Theoretical Description of Relativistic Terms of a Hydrogen Atom in a Magnetic Field: A Variational Approach in the Basis of Hydrogen-Like Spinors
- Authors: Ozerov G.K.1, Bodunov A.A.2, Bezrukov D.S.1
-
Affiliations:
- Skolkovo Institute of Science and Technology
- Faculty of Chemistry, Moscow State University
- Issue: Vol 97, No 7 (2023)
- Pages: 1032-1037
- Section: СТРОЕНИЕ ВЕЩЕСТВА И КВАНТОВАЯ ХИМИЯ
- URL: https://journals.rcsi.science/0044-4537/article/view/136636
- DOI: https://doi.org/10.31857/S0044453723070208
- EDN: https://elibrary.ru/SLRJBT
- ID: 136636
Cite item
Abstract
The incomplete diagonalization of a Dirac Hamiltonian in the basis of the states of an unperturbed atom is used to obtain solutions to the Dirac equation for a hydrogen atom in a constant uniform magnetic field and a wide range of changes in strength. The resulting finite expressions for the matrix elements of the perturbation operator of an arbitrary hydrogen-like atom are used to estimate the action of operators in minimizing the energy dispersion functional. The approach allows precise estimates of the energy of the ground state and values of the energies of transition that are in good agreement with results from earlier studies. It is shown that the proposed technique for minimizing the energy dispersion functional allows the incomplete diagonalization of operators for an arbitrarily chosen block of target states, provided that the initial approximation is correct.
Keywords
About the authors
G. K. Ozerov
Skolkovo Institute of Science and Technology
Email: ozerow.georgiy.c@yandex.ru
121205, Moscow, Russia
A. A. Bodunov
Faculty of Chemistry, Moscow State University
Email: ozerow.georgiy.c@yandex.ru
119991, Moscow, Russia
D. S. Bezrukov
Skolkovo Institute of Science and Technology
Author for correspondence.
Email: ozerow.georgiy.c@yandex.ru
121205, Moscow, Russia
References
- Hanns Ruder, Günter Wunner, Heinz Herold, Florian Geyer. Atoms in Strong Magnetic Fields: Springer Berlin Heidelberg, 1994.
- Zeeman P. // Nature. 1897. V. 55. № 1424. P. 347.
- Holle A., Wiebusch G., Main J. et al. // Physical review letters. 1986. V. 56. № 24. P. 2594.
- Main J., Wiebusch G., Holle A., Welge K.H. // Ibid. 1986. V. 57. № 22. P. 2789.
- Holle A., Main J., Wiebusch G. et al. // Ibid.1988. V. 61. № 2. P. 161.
- Iu Chun-ho, Welch G.R., Kash M.M. et al. // Physical review letters. 1991. V. 66. № 2. P. 145.
- Welch G.R., Kash M.M., Iu Chun-ho et al. // Ibid. 1989. V. 62. № 8. P. 893.
- Yafet Y., Keyes R.W., Adams E.N. // J. of Physics and Chemistry of Solids. 1956. V. 1. № 3. P. 137.
- Elliott R.J., Loudon R. // Ibid.1960. oct. V. 15. № 3–4. P. 196.
- Cabib D., Fabri E., Fiorio G. // Il Nuovo Cimento B (1971–1996). 1972. V. 10. № 1. P. 185.
- Ruderman M. // Annual Review of Astronomy and Astrophysics. 1972. V. 10. P. 427.
- Kemp J.C., Swedlund J.B., Landstreet J.D., Angel J.R.P. // The Astrophysical J. 1970. V. 161. P. L77.
- Garstang R.H. // Reports on Progress in Physics. 1977. V. 40. № 2. P. 105.
- Lasenby A., Doran C., Pritchard J. et al. // Physical Review D. 2005. V. 72. № 10. P. 105014.
- Schmidt G.D., Allen R.G, Smith P.S., Liebert J. // The Astrophysical J. 1996. may. V. 463. P. 320.
- Lai D. // Rev. Mod. Phys. 2001. Aug. V. 73. P. 629.
- Mori K., Ho W.C.G. // Monthly Notices of the Royal Astronomical Society. 2007. May. V. 77. № 2. P. 905.
- Duncan R.C., Thompson C. // The Astrophysical J. 1992. Jun. V. 392. P. L9.
- Kouveliotou C., Dieters S., Strohmayer T. et al. // Nature. 1998. May. V. 393. P. 235.
- Praddaude H.C. // Physical Review A. 1972. Oct. V. 6. № 4. P. 1321.
- Friedrich H. // Ibid. 1982. V. 26. № 4. P. 1827.
- Liu C-R., Starace A.F. // Ibid. 1987. V. 35. № 2. C. 647.
- Rau A.R.P., Spruch L. // The Astrophysical J. 1976. V. 207. P. 671.
- Rosner W., Wunner G., Herold H., Ruder H. // J. of Physics B: Atomic and Molecular Physics (1968–1987). 1984. V. 17. № 1. P. 29.
- Forster H., Strupat W., Rosner W. et al. // J. of Physics B: Atomic and Molecular Physics (1968–1987). 1984. V. 17. № 7. P. 1301.
- Handy C.R., Bessis D., Sigismondi G., Morley T.D. // Physical review letters. 1988. V. 60. № 4. P. 253.
- Shertzer J. // Physical Review A. 1989. V. 39. № 8. P. 3833.
- Fonte G., Falsaperla P., Schiffrer G., Stanzial D. // Ibid. 1990. V. 41. № 11. P. 5807.
- Stubbins C., Das K., Shiferaw Y. // J. of Physics B: Atomic, Molecular and Optical Physics. 2004. V. 37. № 10. P. 2201.
- Lindgren K.A.U., Virtamo J.T. // Ibid. 1979. V. 12. № 21. P. 3465.
- Manakov N.L., Rapoport L.P., Zapryagaev S.A. // Ibid. 1974. V. 7. № 9. P. 1076.
- Szmytkowski R. // Physical Review A. 2002. V. 65. № 3. P. 032314.
- Poszwa A., Rutkowski A. // Ibid. 2004. V. 69. № 2. P. 062320.
- Rutkowski A. // J. of Physics B: Atomic and Molecular Physics. 1986. V. 19. № 2. P. 149.
- Chen Z., Goldman S.C. // Physical Review A. 1991. V. 44. № 7. P. 4459.
- Chen Z., Goldman S.C. // Ibid. 1992. V. 45. № 3. P. 1722.
- Goldman S.C., Chen Z. // Physical review letters. 1991. V. 67. № 11. P. 1403.
- Chen Z., Fonte G., Goldman S.C. // Phys. Rev. A. 1994. Nov. V. 50. P. 3838.
- Hill R.N., Krauthauser C. // Physical review letters. 1994. V. 72. № 14. P. 2151.
- Weaver D.L. // Journal of Mathematical Physics. 1977. V. 18. № 2. P. 306.
- Swainson R.A., Drake G.W.F. // J. of Physics A: Mathematical and General. 1991. V. 24. № 1. P. 79.
- Kutzelnigg W. // Chemical Physics. 2012. feb. V. 395. P. 16.
- Sun S., Stetina T.F., Zhang T. et al. // J. of Chemical Theory and Computation. 2021. V. 17. № 6. P. 3388.
- Chen J.-L., Deng D.-L., Hu M.-G. // Physical Review A. 2008. V. 77. № 3. P. 034102.
- Lanczos C. // J. of Research of the National Bureau of Standards. 1950. V. 45. № 4. P. 255.
- Judd B.R. Operator techniques in atomic spectroscopy: New York, McGraw-Hill Book Co., Inc., 1963. V. 276. P. 82.