An ab initio relativistic coupled-cluster theory of dipole and quadrupole polarizabilities: Applications to a few alkali atoms and alkaline earth ions

Abstract

We present a general approach within the relativistic coupled-cluster theory framework to calculate exactly the first order wave functions due to any rank perturbation operators. Using this method, we calculate the static dipole and quadrupole polarizabilities in some alkali atoms and alkaline earthmetal ions. This may be a good test of the present theory for different rank and parity interaction operators. This shows a wide range of applications including precise calculations of both parity and CP violating amplitudes due to rank zero and rank one weak interaction Hamiltonians. We also give contributions from correlation effects and discuss them in terms of lower order many-body perturbation theory. PACS numbers: 31.15.Ar,31.15.Dv,31.25.Jf,32.10.Dk For a long time, studies of dipole and quadrupole polarizabilities have been highly interesting in many important aspects for both neutral atoms and ions [1,2,3,4,5,6,7,8,9,10,11]. These quantities are used in the case of ions to remove the quadratic Stark shifts in the recent proposed optical frequency standards where suitable instruments are not available for very precise measurements [12,13]. Relativistic effects are also investigated for these properties [14,15]. Often theoretical studies are limited by many approximations to only approximate accuracy of the results [17,21]. In many cases, semiempirical methods, which combine the calculated E1 and E2 matrix elements of important states and the experimental excitation energies, are used to calculate these quantities [18,19]. Core electron contributions are always only estimated in this approach [1,18]. Therefore, an ab initio method is necessary to be able to, in principle, explain the importance of the electron correlation effects in the above properties and also test the manybody theories employed. These results are largely used to determine the van der Waals coefficients or dispersion factors [19,20,21,22]. In some cases, the Dirac-Fock (DF) method and relativistic random-phase approximations (RPA) for the Dalgarno-Lewis [21,22,23] or scalar relativistic Douglas-Kroll [15,16] effective Hamiltonians are used to determine these quantities. A number of calculations on these quantities using molecular codes and pseudopotentials have also been reported [9,15,16,17].Using the relativistic coupled-cluster (RCC) theory, we report here a novel approach for the first time to calculate wave functions up to all orders in the residual Coulomb interaction and first order due to any kind of perturbed operator in one valence systems. This takes care of the sum-over-states approach of the many-body perturbation † theory (MBPT) as an exact solution. This method can be applied to calculate the first order wave function due to dipole and quadrupole transition operators. Hence, polarizabilities can be obtained by calculating the expectation values of the corresponding operators. As an ab initio test of the theory, it is also possible to calculate the light shift ratio in ions like Ba + using the present method as proposed in [24]...

Multipolar blackbody radiation shifts for single-ion clocks

“…The core contribution is comparatively small and the α cn contribution to the ground-state polarizability is zero due to the absence of occupied d states in Ca + . There are two more calculations available in the literature on the same using the RCC methods with different levels of approximations [46,47]. The results reported in Ref.…”

Ba+quadrupole polarizabilities: Theory versus experiment

“…It should be noted that unlike for the dipole operator [9,27], E (1) n results are finite for the quadrupole operator and correspond to the quadrupole moments of the respective states | n .…”

“…Also, we construct triple-excitation configurations from | v perturbatively in the spirit of the CCSD with partially triple excitations [CCSD(T)] approach [9,16,[22][23][24][25][26].…”

“…The amplitudes for both the T and S v operators are determined using the following equations: (9) and…”

“…A wide variety of methods have been used to calculate the polarizabilities of these systems [7][8][9]. Calculations of polarizabilities depend on the matrix elements between different atomic states and the excitation energies between them.…”