Improved lower bounds for the atomic charge density at the nucleus

Lower bounds F( alpha , beta ) to the electronic charge density of atomic systems with N electrons at the nucleus, rho (0), are given by means of any two radial expectation values (r alpha ) and (r beta ), for real alpha not= beta , in a rigorous and simple way. In particular, rho (0)>or=(N/8 pi )(r -2 ) 2 /(r -1 ) which improves bounds found previously. An interesting property of these bounds is that they are equal to the exact value rho (0) in the limit beta to -3 for any fixed alpha value.