Ground state correlation energy of the Be-sequence forZ=4–20 in MCDF approximation

The ground state (J=0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation forZ=4–20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.     

Calculations of electron screening in muonic atoms

The electron screening in mounic atoms (O, Al, Fe, In, Ho, Au, Th) has been calculated forp _3/2,d _5/2 andf _7/2 levels withn _µ≦30 and for circular orbits withn _µ≦12 using a relativistic Dirac-Fock program. Simple empirical formulae are presented which can be employed to calculate the screening corrections for all elements fromZ=8 toZ=90, forp _3/2,d _5/2 andf _7/2 muons up ton _µ=30 Screening corrections are also given for electron configurations with holes in theK andL ₃ shell.     

Dirac—Fock one-centre calculations. The molecules BH,AlH, GaH,InH and TlH

Relativistic and non-relativistic Hartree—Fock calculations including np_{$\text{1}\text{2}$} and np_{$\text{3}\text{2}$} orbitals in the valence MO are reported for the molecules BH, AlH, GaH, InH and TlH. The relativistic contraction of the bond length reaches 7.0% for TlH. Relativistic effects make the chemical bond stronger for AlH, GaH and InH and weaker for TlH. The calculated force constants and dissociation energies are in reasonable agreement with experiment. A change from npσ towards np_{$\text{1}\text{2}$} bonding takes place along the series. For Tl the MO is only 39% p_{$\text{3}\text{2}$} as compared with the non-relativistic value of 67%. This probably explains the dominant monovalency of thallium.     

Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection m_j of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (m_s unrestricted) and spin plus orbital polarized Hartree- Fock (m_s plus m_j unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, S_s(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.     

Two-muonic atoms

X-ray transition energies for two-muonic atoms are calculated. The basis are relativistic self-consistent-field calculations including the corrections normally known in muonic atoms plus the vacuum polarization, magnetic interaction and retardation in the μ-μ-interaction, the specific mass correction and the configuration interaction.