Calculation of the Electron Binding Energies and X-Ray Energies for the Superheavy Elements 114, 126, and 140 Using Relativistic Self-Consistent-Field Atomic Wave Functions

Relativistic Hartree-Fock-Slater atomic wave functions have been calculated for the superheavy elements $Z=114 \mathrm{and} 126$. The calculations have been made both for the atom and for singly ionized states with holes in the $K$ or $L$ shells. A Wigner-Seitz boundary condition is used, and results for both point and finite nuclei are presented. From these solutions, binding energies and x-ray energies have been evaluated. Similar calculations have been made on Au and U, and have been compared with experiment so as to ascertain what degree of confidence one may have in these computations. A discussion is made of the importance of finite nuclear size in determining the $K$-shell binding energy, and a solution for element 140 was obtained to demonstrate the atomic stability in the present approximation of elements above $Z=137$. Finally, the probability for finding an electron within the nuclear radius is given for each of the elements studied, and a brief discussion is given concerning the stability of the superheavy elements against electron capture.