Boundary Conditions Effects on the Ground State of a Two-Electron Atom in a Vacuum Cavity
American Journal of Modern Physics
Volume 3, Issue 2, March 2014, Pages: 73-81
Received: Jan. 2, 2014; Published: Mar. 20, 2014
Views 4121      Downloads 210
Andrey Tolokonnikov, Department of Quantum Theory and High Energy Physics, M.V.Lomonosov Moscow State University, Moscow, Russia
Article Tools
Follow on us
The ground state properties of the two-electron atom with atomic number in the spherical vacuum cavity with general boundary conditions of “not going out” are studied. It is shown that for certain parameters of the cavity such atom could either decay into the one-electron atom with the same atomic number and an electron or be in stable state with the binding and ionization energies several times bigger than the same energies of the free atom. By analogy with the Wigner-Seitz model of metallic bonding, the possibility of the existence of such effects on the lattice formed by the vacuum cavities filled with the two-electron atoms of the same type is discussed.
Two-Electron Atom, Third Type Boundary Condition, Neumann Boundary Condition, Confinement
To cite this article
Andrey Tolokonnikov, Boundary Conditions Effects on the Ground State of a Two-Electron Atom in a Vacuum Cavity, American Journal of Modern Physics. Vol. 3, No. 2, 2014, pp. 73-81. doi: 10.11648/j.ajmp.20140302.16
D.R. Hartree, “The wave mechanics of an atom with a non-coulomb central field I, II”, Cambr. Soc. 24 (1928).
H. Bethe, “Berechnung der Elektronenaffinitaet des Wasserstoffs”, Z. Phys. 57 815 (1929).
E.A.Z. Hylleraas, “Die Elektronenaffinität des Wasserstoffatoms nach der Wellenmechanik”, Z. f. Physik, 60, 624-630 (1930).
W. Jaskolski, “Confined many-electron systems”, Phys.Rep., 271, (1996).
S. Bhattacharyya, J. K. Saha, P.K. Mukherjee and T. K. Mukherjee, “Precise estimation of the energy levels of two-electron atoms under spherical confinement”, Phys. Scr. 87 (2013)065305 (10pp).
T. Sako and G.H.F. Diercksen, “Confined quantum systems: a comparison of the spectral properties of the two-electron quantum dot, the negative hydrogen ion and the helium atom”, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 1681–1702.
C. Laughlin, Shih-I Chu, “A highly accurate study of a helium atom under pressure”, J. Phys. A: Math. Theor. 42 (2009) 265004 (11pp).
H.E. Montgomery Jr., N. Aquino, A. Flores-Riveros, “The ground state energy of a helium atom under strong confinement”, Phys. Lett. A 374 (2010) 2044–2047.
E.V. Ludena, “SCF Hartree–Fock calculations of ground state wavefunctions of compressed atoms”, J. Chem. Phys. 69(4) 1978.
S.H. Patil, Y.P. Varshni, “A simple description of the spectra of confined hydrogen, helium, and lithium”, Can. J. Phys. 82: 647–659 (2004).
J.L. Marin, S.A. Cruz, “Use of the direct variational method for the study of one- and two-electron atomic systems confined by spherical penetrable boxes”, J. Phys. B: At. Mol. Opt. Phys. 25 (1992) 4365-4371.
B.M. Gimarc, “Correlation Energy of the TwoElectron Atom in a Spherical Potential Box”, J. Chem. Phys. 47, 5110 (1967).
C. Le Sech, A. Banerjee, “A variational approach to the Dirichlet boundary condition: application to confined H_, He and Li”, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 105003 (9pp).
N. Aquino, “The Hydrogen and Helium Atoms Confined in Spherical Boxes”, Adv. Quant. Chem. 57. (2009). 123.
V.K. Dolmatov, A.S. Baltenkov, J.P. Connerade, S. Manson, “Structure and hotoionization of confined atoms”, Radiat. Phys. Chem. 70 (2004). 417.
J.R. Sabin, E.J. Brandas (eds), “Theory of Confined Quantum Systems”, Adv. Quant. Chem.57-58. Elsevier. Amsterdam. 2009.
J.P. Connerade, V.K. Dolmatov, P.A. Lakshmi and S.T. Manson, “Electron structure of endohedrally confined atoms: atomic hydrogen in an attractive shell”, J.Phys. B: At. Mol. Opt. Phys. 32 (1999). L239.
J.P. Connerade, V.K. Dolmatov, S.T. Manson, “A unique situation for an endohedral metallofullerene”, J.Phys. B: At. Mol. Opt. Phys. 32 (1999). L395.
K.D. Sen, V.I. Pupyshev, H.E. Montgomery, “Exact Relations for Confined One-Electron Systems”, Adv. Quant. Chem. 57 (2009).
V.I. Pupyshev, “Wall Effects on the State of Hydrogen Atom in a Cavity”, Rus. J. Phys. Chem. 74. (2000). 50–54. (Engl. transl.)
E. Wigner, F. Seitz, “On the constitution of metallic sodium.I, II”, Phys. Rev. 43. (1933). 804; ibid. 46. (1934). 509.
K.A. Sveshnikov, A.V. Tolokonnikov, “Quatum_Mechanical Confinement with the Robin Condition”, Moscow University Physics Bulletin, 2013, 68, No.1, pp. 13–20.
K. Sveshnikov, A. Roenko, “Quantum confinement under Neumann condition: Atomic H filled in a lattice of cavities”, Physica B: Condensed Matter, 427 (2013) 118–125.
K.A. Sveshnikov, “Quantum mechanics and the hydrogen atom in a generalized Wigner-Seitz cell”, Theoretical and Mathematical Physics, 176, Issue 2 (2013) pp 1044-1066.
E.M. Nascimento, F.V. Prudente, M.N. Guimaraes and A.M. Maniero, “A study of the electron structure of endohedrally confined atoms using a model potential”, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 015003 (7pp).
R. Caputo, A. Alavi, “Where do the H atoms reside in PdHX systems?”, Mol. Phys., 101 (2003), NO. 11, 1781–1787.
G. Alefeld and J. Voelkl (eds). “Hydrogen in Metals I, II. Topics in Applied Physics”, 28-29, Springer, Berlin, 1978.
Y. Fukai, “The Metal-Hydrogen System. Basic Bulk Properties”, Springer, Berlin. 1993.
H. Maris, “Electrons in Liquid Helium”, Journ. Phys. Soc. Japan, 77 (2008) 80700.
C.L. Pekeris, “11 S and 23 S States of Helium”, Phys. Rev. 115, 1216 (1959).
T. Koga, S. Morishita, “Optimal Kinoshita wave functions for heliumlike atoms”, Z. Phys. D. 34. 71 (1995).
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186