A procedure is described for the precise nonrelativistic evaluation of the dipole polarizabilities of H_2^+ and D_2^+ that avoids any approximation based on the size of the electron mass relative to the nucleus mass. The procedure is constructed so that sum rules may be used to assess the accuracy of the calculation. The resulting polarizabilities are consistent with experiment within the error bars of the measurements and are far more precise than values obtained by other theoretical methods.
Experimental results and high-level quantum chemical ab initio calculations of the static polarizability $α_0=α(ω=0)$ of the cadmium ${^1S_0}$ state are still in marked disagreement. Here we analyze this discrepancy by using experimentally determined dipole oscillator strength distributions (DOSD). It will be shown that within this procedure the experimentally determined static polarizability $α_0$ will shift from $49.7 \pm 1.6~$au to considerably lower values. We now conclude an experimentally determined polarizability of $α_0=47.5 \pm 2.0~$au in much better agreement with the latest calculat…
High precision measurement of the static dipole polarizability of cesium
用激光冷却和发射的铯原子在电场中的飞行时间测量了铯原子6S_1/2标量偶极极化率α_0。我们发现α_0 = 6.611+-0.009 x 10^-39 C m^2/V= 59.42+-0.08 x 10^-24 cm^3 = 401.0+-0.6 a_0^3。0.14%的不确定度比之前的测量提高了14倍。6P_1/2和6P_3/2寿命以及6S_1/2铯-铯分散系数C_6的值使用Derevianko和Porsev的程序[Phys.Rev.A65，053403（2002）]从α_0确定。
Using a long-range polarization potential for HeH$^{+}$, we can obtain an empirical value for the Boltzmann constant $k_{B}$ with an order of magnitude greater precision than the previous best experimental value based on the dipole polarizability of $^{4}$He. We find that relativistic and QED effects of order $α_{\rm FS}^{3}$ in the fine structure constant are crucial in the quadrupole polarizability in order to fit the dipole polarizbility with this precision using the polarization potential. By calculating finite-mass corrections for $^{3}$He, we also present theoretical values for the dipol…
The static dipole polarizability for the hydrogen molecular ions H$_2^+$, HD$^+$, and D$_2^+$ are calculated. These new data for polarizability takes into account the leading order relativistic corrections to the wave function of the three-body system resulted from the Breit-Pauli Hamiltonian of $mα^4$ order. Our study covers a wide range of rotational ($L=0-5$) and vibrational ($v=0-10$) states, which are of practical interest for precision spectroscopy of the hydrogen molecular ions.
Nonrelativistic and relativistic coupled-cluster calculations extrapolated to the complete basis set limit including excitations up to the quintuple level (CCSDTQP) were carried out to accurately determine the static electric dipole polarizability of the closed-shell palladium atom. The resulting value of $α$ = 26.14(10) a.u. implies that palladium has the smallest dipole polarizability of all known elemental metal atoms due to its unique 4d$^{10}$5s$^0$ configuration. Relativistic effects are found to be already sizeable ($Δ_Rα$= +1.86~a.u.) compared to electron correlation ($Δ_Cα$= +5.06~a.u…
A model for positron binding to polar molecules is considered by combining the dipole potential outside the molecule with a strongly repulsive core of a given radius. Using existing experimental data on binding energies leads to unphysically small core radii for all of the molecules studied. This suggests that electron-positron correlations neglected in the simple model play a large role in determining the binding energy. We account for these by including polarization potential via perturbation theory and non-perturbatively. The perturbative model makes reliable predictions of binding energies…
$^{129}$Xe is an important candidate for the searches of electric dipole moments due to violations of time-reversal and parity violations in diamagnetic atoms. In view of the similarities between the electric dipole moment and the polarizability from the point of view of many-body theory, we have performed rigorous calculations of the ground state polarizability of $^{129}$Xe using a self consistent relativistic coupled-cluster method and the relativistic normal coupled-cluster method. The discrepancy between the results from these two methods is two percent, but each of them differs from the …
The dynamic electric dipole polarizability function for the magnesium atom is formed by assembling the atomic electric dipole oscillator strength distribution from combinations of theoretical and experimental data for resonance oscillator strengths and for photoionization cross sections of valence and inner shell electrons. Consistency with the oscillator strength (Thomas-Reiche-Kuhn) sum rule requires the adopted principal resonance line oscillator strength to be several percent lower than the values given in two critical tabulations, though the value adopted is consistent with a number of th…
Dipolar atoms have unique properties, making them interesting for laser cooling and quantum simulations. But, due to relatively large orbital momentum in the ground state these atoms may have large dynamic tensor and vector polarizabilities in the ground state. This enables the formation of spin-dependent optical traps. In this paper real part of tensor and vector dynamic polarizability was experimentally measured and compared to theoretical simulation. For an optical dipole trap operating around 532.07 nm tensor, polarizability was found to be $ - 145 \pm 53\,\,{\rm{a}}{\rm{.u}}{\rm{.}}$ and …
We have developed a Fock-space relativistic coupled-cluster theory based method for the calculation of electric dipole polarizability of one-valence atoms and ions. We employ this method to compute the ground-state and spin-orbit coupled excited state electric dipole polarizability of Al and In. To check the quality of many-electron wavefunctions, we also compute the excitation energies of some low-lying states of Al and In. The effects of Breit interaction and QED corrections from the Uehling potential and the self-energy are included to improve the accuracy of $α$ further. Our recommended va…
The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves a generalized hypergeometric function ${}_{3}F_{2}$ with the unit argument. Numerical values of the polarizabilities for relativistic planar hydrogenic atoms with atomic numbers $1\leqslant Z\leqslant68$ are provided …
We calculate ground-state energies and densities of a helium atom confined in an impenetrable spherical box within density functional theory. These calculations are performed by variationally solving Kohn-Sham equation with the ground-state orbital expanded in terms of Slater-type orbitals. Using the ground-state densities we then calculate static linear polarizability and nonlinear hyperpolarizability and study their variation with the radius of confinement. We find that polarizability decreases monotonically with decreasing confinement radius and the hyperpolarizability not only decreases bu…
We present electric dipole polarizabilities ($α_d$) of the alkali-metal negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation …
We compute the ground-state electric dipole polarizability of group-IIIA ions using the perturbed relativistic coupled-cluster (PRCC) theory. To account for the relativistic effects and QED corrections, we use the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the PRCC. Our PRCC results for $α$ are good in agreement with the previous theoretical results for all the ions. From our computations we find that the nonlinear terms in PRCC have significant contributions and must be…
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.
Three earlier relativistic coupled-cluster (RCC) calculations of dipole polarizability ($α_d$) of the Cd atom are not in good agreement with the available experimental value of $49.65(1.65) \ e a_0^3$. Among these two are finite-field approaches in which the relativistic effects have been included approximately, while the other calculation uses a four component perturbed RCC method. However, another work adopting an approach similar to the latter perturbed RCC method gives a result very close to that of experiment. The major difference between these two perturbed RCC approaches lies in their i…
We employ a fully relativistic coupled-cluster theory to calculate the ground-state electric dipole polarizability and electron correlation energy of superheavy elements Cn, Nh$^+$ and Og. To assess the trend of electron correlation as function of $Z$, we also calculate the correlation energies for three lighter homologs--Zn, Cd and Hg; Ga$^+$, In$^+$ and Tl$^+$; Kr, Xe and Rn--for each superheavy elements. The relativistic effects and quantum electrodynamical corrections are included using the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy.…
The proton-polarizability contribution to the muonic-hydrogen Lamb shift is a major source of theoretical uncertainty in the extraction of the proton charge radius. An empirical evaluation of this effect, based on the proton structure functions, requires a systematically improvable calculation of the "subtraction function", possibly using lattice QCD. We consider a different subtraction point, with the aim of accessing the subtraction function directly in lattice calculations. A useful feature of this subtraction point is that the corresponding contribution of the structure functions to the La…
We use perturbed relativistic coupled-cluster (PRCC) theory to compute the electric dipole polarizabilities $α$ of Zn, Cd and Hg. The computations are done using the Dirac-Coulomb-Breit Hamiltonian with Uehling potential to incorporate vacuum polarization corrections. The triple excitations are included perturbatively in the PRCC theory, and in the unperturbed sector, it is included non-perturbatively. Our results of $α$, for all the three elements, are in excellent agreement with the experimental data. The other highlight of the results is the orbital energy corrections from Breit interaction…
Fock-space perturbed relativistic coupled-cluster calculations of electric dipole polarizability and nuclear spin-dependent parity non-conservation in Cs
Addendum to "The Dirac-Coulomb Sturmians and the series expansion of the Dirac-Coulomb Green function: application to the relativistic polarizability of the hydrogen-like atom" [J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 825-61, (E) 30 (1997) 2747]
We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths $f_{ik}$, Einstein coefficients $A_{ik}$, state lifetimes $τ_{k}$, transition dipole…
The QED contribution to the dipole polarizability of the $^4$He atom was computed, including the effect of finite nuclear mass. The computationally most challenging contribution of the second electric-field derivative of the Bethe logarithm was obtained using two different methods: the integral representation method of Schwartz and the sum-over-states approach of Goldman and Drake. The results of both calculations are consistent, although the former method turned out to be much more accurate. The obtained value of the electric-field derivative of the Bethe logarithm, equal to $0.048\,557\,2(14…
To operate an optical lattice clock at a fractional uncertainty below $10^{-17}$, one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states $(5s5p)\,{}^{3}\mathrm{P}_{0}$ and $(5s^2)\,{}^{1}\mathrm{S}_{0}$ of strontium [Ushijima e…
The efficiency of optical trapping of ultracold atoms depend on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited level. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the $C_6$ coefficien…
We present precise values of electric polarizabilities for the ground state of Zn due to second-order dipole and quadrupole interactions, and due to third-order dipole-quadrupole interactions. These quantities are evaluated in the linear response theory framework by employing a relativistic version of the normal coupled-cluster (NCC) method. The calculated dipole polarizability value is compared with available experimental and other theoretical results including those are obtained using the ordinary coupled-cluster (CC) methods in both finite-field and expectation value evaluation approaches. …
The finite field calculations are performed for two heavy frequency-standard candidates In$^+$ and Sr. The progressive hierarchy of electron correlations is implemented by the relativistic coupled-cluster and configuration interaction methods combined with basis set of increasing size. The dipole polarizabilities, dipole hyperpolarizabilities, quadrupole moments, and quadrupole polarizabilities are recommended for the ground state 5s$^2$ $^1S_0$ and low-lying states 5s5p $^3P^{\rm o}_{0,1,2}$ of In$^+$ and Sr. Comparative study of the fully and scalar relativistic electron correlation calculat…
We characterize the anisotropic differential ac-Stark shift for the Dy $626$ nm intercombination transition, induced in a far-detuned $1070$ nm optical dipole trap, and observe the existence of a "magic polarization" for which the polarizabilities of the ground and excited states are equal. From our measurements we extract both the scalar and tensorial components of the dynamic dipole polarizability for the excited state, $α_E^\text{s} = 188 (12)\,α_\text{0}$ and $α_E^\text{t} = 34 (12)\,α_\text{0}$, respectively, where $α_\text{0}$ is the atomic unit for the electric polarizability. We also p…
