A one-dimensional model for many-electron atoms in extremely strong magnetic fields: Maximum negative ionization

Journal of Physics A: Mathematical and General

Volumn 32, Issue 13, 1999, Pages 2567-2582

  Brummelhuis, Raymond ^a   Ruskai, Mary Beth ^b  

^a UNIVERSITÉ DE REIMS CHAMPAGNE ARDENNE   (France)

^b University of Massachusetts Lowell   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033515270     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/13/008     Document Type: Article

References (30)

1. Avron Y, Herbst I and Simon B 1978 Schrödinger operators with magnetic fields I. General Interactions Duke Math. J. 45 847-83
2. Avron Y, Herbst I and Simon B 1979 Strongly bound states of hydrogen in intense magnetic field Phys. Rev. A 20 2287-96
3. Avron Y, Herbst I and Simon B 1981 Schrödinger operators with magnetic fields III. Atoms in homogeneous magnetic field Commun. Math. Phys. 79 529-72
4. Baker J D, Freund D E, Hill R N and Morgan J D III 1990 Radius of convergence and analytic behavior of the 1/Z expansion Phys. Rev. A 41 1247-73
5. Baumgartner B 1983 On the degree of ionization in the TFW theory Lett. Math. Phys. 7 439-41
6. Cycon H L, Froese R G, Kirsch W and Simon B 1987 Schrödinger Operators (Berlin: Springer)
7. Fefferman C L and Seco L A 1990 Asymptotic neutrality of large ions Commun. Math. Phys. 128 109-30
8. Haines I K and Roberts D H 1969 One dimensional hydrogen atom Am. J. Phys. 37 1145-54
9. Hoffman-Ostenhof M and Hoffman-Ostenhof T Private communication
10. Ichinose T 1993 Note on the kinetic energy inequality leading to Lieb's negative ionization upper bound Lett. Math. Phys. 28 219-30
11. Ito K and McKean H P 1965 Diffusion Processes and Their Sample Paths (Berlin: Springer) p 17
12. Lieb E H 1981 Thomas-Fermi and related theories of atoms and molecules Rev. Mod. Phys. 53 603-41 (reprinted in [14])
13. Lieb E H 1984 Bound on the maximum negative ionization of atoms and molecules Phys. Rev. A 29 3018-28 (reprinted in [14])
14. Lieb E H 1997 The Stability of Matter: From Atoms to Stars 2nd edn Selecta of E Lieb, ed W Thirring (Berlin: Springer)
15. Lieb E H, Sigal I M, Simon B and Thirring W 1988 Asymptotic neutrality of large-Z ions Commun. Math. Phys. 116 635-44 (reprinted in [14])
16. Lieb E H, Solovej J P and Yngvason J 1992 Heavy atoms in the strong magnetic field of a neutron star Phys. Rev. Lett. 69 749-52
17. Lieb E H, Solovej J P and Yngvason J 1993 Asymptotics of heavy atoms in high magnetic fields I: lowest landau band regions Commun. Pure Appl. Math. 47 513-91
18. Lieb E H, Solovej J P and Yngvason J 1994 Asymptotics of heavy atoms in high magnetic fields II: semiclassical regions Commun. Math. Phys. 161 77-124
19. Rau A R P, Mueller R O and Spruch L 1975 Simple model and wavefunctions for atoms in intense magnetic fields Phys. Rev. A 11 1865-79
20. Ruderman M 1974 Matter in superstrong magnetic fields Physics of Dense Matter ed C J Hansen (Dordrecht: Rediel) pp 117-31
21. Ruskai M B 1982 Absence of discrete spectrum in highly negative ions Commun. Math. Phys. 82457-69 Ruskai M B 1982 Commun. Math. Phys. 85 325-7
22. Ruskai M B 1982 Absence of discrete spectrum in highly negative ions Commun. Math. Phys. 82457-69 Ruskai M B 1982 Commun. Math. Phys. 85 325-7
23. Ruskai M B 1994 Improved estimates on the number of bound states of negative bosonic atoms Ann. Inst. Henri Poincaré Phys. Theor. 61 153-62
24. Ruskai M B and Werner E 1997 A pair of optimal inequalities related to the error function Preprint Austin Math. Phys. Archive 97-564
25. Schiff L and Snyder H 1939 Theory of the quadratic Zeeman effect Phys. Rev. 55 59-63
26. Seco L A, Sigal I M and Solovej P 1990 Bound on the ionization energy of large atoms Commun. Math. Phys. 131 307-15
27. Sigal I M 1984 How many electrons can a nucleus bind? Ann. Phys. 157 307-20
28. Szarek S J and Werner E 1999 A non-symmetric correlation inequality for Gaussian measure J. Multi. Anal. 68 193-211
29. x f (t)dt est convexe Rev. Math. Spéciales 104 187-8
30. Yngvason J 1995 Asymptotics of natural and artificial atoms in strong magnetic fields Proc. of the XIth Int. Cong. of Mathematical Physics ed D lagolnitzer (Cambridge, MA: International) pp 185-205 (reprinted in [14])