Asymptotic forms of two-electron wave functions with a monopole interaction

Abstract

The leading term in the Neumann expansion of $\frac{1}{r_{12}}$ is $\frac{1}{r_{>}}$, where $r_{>}$ signifies the greater of $r_1$ and $r_2$. Defining the monopole Hamiltonian (also called the radial-limit Hamiltonian) as the two-electron Hamiltonian with the replacement $\frac{1}{r_{12}}\to \frac{1}{r_{>}}$, the author presents asymptotic forms of the eigenfunction of this operator. The bound-bound, bound-free, and free-free cases are treated. "Asymptotic" means here that $r_1\to \infty$, $r_2\to \infty$, but $\frac{r_1}{r_2}$ is not restricted.