Intermediate Hamiltonian Fock-space coupled-cluster method: Excitation energies of barium and radium

Abstract

An intermediate Hamiltonian Fock-space coupled cluster method is introduced, based on the formalism developed by Malrieu and co-workers in the context of perturbation theory. The method is designed to make possible the use of large P spaces while avoiding convergence problems traceable to intruder states, which often beset multireference coupled cluster schemes. The essence of the method is the partitioning of P into a main Pm and an intermediate Pi serving as buffer, with concomitant definition of two types of wave and excitation operators. Application to atomic barium and radium yields converged results for a large number of states not accessible by traditional Fock-space coupled cluster. Moreover, states calculated by both methods exhibit better accuracy (by a factor of 2–5) in the intermediate Hamiltonian approach. Energies are given for low-lying states of Ra which have not been observed experimentally.

Spectra of barium, radium, and element 120: Application of the combined correlation-potential, singles-doubles, and configuration-interactionab initiomethods

“…In particular, we have presented the most precise ab initio calculations available. These include different versions of coupled-cluster [18,30,31,45], CP+CI [29], and SD+CI [32]. For the higher levels, where there is only limited data available, we also present for Ba and Ra the results of semi-empirical CP+CI calculations [20].…”

“…Its position was predicted in the early experimental work of Palenius [46] to be 24300±300 cm −1 . It has subsequently been calculated in the works [18,[47][48][49]; there are other calculations of the barium spectra where this level has been missed. We present in the table, alongside our own result, the initial estimate [46] and the value from the most precise calculations [18].…”

“…It has subsequently been calculated in the works [18,[47][48][49]; there are other calculations of the barium spectra where this level has been missed. We present in the table, alongside our own result, the initial estimate [46] and the value from the most precise calculations [18]. Our calculations give the value 25205 cm −1 for this level; looking at the results for other terms with the configuration 5d 2 , we expect that the result for this level could be underestimated, possibly by as much as 100 − 300 cm −1 .…”

“…Moreover, the measured low-lying excitation energies for radium are incomplete, and it is important to have high-precision predictions for these levels. There are already a number of theoretical works devoted to studies of fundamental symmetries violations in radium [7,[9][10][11][12][13][14] and to the radium spectra, lifetimes, and hyperfine structure [15][16][17][18][19][20][21]. There are also recent measurements of a few transition frequencies and lifetimes [22][23][24].…”

All-Order Methods for Relativistic Atomic Structure Calculations

“…We note that the implementation of the coupled-cluster method in Ref. [79] is very different from the all-order method described here and is limited to the calculations of the energies. A very promising method for the calculation of properties of manyparticle systems, involving a combination of the CI and all-order techniques [29] was mentioned in the previous subsection.…”