Collect. Czech. Chem. Commun. 2005, 70, 1133-1156
https://doi.org/10.1135/cccc20051133

Hydrogen Atom and One-Electron Molecular Systems in a Strong Magnetic Field: Are All of Them Alike

Alexander V. Turbinera,*, Alexei B. Kaidalovb and Juan Carlos López Vieyraa

a Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F., México
b Institute for Theoretical and Experimental Physics, Moscow 117259, Russia

References

1. Values of the observed magnetic fields are: white dwarfs (106–109 G), magnetic neutron stars (1012–1013 G), magnetars (1014–1015 G).
2a. Kadomtsev B. B., Kudryavtsev V. S.: Zh. Eksp. Teor. Fiz. 1971, 13, 15, 61 (1971); JETP Lett. (Engl. Transl.) 1971, 13, 9, 42.
2b. Kadomtsev B. B., Kudryavtsev V. S.: Zh. Eksp. Teor. Fiz. 1972, 62, 144; JETP (Engl. Transl.) 1972, 35, 76.
3a. Ruderman M.: Phys. Rev. Lett. 1971, 27, 1306. <https://doi.org/10.1103/PhysRevLett.27.1306>
3b. Ruderman M. in: IAU Symposium 53, Physics of Dense Matter (C. J. Hansen, Ed.), p.117. Reidel, Dordrecht 1974.
4. Turbiner A., Lopez J.-C., Solis H. U.: Pisma Zh. Eksp. Teor. Fiz. 1999, 69, 800; JETP Lett. (Engl. Transl.) 1999, 69, 844, (astro-ph/980929).
5. Turbiner A. V., Lopez V. J. C.: Preprint ICN-UNAM 04-15, p. 7 (December 2004), (astro-th/0412399).
6. Lopez V. J. C., Turbiner A. V.: Phys. Rev. A 2000, 62, 022510, (astro-ph/9911535). <https://doi.org/10.1103/PhysRevA.62.022510>
7. In dimensionless units (a.u.) the parameter of expansion is enormous, 105.
8. Karnakov B. M., Popov V. S.: Zh. Eksp. Teor. Fiz. 2003, 124, 996; JETP (Engl. Transl.) 2003, 97, 890.
9. Garstang R.: Rep. Prog. Phys. 1977, 40, 105. <https://doi.org/10.1088/0034-4885/40/2/001>
10. Ruder H., Wunner G., Herold H., Geyer F.: Atoms in Strong Magnetic Fields. Springer Verlag, Berlin–Heidelberg 1994.
11. Liberman M. A., Johansson B.: Phys. Usp. 1995, 38, 117. <https://doi.org/10.1070/PU1995v038n02ABEH000067>
12. Lai D.: Rev. Mod. Phys. 2001, 73, 629, (astro-ph/0009333). <https://doi.org/10.1103/RevModPhys.73.629>
13. Turbiner A. V., Lopez V. J. C.: Preprint ICN-UNAM 04-17, p. 149 (December 2004), Phys. Rep., submitted.
14. Potekhin A., Turbiner A.: Phys. Rev. A 2001, 63, 065402, (physics/0101050). <https://doi.org/10.1103/PhysRevA.63.065402>
15. Lai D., Salpeter E.: Phys. Rev. A 1996, 53, 152. <https://doi.org/10.1103/PhysRevA.53.152>
16. It has long been recognized that in a strong magnetic field (>> 1012 G) the effects of finite nuclear masses and center of mass motion are non-trivial. Very few quantitative studies which exist are very difficult and mostly limited to atomic type systems. These effects mostly influence the excited states (for discussion, see ref.12 and references therein). Our consideration is focused on the ground states.
17. Landau L. D., Lifshitz E. M.: Quantum Mechanics. Pergamon Press, Oxford–New York– Toronto–Sydney–Paris–Frankfurt 1977.
18. Hasegawa H., Howard R. W.: J. Phys. Chem. Sol. 1961, 21, 179. <https://doi.org/10.1016/0022-3697(61)90097-X>
19. Calculations were made using the trial function (7) from ref.14.
20. Kravchenko Yu. P., Liberman M. A., Johansson B.: Phys. Rev. A 1996, 54, 287. <https://doi.org/10.1103/PhysRevA.54.287>
21. Turbiner A. V.: Yad. Fiz. 1987, 46, 204; Sov. J. Nucl. Phys. (Engl. Transl.) 1987, 46, 125.
22. Turbiner A., Lopez V. J. C.: Phys. Rev. A 2003, 68, 012504, (astro-ph/0212463). <https://doi.org/10.1103/PhysRevA.68.012504>
23. Turbiner A., Lopez V. J. C.: Phys. Rev. A 2004, 69, 053413, (astro-ph/0310849). <https://doi.org/10.1103/PhysRevA.69.053413>
24. Turbiner A., Lopez V. J. C., Guevara N. L.: Phys. Rev. A 2005, 72, 023403, (astro-ph/0406473). <https://doi.org/10.1103/PhysRevA.72.023403>
25. The (HeH)++ molecular ion is characterized by the asymmetric electronic cloud. Therefore, the longitudinal size is defined rl __MATH__, where zmax corresponds to the z-position of the maximum of the electronic distribution.
26. Sanwal D., Pavlov G. G., Zavlin V. E., Teter M. A.: ApJL 2002, 574, L61, (astro-ph/0206195). <https://doi.org/10.1086/342368>
27. Bignami G. F., Caraveo P. A., De Luca A., Mereghetti S.: Nature 2003, 423, 725. <https://doi.org/10.1038/nature01703>
28. Turbiner A. V., Lopez Vieyra J. C.: Mod. Phys. Lett. 2004, A19, 1919, (astro-ph/0404290). <https://doi.org/10.1142/S0217732304015294>
29. van Kerkwijk M. H., Kaplan D. L., Durant M., Kulkarni S. R., Paerels F.: ApJL, 2004, 608, 432, (astro-ph/0311195). <https://doi.org/10.1086/386299>
30. Vink J., de Vries C. P., Méndez M., Verbunt F.: ApJL 2004, 609, L75, (astro-ph/0404195). <https://doi.org/10.1086/422812>