On the weakly-bound (1,1)-states in the three-body ddμ and dtμ muonic ions

The both total and binding energies of the $(1,1)$-states in the weakly-bound three-body muonic ddμ and dtμ ions are determined to high numerical accuracy. The binding energy of the $(1,1)$-state in the muonic dtμ ion is evaluated as $\epsilon (dt\mu )=?0.66033003831(30)\text{eV}$, while for the same state in the muonic ddμ ion we have found that $\epsilon (dd\mu )=?1.9749806166970(30)\text{eV}$. These energies are the most accurate numerical values obtained for these systems and they are sufficient for all current and future experimental needs.     

Asymptotic behavior of two-electron expectation values in two-electron excited states

Singly-excited states of the two-electron atom cease being bound when $Z\to 1$ (from above), the outer orbital becoming infinitely diffuse. The asymptotic relations$\underset{Z\to 1}{\lim }?{(Z?1)}^k〈{(1sns)}^{1,3}S\left|r_{12}^k\right|{(1sns)}^{1,3}S〉=〈(n?1)s^{(0)}\left|r^k\right|(n?1)s^{(0)}〉,$ where $k=?1,1,2,3,?$, are demonstrated to hold. Here, $(n?1)s^{(0)}$ is a hydrogenic s orbital with principal quantum number $(n?1)$. New, more nuanced light is shed on the already challenged dogma that the Pauli principle keeps the electrons further apart in the triplet than in the corresponding singlet.