# Bounds for the second and the third derivatives of the electron density at the nucleus

Physics – Atomic Physics

Scientific paper

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## Details Bounds for the second and the third derivatives of the electron density at the nucleus Bounds for the second and the third derivatives of the electron density at the nucleus

4 pages

Scientific paper

10.1088/1751-8113/41/8/085305

Lower bound for ${\bar \rho}''(0)$, the second derivative of the spherically averaged atomic electronic density at the nucleus, and upper bound for ${\bar \rho}'''(0)$, the third derivative, are obtained respectively. It is shown that, for the ground state, ${\bar \rho}''(0) \ge {10/3} Z^2 \rho(0)$ and ${\bar \rho}'''(0) \le -{14/3}Z^3 \rho(0)$ where $Z$ is the charge of the nucleus, and $\rho(0)$ is the electron density at the nucleus. Tighter bounds for ${\bar \rho}''(0)$ and ${\bar \rho}'''(0)$ are also reported which are valid for both the ground state and excited states. Explicit illustration with the example of one-electron atomic ions is given.

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