Dielectronic recombination rate coefficient for Cu-like Au^50＋ ion

The rate coefficients α^{DR} of dielectronic recombination (DR) for Cu-like Au^{50+} ion collided with the incident free electron are calculated based on the quasi-relativistic multi-configuration Hartree－Fock theory. The results clearly show that the α^{DR} of all recombination channels exhibits resonance characters with electron temperature. At lower temperatures, the recombination for electrons caused by 4s excitation is dominant through outer electron radiative transitions among the intermediate doubly excited autoionizing levels, in which the most components come from 3d^{10}5pns states, whereas with increasing electron temperature, DR caused by 3d excitation turns out to be dominant, and the contribution from the 3d^94s4fnf state to the total rate coefficient of electron 3d is the largest with α^{DR}=1.15×10^{- 11} cm^3·s^{-1} at an electron temperature of T_e=0.35 keV. Under this condition, there exists a strong competition between the two types of recombination channels.     

Hyperfine structure and isotope shift study in singly ionized lead

Hyperfine structure and isotope shifts in five optical transitions: 424.5 nm ( – ), 537.2 nm ( – ), 554.5 nm ( – ), 560.9 nm ( – ) and 666.0 nm ( – ) of Pb  II have been measured. As a light source the discharge tube was used. The hyperfine structure measurements were performed using metallic isotope ²⁰⁷Pb. For isotope shifts measurements natural lead was used. The high resolution spectral apparatus consisted of a silver coated Fabry-Perot etalon and a grating spectrograph combined with a CCD camera used as a detector. In the analysis of the spectra a computer simulation technique was used. The hyperfine structure observations yielded the splitting constants A for seven levels of Pb II. The isotope shift studies enabled to separate the mass and the field shifts and to determine values of changes of the mean square nuclear charge radii.     

An expansion of Hartree-Fock and correlation energies,relativistic corrections and the dipole matrix element in the powers of of 1/Z

Feynman diagrammatic technique was used for the calculation of Hartree-Fock and correlation energies, relativistic corrections, dipole matrix element. The whole energy of atomic system was defined as a polen-electron Green function. Breit operator was used for the calculation of relativistic corrections. The Feynman diagrammatic technique was developed for 〈H_B>. Analytical expressions for the contributions from diagrams were received. The calculations were carried out for the terms of such configurations as 1s² 2sⁿ¹ 2pⁿ² (2 ≧n₁≧ 0, 6≧ n₂ ≧ 0). Numerical results are presented for the energies of the terms in the form $$E = E_0 Z^2 + \Delta {\rm E}_2 + \frac{1}{Z}\Delta {\rm E}_3 + \frac{{\alpha ^2 }}{4}(E_0^r + \Delta {\rm E}_1^r Z^3 )$$ and for fine structure of the terms in the form $$\begin{gathered} \left\langle {1s^2 2s^{n_1 } 2p^{n_2 } LSJ|H_B |1s^2 2s^{n_1 \prime } 2p^{n_2 \prime } L\prime S\prime J} \right\rangle = \hfill \\ = ( - 1)^{\alpha + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 1} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 [E^{(0)} (Z - B) + \varepsilon _{co} ] + \hfill \\ + ( - 1)^{L + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 2} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 \varepsilon _{cc} . \hfill \\ \end{gathered} $$ Dipole matrix elements are necessary for calculations of oscillator strengths and transition probabilities. For dipole matrix elements two members of expansion by 1/Z have been obtained. Numerical results were presented in the form P(a,a′) = a/Z(1+τ/Z).     

Theory of nine elastic constants of biaxial nematics

In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average （Dmn^（l）） （Dm＇n＇^（l＇））, where Dmn^（l） is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ＇, λ, order parameters Q0 = Q0（D00^（2）） ＋Q2（D02^（2）＋D0-2^（2）） and Q2 = Q0（D20^（2）） ＋ Q2（D22^（2）＋D2-2^（2））. Here Γ and Γ＇ depend on the function form of molecular interaction energy vj′j″j （τ12） and probability function fk′k″k （τ12）, where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 are parameters related to multiple moments of molecules. Comparing these results with those obtained from Landau-de Gennes theory, we have obtained relationships between coefficients, order parameters used in both theories. In the special case of uniaxial nematics, both results are reduced to a degenerate case where K11=K33.     

Über die Hyperfeinstruktur der verbotenen Hg II-Linie λ 2815 Å und die Isotopieverschiebungskonstanten des Quecksilbers

Zeitschrift für Physik A Hadrons and nuclei - The hyperfinestructure of the Hg II-line λ 2815 Å $$(5d^{10} 6s{}^2S_{\tfrac{1}{2}} - 5d^9 6s^2 {}^2D_{\tfrac{5}{2}} )$$ , forbidden for...     

Investigation of isotope effects of dynamic properties for H(D) +OF reactions by the quasi-classical trajectory method

Quasi-classical trajectory (QCT) calculations are employed to study the dynamic properties for \mbox{H(D)} + \mbox{OF} reactions on the adiabatic potential energy surface (PES) of the \mbox{1}{ }^{3}\mbox{A}' triplet state. Obvious differences between the reaction probabilities for J = 0, integral cross sections for J \ne 0, branch ratios of the product and internuclear distances as well as product rotational alignments between the title reactions are found. These differences are attributed mainly to the different reduced masses of the reactants and the different zero-point energies (ZPEs) of the transition state.     

The Essence of Operators’ Weyl Ordering Scheme and New Operator Identities for Converting Q−P Ordering to Weyl Ordering

We find new operator formulas for converting Q?P and P?Q ordering to Weyl ordering, where Q and P are the coordinate and momentum operator. In this way we reveal the essence of operators’ Weyl ordering scheme, e.g., Weyl ordered operator polynomial ${_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}}$ , $$\begin{aligned} {_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}} =&\sum_{l=0}^{\min (m,n)} \biggl( \frac{-i\hbar }{2} \biggr) ^{l}l!\binom{m}{l}\binom{n}{l}Q^{m-l}P^{n-l} \\ =& \biggl( \frac{\hbar }{2} \biggr) ^{ ( m+n ) /2}i^{n}H_{m,n} \biggl( \frac{\sqrt{2}Q}{\sqrt{\hbar }},\frac{-i\sqrt{2}P}{\sqrt{\hbar }} \biggr) \bigg|_{Q_{\mathrm{before}}P} \end{aligned}$$ where ${}_{:}^{:}$ ${}_{:}^{:}$ denotes the Weyl ordering symbol, and H _m,n is the two-variable Hermite polynomial. This helps us to know the Weyl ordering more intuitively.     

Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic Oscillator

Let be the spectrum of in L ²(ℝ), where q is an even almost-periodic complex-valued function with bounded primitive and derivative. It is known that , where is the spectrum of the unperturbed operator. Suppose that the asymptotic approximation to the first asymptotic correction is given. We prove the formula that recovers the frequencies and the Fourier coefficients of q in terms of Δμ _n .      

W diffusion in paramagnetic and ferromagnetic <Emphasis Type="Italic">α</Emphasis>-Fe

Diffusion of W in the 723–1153 K temperature range both in paramagnetic and ferromagnetic α-Fe was studied, diffusion couples were manufactured by W evaporation onto high-purity Fe samples. Measurements were made using the Heavy Ion Rutherford Backscattering (HIRBS) technique as the analysis tool. A straight Arrhenius plot was obtained in the paramagnetic region with a break at the Curie temperature (1043 K) followed by a curved plot at lower temperatures as a product of the effect of ferromagnetism on diffusion. A straight Arrhenius plot was obtained in the paramagnetic region with a break at the Curie temperature (1043 K) followed by a curved plot at lower temperatures resulting from the effect of ferromagnetism on diffusion. A previous developed model for the diffusion of non-magnetic impurities in ferromagnetic Fe fits the data perfectly well, giving a temperature dependent diffusivity according to

Unifying the theory of integration within normal-, Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators(which considers normally ordered,antinormally ordered and Weyl ordered product of operators as its special cases).The s-ordered operator expansion(denoted by...) formula of density operators is derived,which is ρ = 2 1 s ∫ d2βπβ|ρ |β exp { 2 s 1(s|β|2 β a + βa a a) }.The s-parameterized quantization scheme is thus completely established.     

Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules

In this article, we construct the color-singlet-color-singlet type currents and the color-singlet-colorsinglet-color-singlet type currents to study the scalar D*■*, D*D* tetraquark molecular states and the vector D*D*■*, D*D*D* hexaquark molecular states with the QCD sum rules in details. In calculations, we choose the pertinent energy scales of the QCD spectral densities with the energy scale formula ■for the tetraquark and hexaquark molecular states respectively in a consistent way. We obtain stable QCD sum rules for the scalar D*■*, D*D*tetraquark molecular states and the vector D*D*■* hexaquark molecular state, but cannot obtain stable QCD sum rules for the vector D*D*D* hexaquark molecular state. The connected(nonfactorizable)Feynman diagrams at the tree level(or the lowest order) and their induced diagrams via substituting the quark lines make positive contributions for the scalar D*D* tetraquark molecular state, but make negative or destructive contributions for the vector D*D*D* hexaquark molecular state. It is of no use or meaningless to distinguish the factorizable and nonfactorizable properties of the Feynman diagrams in the color space in the operator product expansion so as to interpret them in terms of the hadronic observables, we can only obtain information about the short-distance and long-distance contributions.     

One-range Addition Theorems for Noninteger n Slater Functions using Complete Orthonormal Sets of Exponential Type Orbitals in Standard Convention

By the use of complete orthonormal sets of ${\psi ^{(\alpha^{\ast})}}$ -exponential type orbitals ( ${\psi ^{(\alpha^{\ast})}}$ -ETOs) with integer (for α ^* = α) and noninteger self-frictional quantum number α ^*(for α ^* ≠ α) in standard convention introduced by the author, the one-range addition theorems for ${\chi }$ -noninteger n Slater type orbitals ${(\chi}$ -NISTOs) are established. These orbitals are defined as follows $$\begin{array}{ll}\psi _{nlm}^{(\alpha^*)} (\zeta ,\vec {r}) = \frac{(2\zeta )^{3/2}}{\Gamma (p_l ^* + 1)} \left[{\frac{\Gamma (q_l ^* + )}{(2n)^{\alpha ^*}(n - l - 1)!}} \right]^{1/2}e^{-\frac{x}{2}}x^{l}_1 F_1 ({-[ {n - l - 1}]; p_l ^* + 1; x})S_{lm} (\theta ,\varphi )\\ \chi _{n^*lm} (\zeta ,\vec {r}) = (2\zeta )^{3/2}\left[ {\Gamma(2n^* + 1)}\right]^{{-1}/2}x^{n^*-1}e^{-\frac{x}{2}}S_{lm}(\theta ,\varphi ),\end{array}$$ where ${x=2\zeta r, 0<\zeta <\infty , p_l ^{\ast}=2l+2-\alpha ^{\ast}, q_l ^{\ast}=n+l+1-\alpha ^{\ast}, -\infty <\alpha ^{\ast} <3 , -\infty <\alpha \leq 2,_1 F_1 }$ is the confluent hypergeometric function and ${S_{lm} (\theta ,\varphi )}$ are the complex or real spherical harmonics. The origin of the ${\psi ^{(\alpha ^{\ast})} }$ -ETOs, therefore, of the one-range addition theorems obtained in this work for ${\chi}$ -NISTOs is the self-frictional potential of the field produced by the particle itself. The obtained formulas can be useful especially in the electronic structure calculations of atoms, molecules and solids when Hartree–Fock–Roothan approximation is employed.     

Influence of relaxation effects on probabilities of the 2s2p35S2－2s22p2 3P1，2 intercombination transitions in NII

Transition probabilities of the 2s2p^3 {}^5S_2－2s^22p^2 {}^3P_{1,2} intercombination transitions in NII have been calculated by using a large-scale multiconfiguration Dirac－Fock method. In the calculation the most important effects of relativity, correlation, and relaxation are considered. From the calculated transition probabilities, the lifetime of the 2s2p^3 {}^5S_2 metastable state is derived. The result is in excellent agreement with the latest experimental result. In the meantime the influence of anomalously strong relaxation effects on probabilities of the 2s2p^3 {}^5S_2－2s^22p^2 {}^3P_{1,2} lines in NII have been found.     

Temperature-frequency dependence and mechanism of dielectric properties for γ-Y2Si2O7

This paper reports that single-phase γ-Y2Si2O7 is prepared via a sufficient blending and cold-pressed sintering technique from Y2O3 powder and SiO2 nanopowder. It studies the dielectric properties of γ-Y2Si2O7 as a function of the temperature and frequency. The γ-Y2Si2O7 exhibits low dielectric loss and non-Debye relaxation behaviour from 25 to 1400℃ in the range of 7.3-18 GHz. The mechanism for polarization relaxation of the as-prepared γ-Y2Si2O7 differing from that of SiO 2 is explained. Such particular dielectric properties could potentially make specific attraction for extensive practical applications.     

Loss of collectivity in 79Rb

High-spin states in ⁷⁹Rb were populated in the reaction at E(beam) = 60 MeV. The lifetimes of the excited states of the positive-parity yrast band and of the negative-parity band in ⁷⁹Rb were measured by the Doppler Shift Attenuation Method. The deduced transition quadrupole moments Q_t are found to have a decreasing trend with rotational frequency for both the bands, consistent with those found experimentally in neighbouring nuclei. An erratum to this article is available at .     

Hyperfine structure and isotope shifts in near-infrared transitions of atomic nitrogen

We have obtained Doppler-free spectra of transitions in the → 2p²(³P) and → multiplets of atomic nitrogen using saturated absorption spectroscopy. These multiplets consist of respectively of seven and eight transitions, and have center of gravity wavelengths of 821 nm and 869 nm. Values for the hyperfine structure coupling constants of all the upper and lower states for these multiplets were obtained for both ¹⁴N and ¹⁵N. Isotope shifts of three transitions in each multiplet were also measured, and a significant J-dependence to the shifts was observed.     

Empirical formulas for the fermion spectra and Yukawa matrices

We present empirical relations that connect the dimensionless ratios of low energy fermion masses for the charged lepton, up-type quark and down-type quark sectors and the CKM elements: and . Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases, . According to this relation the measured value of is close to the maximum value that can be reached, for . Finally, the particular mass relations between the quark and charged lepton sectors find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.Received: 31 July 2004, Revised: 22 September 2004, Published online: 9 November 2004     

Theoretical studies on dielectronic recombination of neonlike gold and its effects on plasma ionization balance and radiation energy

The dielectronic recombination (DR) of neonlike gold ions is investigated employing the flexible atomic code based on the relativistic configuration interaction method, and its influence on the ionization balance and radiation energy in high-temperature plasma is also studied. The total resonance strength for LMM configuration complex is in a good agreement with the experimental measurement and other theoretical works. The DR rate coefficients are calculated and compared with the three-body recombination and radiative recombination rate coefficients. The DR process is the dominant recombination mechanism of Ne-like gold ions for plasma with temperature T_e≥6.5 keV and density n_e≤2×10²² cm^-3, which is close to the condition of X-ray conversion region in the inertial confinement fusion. Moreover, the DR satellite spectra of LMM, LMN and LMO resonances are simulated, and compared with the intensities of the corresponding resonance lines induced by the electron impact excitation. The intensity ratio of the satellite line 3D’ [(2p⁵_3/23d_3/23d_5/2)_J=5/2[(2p^{5}_{3/2}3d_{3/2}3d_{5/2})_{J=5/2}–(2p⁶3d_3/2) _J=3/2](2p^{6}3d_{3/2})_{ J=3/2}] and the resonance line 3D [(2p⁵_3/23d_5/2)_J=1[(2p^{5}_{3/2}3d_{5/2})_{J=1}–(2p⁶)_J=0](2p^{6})_{J=0}] is given, which can be applied for diagnostics of plasma temperature.     

Critical radius and dipole polarizability for a confined system

The analytical transfer matrix method (ATMM) is applied to calculating the critical radius $r_{\rm c}$ and the dipole polarizability $\alpha_{\rm d}$ in two confined systems: the hydrogen atom and the Hulth\'{e}n potential. We find that there exists a linear relation between $r_{\rm c}^{1/2}$ and the quantum number $n_{r}$ for a fixed angular quantum number $l$, moreover, the three bounds of $\alpha_{\rm d}$ ($\alpha_{\rm d}^{K}$, $\alpha_{\rm d}^{B}$, $\alpha_{\rm d}^{U}$) satisfy an inequality: $\alpha_{\rm d}^{K}\leq\alpha_{\rm d}^{B}\leq\alpha_{\rm d}^{U}$. A comparison between the ATMM, the exact numerical analysis, and the variational wavefunctions shows that our method works very well in the systems.     

Collective Dand Structures in Doubly Odd 136La Nucleus

Using heavy-ion nuclear reaction and in-beam γ-ray spectroscopy technique,high spin states of ¹³⁶La have been studied. The nuclear reaction used is ¹³⁰Te(¹¹B,5n) with a beam energy 60MeV. The level scheme with three collective band structures has been updated with spin up to 20h. The collective backbending has been observed in $\uppi h_{11/2}\otimes \upnu h_{11/2}$ band. According to the TRS calculations,this backbending is due to the alignment of a pair of h_11/2 neutrons. The signature splitting and inversion for the $\uppi h_{11/2}\otimes \upnu h_{11/2}$ band were also discussed. Other two bands based on $12^-$ and $16^+$ levels were proposed as oblate deformation with $\gamma\approx -60^\circ$. They most probably originate from four- and six- quasiparticle configurations, that is,$\uppi h_{11/2}\otimes\upnu g_{7/2} h_{11/2}^2$ and $\uppi g_{7/2}\otimes\upnu g_{7/2}^2 d_{5/2}h_{11/2}^2$ respectively.