gaussian beams

The focal switch of cosine-Gaussian (CsG) beams passing through a system with the aperture and lens separated is studied analytically and numerically. It is shown that the focal switch of CsG beams can appear not only for the apertured case, but also for the unapertured case. The necessary condition for the focal switch is that truncation parameter α > α_c and the beam parameter β > β_c, α_c, β_c being the corresponding critical values. There exists a maximum of the relative transition height Δz _sw as α varies, and Δz _sw increases with increasing β and decreasing N _w. The normalized axial intensity minimum I _min / I _max decreases with an increase of α and β, and I _min / I _max remains unchanged as N _w varies.     

Spatial characteristics of Kα radiation from weakly relativistic laser plasmas

The spatial dependence of K _α emission generated from laser-produced hot electrons is investigated experimentally and theoretically. In addition, the conversion efficiency of K _α production as a function of laser intensity is measured and compared with modeling results. We use the terawatt Ti:sapphire laser at MPQ and vary the peak intensity from 10¹⁵ to 10¹⁸ W/cm² with a pulse duration of 200 fs. A solid Cu target is placed at various positions in the laser focus, which allows one to vary the intensity but keep the total energy on the target constant. When the target is near best focus, the FWHM of the K _α emission, measured using a knife-edge, is considerably larger than the FWHM of the laser intensity. In measuring the efficiency of K _α production using the fundamental wavelength of the laser, a clear maximum of K _α emission is observed at a position away from best focus, where the peak intensity is down by more than an order of magnitude from the value at best focus. When the second harmonic of the laser is used, the K _α emission is peaked near best focus. The K _α emission from layer targets is used to obtain an estimate of the temperature of the hot electrons. Modeling of K _α production, using a Monte Carlo electron/photon transport code, shows the relationship between incident electron energy and the emitted K _α emission. Efficient K _α generation from the low-intensity wings of the laser pulse contributes to the large spot size of the K _α emission. The lower electron temperatures that are expected for the second harmonic explain the differences in the location of maximum K _α emission for the two wavelengths. We discuss the use of K _α emission in photoionizing inner-shell electrons with the goal of achieving X-ray lasing at short wavelengths. Received: 6 April 1999 / Revised version: 31 May 1999 / Published online: 11 August 1999     

C*-Algebras associated with one dimensional almost periodic tilings

For each irrational number, 0<α<1, we consider the space of one dimensional almost periodic tilings obtained by the projection method using a line of slope α. On this space we put the relation generated by translation and the identification of the “singular pairs”. We represent this as a topological spaceX _α with an equivalence relationR _α. OnR _α there is a natural locally Hausdorff topology from which we obtain a topological groupoid with a Haar system. We then construct the C^*-algebra of this groupoid and show that it is the irrational rotation C^*-algebra,A _α. Research supported by the Natural Sciences and Engineering Research Council of Canada and the Fields Institute for Research in Mathematical Sciences.     

Doppler shapes of the γ line in the <Superscript>9</Superscript>Be(α, nγ)<Superscript>12</Superscript>C reaction in plasma at temperatures <Emphasis Type="Italic">T</Emphasis><Subscript>α</Subscript> < 0.6 MeV

A parametrization of the partial cross section of the ⁹Be(α, nγ)¹²C reaction in the α-particle energy range of 0.3–7.9 MeV is presented, along with the count rates of γ quanta. The need to consider subbarrier (Eα < 1.9 MeV) α-particles in plasma for temperatures T _α < 0.2 MeV is substantiated. The shapes of the Doppler-broadened 4.44 MeV γ line and the count rates of γ quanta in the plasma of the JET tokamak are measured for the first time and compared to the calculated values. An estimated T _α ≲ 160 keV is obtained.     

Two-phase reaction mechanism during chemical lithium insertion into α-MoO<Subscript>3</Subscript>

The phase transition during chemical lithium insertion into α-MoO₃ was investigated by chemical analysis, X-ray diffraction (XRD) and electrochemical characterisation. The samples have been prepared by reaction of various amounts of water-free lithium iodide with fine-particulate orthorhombic molybdenum trioxide in n-hexane (non-aqueous media), which yielded materials with different Li/Mo ratio. XRD investigations of these materials proved that the crystal structure of the layered α-MoO₃ has been changed after the chemical lithiation. The phase transition ranged from 0.25 < x < 0.5 in Li _x MoO₃ upon chemical lithium insertion into α-MoO₃. The XRD lines of lithium inserted phase Li _x MoO₃ grew at the expense of the XRD lines of the pristine α-MoO₃ as lithium ions were chemically inserted until the disappearance of lines related to α-MoO₃. The electrochemical performance of the lithiated samples is improved in comparison with the starting material (non-lithiated α-MoO₃).     

A convergent star product for linear Poisson structures

An explicit star product ⋆ _α ^Γ on the dual of a general Lie algebra equipped with the linear Poisson bracket is constructed. An equivalence operator between this star product and the Kontsevich star product in [K₁] is given and diverse properties of the star product ⋆ _α ^Γ are studied. It is also proved that the star product ⋆ _α ^Γ provides a convergent deformation quantization in the sense of Rieffel [R₁].     

Measurement of the spindependent relative conversion coefficients in α-Fe and α-Fe2O3

The relative differences δ _ns (n=1, 2, 3) of the spindependent conversion coefficients were measured for α-Fe and α=Fe₂O₃. In contrast to theoretical predictions of δ_1s≃−10⁻⁵ we found δ_1s≃−1.0(4)x10⁻² for both α-Fe and α-Fe₂O₃. As a possible source for this difference we consider a dynamic coupling with the atomic spin during the conversion process.     

QCD coupling constant below 1 GeV in the poincare-covariant model

The behavior of the running coupling constant α _s (Q ²) phenomenologically parameterized in the region of Q < 1 GeV is considered within the framework of the Poincare-covariant quark model in a variety of regimes. An analysis was carried out for pseudoscalar and vector mesons with the lepton masses and decay constants (obtained by the model calculations) required to match their experimental counterparts. It shows that the constant α _s is likely to behave with α_crit = α _s (Q ² = 0) ∼ 0.667 − 0.821 in the case of a frozen regime and α_crit =0.300 − 0.692 for peaked curves, which follows from the experimental values of the leptonic decay constants and masses.     

Microstructure and gas sensitive properties of α(M: Sn and Ti) materials prepared by ball milling

Metastable α-Fe₂O₃-MO₂(M: Sn and Ti) solid solutions can be synthesized by mechanical alloying. The alloy formation, microstructure, and gas sensitive properties of mechanically milled α-Fe₂O₃-SnO₂ materials are discussed. Tin ions in α-Fe₂O₃ are found to occupy the empty octahedral holes in the α-Fe₂O₃ lattice. This interstitial model can also describe the structure of α-Fe₂O₃-TiO₂solid solutions. Finally, a correlation of gas sensitive properties with microstructure of α-Fe₂O₃-SnO₂ materials is presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal stabilization of tin- and cobalt-doped manganese dioxide

We study the thermal stability, local structure, and electrical properties of the α-MnO₂ phase doped with Sn and Co. It is found that doping prevents the transformation from α-MnO₂ to α-Mn₂O₃ that occurred in the temperature range of 500–600 °C. Samples have been synthesized in an acidic medium using the reduction of potassium permanganate by fumaric acid. X-ray diffraction patterns (XRD) of pure and doped α-MnO₂ prepared at 450 °C do not show new peaks related to dopant species. Thermogravimetric analysis (TGA) of the Sn and Co doped MnO₂ reveals that transformation from MnO₂ to α-Mn₂O₃ starts above 700 °C. The increase in the thermal stability is attributed to the presence of Sn or Co ions incorporated inside the large 2 × 2 tunnels as revealed by Fourier transform infrared (FTIR) spectra measurements. An increase in the electrical conductivity with the presence of Sn or Co ions is observed. Electrochemical features of the doped MnO₂ samples in alkaline cells are reported and compared with that of the pristine α-MnO₂ phase.     

Single α-particle orbits and Bose-Einstein condensation in <Superscript>12</Superscript>C

Bosonic properties of α particles such as single-α orbits and occupation numbers in J^π = 0⁺, 2⁺, 1^- and 3^- states of ¹²C around the 3α threshold are investigated with the semi-microscopic 3α cluster model. As in other studies, we found that the 0⁺₂ (2⁺₂) state has dilute-3α-condensate-like structure in which the α particle is occupied in the single S (D) orbit with about 70% (80%) probability. The radial behaviors of the single-α orbits as well as the occupation numbers are discussed in detail in comparison with those for the 0⁺₁ and 2⁺₁ states together with the 1^-₁ and 3^-₁ states.