The self-consistent relativistic Thomas-Fermi theory of heavy positive ions with N electrons and nuclear charge Ze is shown to lead to a chemical potential f i which has the scaling property p =Z4/3F(N/Z;~/Z2/3), with E = a 2 Z 2a, being the fine structure constant. Combining this with the Layzer-Bahcall expansion for the total energy E(Z,N),namely, E(Z,N)=Z2 I:E,,(N)E"'Z-", mm n=O m=O itisprovedthatthecoefficientsE,,(N) atlargeNhavetheasymptoticbehaviorNn-2m'3+1./ The corresponding result for the scaling of the relativistic Thomas-Fermi energy is ETF(ZN, )=Z7/3F,(N/Z; Scaling properties of the higher order terms in Enm(Na)nd E(Z,N )are also proposed.
Relativistic Theory of the binding energies of heavy atomic ions
MARINI BETTOLO MARCONI, Umberto;
1981-01-01
Abstract
The self-consistent relativistic Thomas-Fermi theory of heavy positive ions with N electrons and nuclear charge Ze is shown to lead to a chemical potential f i which has the scaling property p =Z4/3F(N/Z;~/Z2/3), with E = a 2 Z 2a, being the fine structure constant. Combining this with the Layzer-Bahcall expansion for the total energy E(Z,N),namely, E(Z,N)=Z2 I:E,,(N)E"'Z-", mm n=O m=O itisprovedthatthecoefficientsE,,(N) atlargeNhavetheasymptoticbehaviorNn-2m'3+1./ The corresponding result for the scaling of the relativistic Thomas-Fermi energy is ETF(ZN, )=Z7/3F,(N/Z; Scaling properties of the higher order terms in Enm(Na)nd E(Z,N )are also proposed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
