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With increasing demand for accurate calculation of isotope shifts of atomic systems for fundamental and nuclear structure research, an analytic energy derivative approach is presented in the relativistic coupled-cluster theory framework to determine the atomic field shift and mass shift factors. This approach allows the determination of expectation values of atomic operators, overcoming fundamental problems that are present in existing atomic physics methods, i.e. it satisfies the Hellmann-Feynman theorem, does not involve any non-terminating series, and is free from choice of any perturbative parameter. As a proof of concept, the developed analytic response relativistic coupled-cluster theory has been applied to determine mass shift and field shift factors for different atomic states of indium. High-precision isotope-shift measurements of $^{104-127}$In were performed in the 246.8-nm (5p $^2$P$_{3/2}$ $rightarrow$ 9s $^2$S$_{1/2}$) and 246.0-nm (5p $^2$P$_{1/2}$ $rightarrow$ 8s $^2$S$_{1/2}$) transitions to test our theoretical results. An excellent agreement between the theoretical and measured values is found, which is known to be challenging in multi-electron atoms. The calculated atomic factors allowed an accurate determination of the nuclear charge radii of the ground and isomeric states of the $^{104-127}$In isotopes, providing an isotone-independent comparison of the absolute charge radii.
A relativistic coupled-cluster (RCC) theory is implemented to study electron impact excitations of atomic species. As a test case, the electron impact excitations of the $3s ~ ^2S_{1/2} - 3p ~ ^2P_{1/2;3/2}$ resonance transitions are investigated in
We develop an analytic-gradient based method for relativistic coupled-cluster calculations of effective electric field, $mathcal{E}_{text{eff}}$, with improved efficiency and robustness over the previous state of the art. The enhanced capability to c
Relativistic calculations of the isotope shifts of energy levels in highly charged Li-like ions are performed. The nuclear recoil (mass shift) contributions are calculated by merging the perturbative and large-scale configuration-interaction Dirac-Fo
We present high accuracy relativistic coupled cluster calculations of the P-odd interaction coefficient $W_A$ describing the nuclear anapole moment effect on the molecular electronic structure. The molecule under study, BaF, is considered a promising
Ionization potentials, excitation energies, transition properties, and hyperfine structure constants of the low-lying $3p^6 3d^{9} ^2D_{5/2}$, $3p^6 3d^{9} ^2D_{3/2}$, $3p^5 3d^{10} ^2P_{3/2}$ and $3p^5 3d^{10} ^2P_{1/2}$ atomic states of the Co-