scholarly journals An upper and lower solution approach for a generalized Thomas–Fermi theory of neutral atoms

2002 ◽  
Vol 8 (2) ◽  
pp. 135-142 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Neutral Atom ◽  
Lower Solution ◽  
Solution Theory ◽  
Bohr Radius ◽  
Fermi Theory ◽  
Upper And Lower Solution ◽  
Solution Approach ◽  
Thomas Fermi

This paper presents an upper and lower solution theory for boundary value problems modelled from the Thomas–Fermi equation subject to a boundary condition corresponding to the neutral atom with Bohr radius.

scholarly journals ATOMS IN THE ANIONIC DOMAIN, Z < N

2013 ◽  
Vol 27 (24) ◽  
pp. 1350178 ◽  
Author(s):  
GABRIEL GIL ◽  
AUGUSTO GONZALEZ
Keyword(s):  
Ionization Potential ◽  
Neutral Atom ◽  
Nuclear Charge ◽  
Instability Threshold ◽  
The Other ◽  
Covalent Radius ◽  
Energy Curve ◽  
Fermi Theory ◽  
Thomas Fermi ◽  
Linear Behavior

We study atoms with N electrons, and nuclear charge Z. It is well known that the cationic regime, Z > N, is qualitatively described by Thomas–Fermi theory. The anionic regime, Z < N, on the other hand, is characterized by an instability threshold at Zc ≲ N-1, below which the atom spontaneously emits an electron. We compute the slope of the energy curve at Z = N - 1 by means of a simple model that depends on the electron affinity and the covalent radius of the neutral atom with N - 1 electrons. This slope is used in order to estimate Zc, which is compared with previous numerical results. Extrapolation of the linear behavior in the opposite direction, up to Z = N, allows us to estimate the ionization potential of the atom with N electrons. The fact that the obtained ionization potentials are qualitatively correct is an indication that, with regard to certain properties, neutral atoms are closer to the anionic instability threshold than they are to the Thomas–Fermi, large Z, region. A regularized series is written for the ionization potential that fits both, the large Z and Z → Zc limits.

An upper and lower solution theory for singular Emden–Fowler equations

2002 ◽  
Vol 3 (2) ◽  
pp. 275-291 ◽  
Author(s):  
R.P. Agarwal ◽  
Donal O'Regan ◽  
V. Lakshmikantham ◽  
S. Leela
Keyword(s):  
Lower Solution ◽  
Solution Theory ◽  
Upper And Lower Solution
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