The polarizabilities and hyperpolarizabilities of the Be$^+$ ion in the $2^2S$ state and the $2^2P$ state are determined. Calculations are performed using two independent methods: i) variationally determined wave functions using Hylleraas basis set expansions and ii) single electron calculations utilizing a frozen-core Hamiltonian. The first few parameters in the long-range interaction potential between a Be$^+$ ion and a H, He, or Li atom, and the leading parameters of the effective potential for the high-$L$ Rydberg states of beryllium were also computed. All the values reported are the results of calculations close to convergence. Comparisons are made with published results where available.
We address the problem of the lattice Stark shifts in the Sr clock caused by the multipolar $M1$ and $E2$ atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. We have developed an approach to calculate hyperpolarizabilities for atoms and ions based on a solution of the inhomogeneous equation which allows to effectively and accurately carry out complete summations over intermediate states. We applied our method to the calculation of the hyperpolarizabilities for the clock states in Sr. We also carried out an accurate calculation of th…
The progress in optical clock with uncertainty at a level of $10^{-18}$ requires unprecedented precision in estimating the contribution of multipolar and higher-order effects of atom-field interactions. Current theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the magic wavelength for the Sr clock differ substantially. We develop a combined approach of the Dirac-Fock plus core polarization (DFCP) and relativistic configuration interaction (RCI) methods to calculate dynamic multipolar polarizabilities and hyperpolarizabilities of the Sr ato…
High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for the lowlying vibrational-rotational states of hydrogen molecular ions
Finite-field calculation of the polarizabilities and hyperpolarizabilities of Al$^{+}$
在这项研究中，精确的静态偶极极化率和超极化率计算Al $^+$基态3s $^{2}$ $^{1}$ S $_{0}$和激发态$3s3p$ $^{3}$ P $_{J}$的$J$ =0，1，2。有限场计算使用相对论组态相互作用方法和相对论耦合团簇方法获得的能量。Al $^{+}$基态3s $^{2}$ $^{1}$ S $_{0}$和激发态$3s3p$ $^{3}$ P $_{0}$的偶极极化率以及基态3s $^{2}$ $^{1}$ S $_{0}$的超极化率与以前推荐的值非常一致。给出了Al $^{+}$ $3s3p$ $^{3}$ P $_{1}$和$^{3}$ P $_{2}$的偶极极化率以及Al $^{+}$ $3s3p$ $^{3}$ P $_{0}$、$^{3}$ P $_{1}$和$^{3}$ P $_{2}$的超极化率的推荐值。通过分析偶极极化率和超极化率与角动量的关系，并比较完全相对论和标量相对论的计算结果，阐明了相对论和自旋轨道耦合的影响.结果表明，相对论和自旋轨道耦合对偶极极化率的影响很小，但对超极化率的影响很大。最后，计算了Al $^{+}$ 3s $^{2}$ $^{1}$ S $_{0}$到$3s3p$ $^{3}$ P $_{J}$（$J$ = 0，1，2）跃迁的偶极极化率和超极化率分别对黑体辐射位移的贡献.
Relativistic Hartree-Fock and random phase approximation methods for open shells are used to calculate ionization potentials and static scalar polarizabilities of eight superheavy elements with open $6d$-shell, which include Db, Sg, Bh, Hs, Mt, Ds, Rg and Cn ($Z$=105 to 112). Inter-electron correlations are taken into account with the use of the semi-empirical polarization potential. Its parameters are chosen to fit the known ionization potentials of lighter atoms. Calculations for lighter atoms are also used to illustrate the accuracy of the approach.
The present work determines the precise values of magic wavelengths corresponding to the clock transitions 5$^2S$-4$^2D$ of Y$^{2+}$ ion both at the levels of fine- and hyperfine-structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substan…
Relativistic many-body calculation of energies, oscillator strengths, transition rates, lifetimes, polarizabilities, and quadrupole moment of Fr-like Th IV ion
We present precise values of the dipole polarizabilities ($α$) of the ground $\rm [4f^{14}6s] ~ ^2S_{1/2}$ and metastable $\rm [4f^{14} 5d] ~ ^2D_{3/2}$ states of Yb$^+$, that are %vital {\bf important} in reducing systematics in the clock frequency of the $\rm[4f^{14}6s] ~ ^2S_{1/2} \rightarrow [4f^{14}5d] ~ ^2D_{3/2}$ transition. The static values of $α$ for the ground and $\rm [4f^{14} 5d] ~ ^2D_{3/2}$ states are estimated to be $9.8(1) \times 10^{-40} \,\,\rm Jm^2V^{-2}$ and $17.6(5) \times 10^{-40}\,\, \rm Jm^2V^{-2}$, respectively, while the tensor contribution to the $\rm [4f^{14} 5d] ~…
Energy levels of 30 low-lying states of Lu2+ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates and lifetimes of the metastable 5d(3/2) and 5d(5/2) states are calculated. Recommended values are given for stati…
Ionic clocks exhibit as the most promising candidates for the frequency standards. Recent investigations show the profound advantages of interrogating two laser beams with different frequencies in developing the frequency standards. Here we present a scheme of a two-photon mechanism to calculate the dynamic polarizabilities for the clock states, 6$^2$S$_{\frac{1}{2}}$ and 5$^2$D$_{\frac{3}{2}, \frac{5}{2}}$, of Ba$^+$ by employing relativistic coupled-cluster method. We illustrate the Stark-shift cancellation between these clock states at the two-photon magic wavelengths. These magic wavelengt…
Study of quadrupole polarizabilities with combined configuration interaction and coupled-cluster method
最近开发的结合构型相互作用和耦合簇方法的方法被证明可以提供二价原子系统中相关校正的准确处理[M. S. Safronova，M. G. Kozlov和C. W. Clark，Phys. Rev. Lett. 107，143006（2011）]。我们将这种方法推广到四极极化率α_2的计算中，并应用于计算Mg和类Mg Si^{2+}的基态的α_2。在三个不同的近似值中进行计算，使我们能够将最终结果的不确定性的上限。推荐值α_2（3s^2 1 S 0）= 35.86（13）a.u. Si^{2+}和α_2（3s^2 1S0）= 814（3）a.u.对Mg的估计精确到0.37%。讨论了中性Mg和Si^{2+}离子四极极化率贡献的差异。
Roles of electron correlation effects in the determination of attachment energies, magnetic dipole hyperfine structure constants and electric dipole (E1) matrix elements of the low-lying states in the singly charged cadmium ion (Cd$^+$) have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation, second-order many-body perturbation theory and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation…
The ^1Σ^+ electronic ground states of MgLi^+ and CaLi^+ molecular ions are investigated for their spectroscopic constants and properties such as the dipole- and quadrupole moments, and static dipole polarizabilities. The quadrupole moments and the static dipole polarizabilities for these ions have been calculated and reported here, for the first time. The maximum possible error bars, arising due to the finite basis set and the exclusion of higher correlation effects beyond partial triples, are quoted for reliability. Further, the adiabatic effects such as diagonal Born-Oppenheimer corrections …
Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a m…
We measure the dynamic differential scalar polarizabilities at 10.6 $μ$m for two candidate clock transitions in $^{176}\mathrm{Lu}^+$. The fractional black body radiation (BBR) shifts at 300 K for the $^1S_0 \leftrightarrow {^3D_1}$ and $^1S_0 \leftrightarrow {^3D_2}$ transitions are evaluated to be $-1.36\,(9) \times 10^{-18}$ and $2.70 \,(21) \times10^{-17}$, respectively. The former is the lowest of any established optical atomic clock.
Precision measurement of Cs($nF_J$) quantum defects and calculations of scalar and tensor polarizabilities of the $nS_{1/2}$, $nP_J$ ,$nD_J$ , and $nF_J$ series
