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Register a new userDipole Polarizability Calculation of Cd Atom: Inconsistency with experiment
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Three earlier relativistic coupled-cluster (RCC) calculations of dipole polarizability ($alpha_d$) 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 implementation. To resolve this ambiguity, we have developed and employed the relativistic normal coupled-cluster (RNCC) theory to evaluate the $alpha_d$ value of Cd. The distinct features of the RNCC method are that the expression for the expectation value in this approach terminates naturally and that it satisfies the Hellmann-Feynman theorem. In addition, we determine this quantity in the finite-field approach in the framework of A four-component relativistic coupled-cluster theory. Considering the results from both these approaches, we arrive at a reliable value of $alpha_d=46.02(50) e a_0^3$. We also demonstrate that the contribution from the triples excitations in this atom is significant.
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We present electric dipole polarizabilities ($alpha_d$) 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 theory, random phase approximation and coupled-cluster (CC) theory. Roles of electron correlation effects and relativistic corrections are analyzed using the above many-body methods with size of the ions. We finally quote precise values of $alpha_d$ of the above negative ions by estimating uncertainties to the CC results, and compare them with other calculations wherever available.
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 effects in this ion. Contributions from important RCC terms are also given to highlight importance of various correlation effects in the evaluation of these properties. At the end, we also determine E1 polarizabilities ($alpha^{E1}$) of the ground and $5p ^2P_{1/2;3/2}$ states of Cd$^+$ in the {it ab initio} approach. We estimate them again by replacing some of the E1 matrix elements and energies from the measurements to reduce their uncertainties so that they can be used in the high precision experiments of this ion.
The cesium 6S_1/2 scalar dipole polarizability alpha_0 has been determined from the time-of-flight of laser cooled and launched cesium atoms traveling through an electric field. We find alpha_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. The 0.14% uncertainty is a factor of fourteen improvement over the previous measurement. Values for the 6P_1/2 and 6P_3/2 lifetimes and the 6S_1/2 cesium-cesium dispersion coefficient C_6 are determined from alpha_0 using the procedure of Derevianko and Porsev [Phys. Rev. A 65, 053403 (2002)].
Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems involves an infinite sum over all excited (bound and continuum) states, concealing the physical interpretation of polarization mechanisms and complicating the derivation of efficient response models. Approximate expressions for the dipole polarizability, $alpha$, rely on different scaling laws $alpha propto$ $R^3$, $R^4$, or $R^7$, for various definitions of the system radius $R$. Here, we consider a range of atom-like quantum systems of varying spatial dimensionality and having qualitatively different spectra, demonstrating that their polarizability follows a universal four-dimensional scaling law $alpha = C (4 mu q^2/hbar^2)L^4$, where $mu$ and $q$ are the (effective) particle mass and charge, $C$ is a dimensionless ratio between effective excitation energies, and the characteristic length $L$ is defined via the $mathcal{L}^2$-norm of the position operator. The applicability of this unified formula is demonstrated by accurately predicting the dipole polarizability of 36 atoms and 1641 small organic~molecules.
The Ti:Saphire laser operated within 13800 - 11800 cm$^{-1}$ range was used to excite the $c^3Sigma^+$ state of KCs molecule directly from the ground $X^1Sigma^+$ state. The laser-induced fluorescence (LIF) spectra of the $c^3Sigma^+ rightarrow a^3Sigma^+$ transition were recorded with Fourier-transform spectrometer within 8000 to 10000 cm$^{-1}$ range. Overall 673 rovibronic term values belonging to both $e/f$-components of the $c^3Sigma^+(Omega=1^{pm})$ state of $^{39}$KCs, covering vibrational levels from $v$ = 0 to about 45, and rotational levels $Jin [11,149]$ were determined with the accuracy of about 0.01 cm$^{-1}$; among them 7 values for $^{41}$KCs. The experimental term values with $vin [0,22]$ were involved in a direct point-wise potential reconstruction for the $c^3Sigma^+(Omega=1^{pm})$ state, which takes into account the $Omega$-doubling effect caused by the spin-rotational interaction with the nearby $c^3Sigma^+(Omega=0^-)$ state. The analysis and interpretation were facilitated by the fully-relativistic coupled cluster calculation of the potential energy curves for the $B^1Pi$, $c^3Sigma^+$, and $b^3Pi$ states, as well as of spin-forbidden $c-X$ and spin-allowed $c-a$ transition dipole moments; radiative lifetimes and vibronic branching ratios were calculated. A comparison of relative intensity distributions measured in vibrational $c-a$ LIF progressions with their theoretical counterparts unambiguously confirms the vibrational assignment suggested in [emph{J. Szczepkovski, et. al.}, JQSRT, textbf{204}, 133-137 (2018)].
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