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arXiv:0804.4697 · Physical Review A

Convergence of all-order many-body methods: Coupled-cluster study for Li

Andrei Derevianko, S. G. Porsev, K. Beloy

Published Jul 11, 2008• 30 citations
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Abstract

We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the $2s$, $2{p}_{1∕2}$, and $2{p}_{3∕2}$ states of Li atom. The calculations are complete through the fourth order of many-body perturbation theory for energies and through the fifth order for matrix elements and subsume certain chains of diagrams in all orders. A nearly complete many-body calculation allows us to draw conclusions on the convergence pattern of the coupled-cluster method. Our analysis suggests that the high-order many-body contributions to energies and matrix elements scale proportionally and provide a quantitative ground for semiempirical fits of ab initio matrix elements to experimental energies.

DOI
10.1103/physreva.78.010503

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The molecular dipole moment and magnetic hyperfine-structure constant demand an accurate wave function far from the nucleus and in the near nuclear region, respectively. We, therefore, employ the so-called Z-vector method in the domain of relativistic-coupled-cluster theory to calculate the first-order property of molecular systems in their open-shell ground-state configuration. The implemented method is applied to calculate the molecular dipole moment and parallel component of the magnetic hyperfine-structure constant of the SrF molecule. The results of our calculation are compared with the experimental and other available theoretically calculated values. We are successful in achieving good accordance with the experimental results. The result of our calculation of the molecular dipole moment is in the accuracy of $\ensuremath{\sim}0.5$%, which is clearly an improvement over the previous calculation based on the expectation value method in the four-component coupled-cluster framework [V. S. Prasannaa et al., Phys. Rev. A 90, 052507 (2014)]. Thus, it can be inferred that the Z-vector method can provide an accurate wave function in both the near and far nuclear region, which is evident from our calculated results.