Atomic Thomas‐Fermi theory and electron subshell filling

Abstract

AbstractIn previous work on electron subshell filling, the existence condition of the integrals involved has not been taken into proper account. As a result, part of the calculated subshell occupation numbers is meaningless.In Theis' theory [9] the average number of electrons in a subshell is calculated as the difference between two integrals. With each of these integrals an existence condition is associated. Because of this, the number of electrons with angular momentum quantum number l can only be calculated for atoms of which the Z value is (much) larger than the corresponding empirical first‐appearance Z value. Thus, the range of Z for which such numbers can be calculated, is restricted considerably, especially for larger values of l.Results obtained from a normalized version of Mason's approximation [13] to the exact Thomas‐Fermi function, have been compared with a least‐squares fit of the empirical subshell occupation numbers, and these are found to be as good as one may expect from a statistical theory.A lower bound to each of the empirical first‐appearance Z values has been calculated. The results agree well with those reported in other work.