Hylleraas method for many‐electron atoms. I. The Hamiltonian

Ruiz, María Belén

doi:10.1002/qua.20197

Cited by 39 publications

(22 citation statements)

References 65 publications

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“…We now move on to the 2 + unbound excited state of 6 He. To assess the accuracy of computing this state in the GSM, we test the sensitivity of calculations to the HO expansion (30). It is worth noting that in the GSM method only the two-body interaction and recoil terms are treated within the HO expansion.…”

Section: A Energiesmentioning

confidence: 99%

Nuclear three-body problem in the complex energy plane: Complex-scaling Slater method

et al. 2014

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Background:The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape toward the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. Purpose:To describe open quantum systems, we introduce a complex-scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow shell model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6 He viewed as an α + n + n cluster system. Methods: Both CS and GSM approaches are applied to a translationally invariant Hamiltonian with the two-body interaction approximated by the finite-range central Minnesota force. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. Results: We show that the CS-Slater method is both accurate and efficient. Its equivalence to the GSM approach has been demonstrated numerically for both energies and wave functions of 6 He. One important technical aspect of our calculation was to fully retrieve the correct asymptotic behavior of a resonance state from the complex-scaled (square-integrable) wave function. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. Conclusions:The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method-if it can be applied-can provide additional information about partial energy widths associated with individual thresholds.

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Section: A Energiesmentioning

confidence: 99%

Nuclear three-body problem in the complex energy plane: Complex-scaling Slater method

et al. 2014

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“…Recently, calculations on the ground state of boron atom have been made using the singleterm and 150-term wave functions constructed with Slater orbitals [21]. The obtained energies lie between the Hartree-Fock and the CI energies, including about 28 per cent of the correlation energy.…”

Section: Introductionmentioning

confidence: 99%

Variational Calculations on the 2p1/2 Ground State of Boron Atom Using Hydrogenlike Orbitals*

Belén¹,

Rojas²

2003

CMST

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Variational calculations of the 2 P 1/2 ground state of boron atom are performed using a singleterm reference wave function and a 150-term wave function expansion without interelectronic distances. The wave function is constructed with hydrogenlike orbitals. These orbitals are superior to Slater orbitals, because the orbital 2s contains nodes. The calculated energy-24.550233 a.u. is compared with-24.541246 a.u. using Slater orbitals and the same basis function expansion, and with-24.5689998 a.u. obtained from full-CI calculations using a 4-31G basis set. The single-term wave function constructed with hydrogenlike orbitals leads to an energy value of-24.501187 a.u., which is lower than the Hartree-Fock energy using a single-zeta basis set of Slater orbitals and it is also lower than with a single-term wave function with Slater orbitals, both lead to an energy of-24.498369 a.u. The behavior of the node of the 2s orbital and its radial distribution function of the wave function series are discussed.

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“…In a previous article [16], we have reported an energy of −24.541246 a.u. with a 150-term type ssssp CI wave function with the restriction of double occupancy of the orbitals and one set of optimized exponents for all terms of the wave function expansion.…”

Section: Boron Atommentioning

confidence: 96%

“…For the evaluation of the matrix elements, we have used the Hamiltonian defined in Hylleraas coordinates [16]. With this form of the Hamiltonian, the kinetic energy integrals do not need any further transformation to be evaluated as one-electron integrals.…”

Section: Theorymentioning

confidence: 99%

Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals

Ruiz

Rojas

Chicón

et al. 2011

Int J of Quantum Chemistry

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Configuration Interaction (CI) calculations on the ground 2 P state of boron atom are presented using a wave function expansion constructed with L-S eigenfunction configurations of s-, p-, and d-Slater orbitals. Two procedures of optimization of the orbital exponents have been investigated. First, CI(SD) calculations including few types of configurations and full optimization of the orbital exponents led to the energy −24.63704575 a.u. Second, full-CI (FCI) calculations including a large number of configuration types using a fixed set of orbital exponents for all configurations gave −24.63405222 a.u. using the basis [4s3p2d] and 2157 configurations, and to an improved result of −24.64013999 a.u. for 3957 configurations and a [5s4p3d] basis. This last result is better than earlier calculations of Schaefer and Harris (Phys Rev 1968, 167, 67), and compares well with the recent ones from Froese Fischer and Bunge (personal communication). In addition, using the same wave functions, CI calculations of the boron isoelectronic ion C + have been performed obtaining an energy of −37.41027598 a.u.

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Hylleraas method for many‐electron atoms. I. The Hamiltonian

Cited by 39 publications

References 65 publications

Nuclear three-body problem in the complex energy plane: Complex-scaling Slater method

Nuclear three-body problem in the complex energy plane: Complex-scaling Slater method

Variational Calculations on the 2p1/2 Ground State of Boron Atom Using Hydrogenlike Orbitals*

Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals

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Hylleraas method for many‐electron atoms. I. The Hamiltonian

Cited by 39 publications

References 65 publications

Nuclear three-body problem in the complex energy plane: Complex-scaling Slater method

Nuclear three-body problem in the complex energy plane: Complex-scaling Slater method

Variational Calculations on the 2p1/2 Ground State of Boron Atom Using Hydrogenlike Orbitals*

Configuration interaction calculations on the 2P ground state of boron atom and C+ using Slater orbitals

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Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals