Analysis of singular operators in the relativistic calculation of magnetic molecular properties
In the relativistic theory of magnetic molecular properties which involve the magnetic field of a magnetic nucleus, difficulties associated with the divergence of four-component Dirac spinors in the vicinity of the nucleus need be considered with care. Within the point dipole model of the nucleus, s...
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todo:paper_10502947_v76_n2_p_Zaccari2023-10-03T15:59:55Z Analysis of singular operators in the relativistic calculation of magnetic molecular properties Zaccari, D. Ruiz De Azúa, M.C. Giribet, C.G. Anisotropy Magnetic fields Magnetic shielding Matrix algebra Numerical analysis Paramagnetic resonance Tensors Dirac spinors Fermi contact Magnetic nucleus Relativistic theory Singular operators Spin-spin coupling Relativity In the relativistic theory of magnetic molecular properties which involve the magnetic field of a magnetic nucleus, difficulties associated with the divergence of four-component Dirac spinors in the vicinity of the nucleus need be considered with care. Within the point dipole model of the nucleus, singular operators may be involved. This is the case, for instance, of the relativistic calculation of the nuclear magnetic shielding tensor and indirect spin-spin coupling tensor in the context of Kutzelnigg's minimal coupling approach. We show that matrix elements of the magnetic interaction yield divergent values for every single Fermi contact, spin dipolar, paramagnetic spin orbit, and Kutzelnigg's anisotropic Dirac's δ operator. However, when all terms are added together the divergent results cancel each other and a finite convergent result is obtained. It is concluded that Kutzelnigg's minimal coupling approach can be safely applied in the case of a point dipole model of the nucleus, and numerical results should be equivalent to those of the direct linear response approach for the operator V=eαA. The importance of the inclusion of the anisotropic Dirac's δ operator is emphasized. © 2007 The American Physical Society. Fil:Zaccari, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Ruiz De Azúa, M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Giribet, C.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10502947_v76_n2_p_Zaccari |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Anisotropy Magnetic fields Magnetic shielding Matrix algebra Numerical analysis Paramagnetic resonance Tensors Dirac spinors Fermi contact Magnetic nucleus Relativistic theory Singular operators Spin-spin coupling Relativity |
| spellingShingle |
Anisotropy Magnetic fields Magnetic shielding Matrix algebra Numerical analysis Paramagnetic resonance Tensors Dirac spinors Fermi contact Magnetic nucleus Relativistic theory Singular operators Spin-spin coupling Relativity Zaccari, D. Ruiz De Azúa, M.C. Giribet, C.G. Analysis of singular operators in the relativistic calculation of magnetic molecular properties |
| topic_facet |
Anisotropy Magnetic fields Magnetic shielding Matrix algebra Numerical analysis Paramagnetic resonance Tensors Dirac spinors Fermi contact Magnetic nucleus Relativistic theory Singular operators Spin-spin coupling Relativity |
| description |
In the relativistic theory of magnetic molecular properties which involve the magnetic field of a magnetic nucleus, difficulties associated with the divergence of four-component Dirac spinors in the vicinity of the nucleus need be considered with care. Within the point dipole model of the nucleus, singular operators may be involved. This is the case, for instance, of the relativistic calculation of the nuclear magnetic shielding tensor and indirect spin-spin coupling tensor in the context of Kutzelnigg's minimal coupling approach. We show that matrix elements of the magnetic interaction yield divergent values for every single Fermi contact, spin dipolar, paramagnetic spin orbit, and Kutzelnigg's anisotropic Dirac's δ operator. However, when all terms are added together the divergent results cancel each other and a finite convergent result is obtained. It is concluded that Kutzelnigg's minimal coupling approach can be safely applied in the case of a point dipole model of the nucleus, and numerical results should be equivalent to those of the direct linear response approach for the operator V=eαA. The importance of the inclusion of the anisotropic Dirac's δ operator is emphasized. © 2007 The American Physical Society. |
| format |
JOUR |
| author |
Zaccari, D. Ruiz De Azúa, M.C. Giribet, C.G. |
| author_facet |
Zaccari, D. Ruiz De Azúa, M.C. Giribet, C.G. |
| author_sort |
Zaccari, D. |
| title |
Analysis of singular operators in the relativistic calculation of magnetic molecular properties |
| title_short |
Analysis of singular operators in the relativistic calculation of magnetic molecular properties |
| title_full |
Analysis of singular operators in the relativistic calculation of magnetic molecular properties |
| title_fullStr |
Analysis of singular operators in the relativistic calculation of magnetic molecular properties |
| title_full_unstemmed |
Analysis of singular operators in the relativistic calculation of magnetic molecular properties |
| title_sort |
analysis of singular operators in the relativistic calculation of magnetic molecular properties |
| url |
http://hdl.handle.net/20.500.12110/paper_10502947_v76_n2_p_Zaccari |
| work_keys_str_mv |
AT zaccarid analysisofsingularoperatorsintherelativisticcalculationofmagneticmolecularproperties AT ruizdeazuamc analysisofsingularoperatorsintherelativisticcalculationofmagneticmolecularproperties AT giribetcg analysisofsingularoperatorsintherelativisticcalculationofmagneticmolecularproperties |
| _version_ |
1782029902205157376 |