Characterization of kinetic energy density for central fields by total and s-state Slater sums

The result of the kinetic energy operator -(${ħ}^2$/2m) ${\nabla }_{\mathrm{r}}^2$, acting on the canonical density matrix C(r,${\mathrm{r}}_0$,β) and then evaluated on the diagonal ${\mathrm{r}}_0$=r, is expressed solely in terms of the so-called Slater sum C(r,r,β) and the same sum for s states only, for arbitrary central fields.