arXiv subjects
Publications and source records attributed to Peter Hearnshaw.
We show that the angular momentum distribution of neutral atoms, in the sense of occupation numbers, follows the Thomas-Fermi angular momentum distribution in the limit of large atomic number. In particular, we show that the angular momentum distribution of large atoms deviates from the well-known Madelung rule.
For bound states of atoms and molecules of $N$ electrons we consider the corresponding $K$-particle reduced density matrices, $\Gamma^{(K)}$, for $1 \le K \le N-1$. Previously, eigenvalue bounds were obtained in the case of $K=1$ and $K=N-1$ by A.V. Sobolev. The purpose of the current work is to obtain bounds in the case of $2 \le K \le N-2$. For such $K$ we label the eigenvalues of the positive, trace class operators $\Gamma^{(K)}$ by $\lambda_n(\Gamma^{(K)})$ for $n=1,2,\dots$, and obtain the bounds $\lambda_n(\Gamma^{(K)}) \le Cn^{-\alpha_K}$ for all $n$, where $\alpha_K = 1 + 7/(3L)$ and $L = \min\{K,N-K\}$.
Boundedness is demonstrated for the fifth derivative of the one-particle reduced density matrix for non-relativistic Coulombic wavefunctions in the vicinity of the diagonal. To prove this result, strong pointwise bounds are obtained for cluster derivatives of wavefunctions involving multiple clusters.
We obtain bounds for all derivatives of the non-relativistic Coulombic one-particle density matrix $γ(x, y)$ near the diagonal $x = y$.
It is proved that the one-particle density matrix $γ(x, y)$ for multi-particle systems is analytic away from the nuclei and from the diagonal $x = y$.