| Title |
|
|
|
Analytic structure of ground-state energies and wave functions for the inhomogeneous electron liquid in non-relativistic He-like 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 ground-state wave function Psi and corresponding electron density n(r). Here, we extend the existing studies by focussing attention on the non-relativistic series of He-like atomic ions with nuclear charge Z. We then find it instructive to start from the energy E(Z) of such a two-electron spin-compensated problem. This is known to have non-analytic 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 ground-state 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 two-Fermion 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 |
|
|
|
0031-9104
| |
| Volume/pages |
|
|
|
50:3(2012), p. 389-398
| |
| ISI |
|
|
|
000304271500010
| |
| Full text (Publisher's DOI) |
|
|
| | |
|