Sturmian bases for two-electron systems in hyperspherical coordinates
We give a detailed account of an ab initio spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential ex...
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todo:paper_09534075_v49_n23_p_Abdouraman2023-10-03T15:51:08Z Sturmian bases for two-electron systems in hyperspherical coordinates Abdouraman, A. Frapiccini, A.L. Hamido, A. Mota-Furtado, F. O'Mahony, P.F. Mitnik, D. Gasaneo, G. Piraux, B. hyperspherical resonances Sturmian Calculations Electric fields Electron-electron interactions Electrons Resonance Wave functions Analytical expressions Electric dipole oscillators Hyperspherical Hyperspherical coordinates Hyperspherical harmonics Multipole expansions State-of-the-art methods Sturmian Hamiltonians We give a detailed account of an ab initio spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular Sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron-electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb-Sturmian functions of half integer angular momentum. We show that, in the case of H-, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method. © 2016 IOP Publishing Ltd. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09534075_v49_n23_p_Abdouraman |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
hyperspherical resonances Sturmian Calculations Electric fields Electron-electron interactions Electrons Resonance Wave functions Analytical expressions Electric dipole oscillators Hyperspherical Hyperspherical coordinates Hyperspherical harmonics Multipole expansions State-of-the-art methods Sturmian Hamiltonians |
| spellingShingle |
hyperspherical resonances Sturmian Calculations Electric fields Electron-electron interactions Electrons Resonance Wave functions Analytical expressions Electric dipole oscillators Hyperspherical Hyperspherical coordinates Hyperspherical harmonics Multipole expansions State-of-the-art methods Sturmian Hamiltonians Abdouraman, A. Frapiccini, A.L. Hamido, A. Mota-Furtado, F. O'Mahony, P.F. Mitnik, D. Gasaneo, G. Piraux, B. Sturmian bases for two-electron systems in hyperspherical coordinates |
| topic_facet |
hyperspherical resonances Sturmian Calculations Electric fields Electron-electron interactions Electrons Resonance Wave functions Analytical expressions Electric dipole oscillators Hyperspherical Hyperspherical coordinates Hyperspherical harmonics Multipole expansions State-of-the-art methods Sturmian Hamiltonians |
| description |
We give a detailed account of an ab initio spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular Sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron-electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb-Sturmian functions of half integer angular momentum. We show that, in the case of H-, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method. © 2016 IOP Publishing Ltd. |
| format |
JOUR |
| author |
Abdouraman, A. Frapiccini, A.L. Hamido, A. Mota-Furtado, F. O'Mahony, P.F. Mitnik, D. Gasaneo, G. Piraux, B. |
| author_facet |
Abdouraman, A. Frapiccini, A.L. Hamido, A. Mota-Furtado, F. O'Mahony, P.F. Mitnik, D. Gasaneo, G. Piraux, B. |
| author_sort |
Abdouraman, A. |
| title |
Sturmian bases for two-electron systems in hyperspherical coordinates |
| title_short |
Sturmian bases for two-electron systems in hyperspherical coordinates |
| title_full |
Sturmian bases for two-electron systems in hyperspherical coordinates |
| title_fullStr |
Sturmian bases for two-electron systems in hyperspherical coordinates |
| title_full_unstemmed |
Sturmian bases for two-electron systems in hyperspherical coordinates |
| title_sort |
sturmian bases for two-electron systems in hyperspherical coordinates |
| url |
http://hdl.handle.net/20.500.12110/paper_09534075_v49_n23_p_Abdouraman |
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