Title 



Analytic structure of groundstate energies and wave functions for the inhomogeneous electron liquid in nonrelativistic Helike atomic ions with nuclear charge Ze
 
Author 



 
Abstract 



The ground state of the He atom for fixed nucleus remains intractable so far as regards exact analytic solutions. However, some important results already exist pertaining to its groundstate wave function Psi and corresponding electron density n(r). Here, we extend the existing studies by focussing attention on the nonrelativistic series of Helike atomic ions with nuclear charge Z. We then find it instructive to start from the energy E(Z) of such a twoelectron spincompensated problem. This is known to have nonanalytic behaviour at a critical Z, say Z(c), equal to 0.911028. A form of Darboux transformation going back at very least to Brandas and Goscinski [E. Brandas and O. Goscinski, Int. J. Quantum Chem. 6, 59 (1972)] is refined somewhat here, and compared with a more intuitive approach of Callan [E. Callan, Int. J. Quantum Chem. 6, 431 (1972)]. The important 1/Z expansion of E(Z) is also invoked. The electron density n(r) and the groundstate wave function Psi are then treated in turn, in a related manner; especially their asymptotic behaviour far from the nucleus. Finally, two exact wave functions for analytically solvable twoFermion models are shown to sum the infinite series proposed by Fock [V. Fock, Izv. Akad. Nauk SSSR, Ser. Fiz. 18, 161 (1954)].   
Language 



English
 
Source (journal) 



Physics and chemistry of liquids.  London  
Publication 



London : 2012
 
ISSN 



00319104
 
Volume/pages 



50:3(2012), p. 389398
 
ISI 



000304271500010
 
Full text (Publisher's DOI) 


  
