Finite-field calculation of electric quadrupole moments of ~2P_(3/2),~2D_(3/2,5/2),and ~2F_(5/2,7/2) states for Yb~+ ion

Electric quadrupole moments of low-lying excited states of Yb~+ are calculated by relativistic coupled-cluster theory with perturbations from external fields.The field-dependent energy differentiation provides accurate values of the electric quadrupole moments o f~2P_(3/2),~2D_(3/2,5/2),and~2F_(5/2,7/2) states which agree well with experimental values.The important role of the electronic correlation to the electric quadrupole moments is investigated.Our calculations indicate the early dispute of the electric quadrupole moment of the Yb~+(~2F_(7/2))state for which the measured and theoretical values have a large discrepancy.These electric quadrupole moment values can help us to determine the electric quadrupole shifts in start-of-the-art experiments of the Yb~+ ion.     

An Investigation of ~4He+~(12)C and ~4He+~(16)O Reactions Using the Cluster Model

The α-target semimicroscopic single folding potentials have been derived by folding a composite (repul-sive and attractive) effective α-α interaction with the α-cluster distribution density in the target nuclei. The obtained potentials are considered as the real part of the nuclear optical model potentials, while the imaginary parts are phe-nomenologicaly expressed using the Woods-Saxon form. Nine sets of measured experimental data of the 4He+12C and 4 He+16O elastic rainbow scattering over the energy range 80-240 MeV are analyzed using the obtained potentials. The data are successfully reproduced using the extracted potentials. The resulted reaction cross sections are also investigated and compared with the available corresponding data.     

Relationship measurement between ac-Stark shift of ~(40)Ca~+ clock transition and laser polarization direction

Ac-Stark shift of atom levels is caused by an ac-electromagnetic field. As an electromagnetic wave, laser light does induce ac-Stark shift. It is proved experimentally that if the light is linearly polarized, the dynamic polarizability changes with polarization direction. The polarization direction of the linearly-polarized laser is tuned by 720?, and the ac-Stark shifts of the 4S_(1/2),m=±1/2→3D_(5/2,m=±1/2) clock transitions in ~(40)Ca~+ are measured in steps of 10?. The frequency shifts change with laser polarization in a periodical manner and have values opposite to each other.     

Evaluation of the frequency instability limited by Dick effect in the microwave ~(199)Hg~+ trapped-ion clock

In the microwave ~(199)Hg~+ trapped-ion clock, the frequency instability degradation caused by the Dick effect is unavoidable because of the periodical interrogating field. In this paper, the general expression of the sensitivity function g(t)to the frequency fluctuation of the interrogating field with Nπ-pulse(N is odd) is derived. According to the measured phase noise of the 40.5-GHz microwave synthesizer, the Dick-effect limited Allan deviation of our ~(199)Hg~+ trapped-ion clock is worked out. The results indicate that the limited Allan deviations are about 1.75 × 10~(-13)τ~(1/2) and 3.03 × 10~(-13)τ~(1/2) respectively in the linear ion trap and in the two-segment extended linear ion trap under our present experimental parameters.     

Suppression of servo error uncertainty to 10~(-18) level using double integrator algorithm in ion optical clock

A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator.Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments. The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters. According to the experimental results, the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107. In a week-long comparison of optical clocks, the relative uncertainty of the servo error is determined to be 1.9 × 10~(-18), which is meaningful for the systematic uncertainty of the transportable single ~(40)Ca~+ ion optical clock entering the 10~(-18) level.     

Comparison experiments of neon and helium buffer gases cooling in trapped ~(199)Hg~+ ions linear trap

The influences of different buffer gas, neon and helium, on199Hg+clock transition are compared in trapped199Hg+linear trap. By the technique of time domain’s Ramsey separated oscillatory fields, the buffer gas pressure frequency shifts of199Hg+clock transition are measured to be(d f /dPNe)(1/ f) = 1.8 × 10-8Torr-1for neon and(d f /dPHe)(1/ f) = 9.1 × 10-8Torr-1for helium. Meanwhile, the line-width of199Hg+clock transition spectrum with the buffer gas neon is narrower than that with helium at the same pressure. These experimental results show that neon is a more suitable buffer gas than helium in199Hg+ions microwave frequency standards because of the199Hg+clock transition is less sensitive to neon variations and the better cooling effect of neon. The optimum operating pressure for neon is found to be about 1.0 × 10-5Torr in our linear ion trap system.     

Anomalous concentration dependence of the coordination behavior of Cl− ion to Ln3+ ion (Ln3+ = rare‐earth ion) in anhydrous LnCl3 alcohol solutions

Raman spectroscopic measurements were carried out for the anhydrous LnCl₃·20ROH·XLiCl solutions (Ln³⁺ = La³⁺− Lu³⁺, X = 0–3; ROH = MeOH, EtOH, n‐PrOH) in the liquid state. The salt concentration (X) dependence of the wavenumber for the Ln–Cl stretching Raman band (ν_Ln–Cl) is examined in conjunction with the formation of chloro‐rare‐earth complexes. We have obtained very intriguing results including the fact that the chloro complexations of the middle rare‐earth ions (e.g. gadolinium, holmium ions, etc.) in the MeOH and EtOH solutions show peculiar behavior with regard to the salt concentration dependence: the ν_Ln–Cl wavenumber increases with the increasing chloride concentration. However, the ν_Ln–Cl wavenumbers of the light and heavy rare‐earth (e.g. lanthanum, lutetium, etc.) salt solutions show normal behavior; i.e. ν_Ln–Cl decreases with the increasing chloride concentration. On the other hand, in the n‐PrOH solutions, the ν_Ln–Cl frequency in the solutions of all the rare‐earth elements exhibits a normal behavior. We now present a possible mechanism for this anomalous concentration dependence of coordination of Cl⁻ ions to Ln³⁺ ions in anhydrous LnCl₃ alcohol solutions. Copyright © 2007 John Wiley & Sons, Ltd.     

An Invariance for (2+1)-Extension of Burgers Equation and Formulae to Obtain Solutions of KP Equation

In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Bäcklund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functions for (2+1)-extension of Burgers equation is worked out. Given a known solution and using the invariance, we can find solutions of the (2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgers equation which cannot be directly obtained by constraining the invariance of the (2+1)-extension of Burgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgers equation can help us find the solutions of KP equation. At last, based on the invariance of Burgers equation, the corresponding recursion formulae for finding solutions of KP equation are digged out. As the application of our theory, some examples have been put forward in this article and some solutions of the (2+1)-extension of Burgers equation, Burgers equation and KP equation are obtained.     

An Alternative Approach to Obtain the Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p+p(1/x) Terms

By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics 42, 853]. PACS: 03.65Ge; 03.65Fd; 03.65Bz