Relativistic Self-Consistent-Field Calculation of the Wave Functions, Eigenvalues, Isotope Shifts, and the6sHyperfine-Structure Coupling Constant as a Function of Pressure for Metallic Gold in the Wigner-Seitz Model

Abstract

We describe a versatile code for the calculation of the electronic properties of atoms in the Hartree-Dirac approximation. Calculations may be made for excited-state and multihole configurations as well as for the ground state of the neutral atom. Exchange may be included in the Slater approximation. The properties of metals may be calculated in the Wigner-Seitz approximation. The calculations may be made for a point nucleus or for a finite nucleus with a diffuse surface. We give results from a calculation made in the Wigner-Seitz approximation of the way a gold atom changes as a result of compression. This includes results about the way the charge density changes both near the gold nucleus and throughout the atom as the Wigner-Seitz radius is decreased from infinity to a value somewhat less than that for metallic gold at zero pressure. It was found that the charge density near the nucleus goes through a minimum which is related to the Wigner-Seitz boundary condition. The eigenvalues for all of the states occupied in atomic gold are given as a function of compression, of Slater exchange, and of nuclear size. Using these, the change with nuclear size of the eigenvalues of all of the electronic $s$ states is calculated and is compared with a first-order perturbation-theory calculation of this change. The hfs coupling constant of the $6s$ state of a free atom of gold is calculated and compared with experiment. The core polarization in gold is discussed. Finally, a brief discussion of internal conversion in $^{169}\mathrm{Tm}$ is given. The calculations given for gold are pertinent to a measurement of the change of energy of the resonance $\ensuremath{\gamma}$ ray of $^{197}\mathrm{Au}$ with pressure. This measurement was made through the use of the M\"ossbauer effect.