Pauli potential in terms of kinetic energy density and electron density in the leading Coulombic term of the nonrelativistic 1/Z expansion of spherical atomic ions

The Pauli potential VP in density functional theory is known to be the difference between the functional derivative of the single-particle kinetic energy Ts[n] with respect to the electron density n and its von Weizsaecker counterpart. For the leading Coulombic term in the 1/Z expansion for spherical atomic ions, VP[n] is written in terms of the kinetic energy density plus n(r) and its low-order derivatives. For comparison, the example of an arbitrary number of closed shells with purely harmonic confinement is also treated.