Electric dipole and quadrupole transition amplitudes for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Ba</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>using the relativistic coupled-cluster method

Gopakumar, Geetha; Merlitz, Holger; Chaudhuri, Rajat K.; Das, B. P.; Mahapatra, Uttam Sinha; Mukherjee, Debashis

doi:10.1103/physreva.66.032505

Cited by 45 publications

(67 citation statements)

References 28 publications

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“…Since the calculation of transition probabilities/lifetimes are extremely sensitive to the excitation energies. Gopakumar et al [14] have shown that the hybrid basis can serve this purpose very well. Our UCCSD(T) calculations yield ionization potentials (IPs) to an accuracy of about 0.1%, and 0.07% for the 6 2 S 1/2 and 5 2 D 3/2 states of Ba + respectively.…”

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confidence: 99%

“…The values of the calculated and experimental lifetimes are given in table II. Dzuba et al [15], Guet et al [16] and Gopakumar et al [14] have not considered the M 1 channel in their calculations. Gopakumar et al have used CCSD(T), but Guet et al and Dzuba et al have used different variants of many-body perturbation theory (MBPT) with certain semi-empirical features to calculate the transition amplitudes.…”

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confidence: 99%

“…These calculations are Excitation energy τ UCCSD(T) 4789 81.01 CCSD(T) [14] 4809 87.06 Dzuba et al [15] 4411 81.5 Guet et al [16] 4688 83.7 Experiment [17] 4874 79±4.6…”

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confidence: 99%

“…(12) and (13) the line-strength S f i is |M 1 f i | 2 and |E2 f i | 2 respectively and M 1 f i and E2 f i are the corresponding one electron reduced matrix elements of magnetic dipole and electric quadrupole transitions [13]. The net probability for a given transition which allows two different channels is given by [12] A = A M1 + A E2 (14) and the corresponding lifetime, which is the inverse of the transition probability is expressed as…”

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Relativistic unitary coupled cluster theory and applications

Sur

Chaudhuri

Sahoo

et al. 2008

J. Phys. B: At. Mol. Opt. Phys.

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We present the first formulation and application of relativistic unitary coupled cluster theory to atomic properties. The remarkable features of this theory are highlighted, and it is used to calculate the lifetimes of 5 2 D 3/2 and 6 2 P 3/2 states of Ba + and P b + respectively. The results clearly suggest that it is very well suited for accurate ab initio calculations of properties of heavy atomic systems.PACS numbers: 31.15. Ar, 31.15.Dv, 31.25.Jf, 32.10.Fn There have been a number of attempts to modify coupled-cluster (CC) theory [1], despite its spectacular success in elucidating the properties of a wide range of many-body systems [1,2,3,4,5]. One interesting case in point is unitary coupled-cluster (UCC) theory which was first proposed by Kutzelnigg [6]. In this theory, the effective Hamiltonian is Hermitian by construction and the energy which is the expectation value of this operator in the reference state is unlike in CC theory, an upper bound to the ground state energy [5]. Another attractive feature of this theory which we shall discuss later is that at a given level of approximation it incorporates certain higher order excitations that are not present in CC theory. Furthermore, it is well suited for the calculation of properties where core relaxation effects are important [7,8]. In spite of the aforementioned advantages, there have been relatively few studies based on this method [9,10]. This work is the first relativistic formulation of unitary coupled cluster (UCC) theory and also the first application of this theory to atomic properties. In this letter, we first present the formal aspects of relativistic UCC theory and then apply it to calculate the lifetimes of the 5 2 D 3/2 and 6 2 P 3/2 states of Ba + and P b + respectively; which depend strongly on both relativistic and correlation effects. The comparison of the results of these calculations with accurate experimental data would constitute an important test of this theory.The exact wave function for a closed shell state in CC theory is obtained by the action of the operator exp(T ) on the reference state |Φ . However, in UCC theory [10], it is written aswhere σ = T − T † ; and T and T † are the excitation and deexcitation operators respectively. σ is clearly antiHermitian, since σ † = −σ. Using this unitary ansatz for the correlated wave function, the relativistic UCC equation in the Dirac-Coulomb approximation can be written aswhere H is the Dirac-Coulomb HamiltonianUsing the normal ordered Hamiltonian, Eq.(2) can be rewritten aswhere the normal ordered Hamiltonian is defined as H N = H − Φ| H |Φ and ∆E = E − Φ| H |Φ . . The choice of the operator σ makes the effective Hamiltonian H N = exp(−σ)H N exp(σ) Hermitian.The effective Hamiltonian is expressed by the Hausdorff expansion in CC theory as

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confidence: 99%

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“…These calculations are Excitation energy τ UCCSD(T) 4789 81.01 CCSD(T) [14] 4809 87.06 Dzuba et al [15] 4411 81.5 Guet et al [16] 4688 83.7 Experiment [17] 4874 79±4.6…”

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confidence: 99%

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Relativistic unitary coupled cluster theory and applications

Sur

Chaudhuri

Sahoo

et al. 2008

J. Phys. B: At. Mol. Opt. Phys.

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“…This property is essential for long distance entanglement between ionic qubits [9,10], since the post selection entanglement process is mediated by emitted photons [11]. Finally, barium atomic structure is well understood, since it has been studied extensively both theoretically [12,13] and experimentally for possible applications as an optical frequency standard [14,15] and for a test of parity non-conservation [16,17].…”

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confidence: 99%