Physics – General Physics
Scientific paper
May 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrva..35.4035c&link_type=abstract
Physical Review A (General Physics), Volume 35, Issue 10, May 15, 1987, pp.4035-4043
Physics
General Physics
3
Neutron Stars
Scientific paper
One can easily obtain a good estimate of the total energy E(Z) of a ground-state neutral atom with Z (>>1) electrons, primarily because an effective central potential Veff(r) provides a very good starting point. A sufficient, if not necessary, condition for there to be such a Veff is for the ratio ρ(Z)≡Ve-e(Z)/Ve-ν(Z) of the electron-electron and electron-nuclear contributions to E(Z) to be small, and it is found to be only about (1/7) for large Z. In the (statistical) nonrelativistic Thomas-Fermi (TF) model, which becomes exact as Z~∞, E(Z) (in rydbergs) is approximated by ETF(Z)=-c7Z7/3 for all Z, with c7 a known constant, while ρ(Z) is approximated by ρTF(Z)=(1/7) for all Z. A simple proof that ρ(Z)~(1/7) as Z~∞, by Rau (unpublished) and by Thirring [Quantum Mechanics of Large Systems (Springer-Verlag, New York, 1983)], used only the assumption (built into TF theory) that the binding energy of the last electron in a neutral atom is negligible. We use that fact, the (recently developed) corrected TF result E(Z) ~=-(c7Z7/3+c6Z6/3+c5X5/3) (with c7, c6, and c5 theoretically determined), and the virial theorem, and we show that Ve-ν(Z)~=Z(dE/dZ) with an error that is at most of order Z4/3; we thereby obtain an expression for ρ(Z) which approaches (1/7) as Z~∞, the error for large Z being of order 1/Z, and is reasonably accurate even for moderate values of Z. One finds ρ(Z)~=J(n-6)sn/Jnsn, where each sum is over n=7, 6, and 5, and where sn=cnZ(n-7)/3. The value of ρ(Z) for heavy atoms in ``strong'' magnetic fields, those describable by a one-dimensional (statistical) TF-like theory, is discussed briefly. Some numerical studies are included. The results obtained are of interest in atomic theory itself, and in low-energy β-decay processes for which the difference in atomic binding energies is important.
Chen Zonghua
Spruch Larry
No associations
LandOfFree
Relative contributions of the electron-electron and electron-nuclear interactions to the ground-state energy of a neutral atom does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Relative contributions of the electron-electron and electron-nuclear interactions to the ground-state energy of a neutral atom, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Relative contributions of the electron-electron and electron-nuclear interactions to the ground-state energy of a neutral atom will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-860306