On the weakly-bound (1,1)-states in the three-body $d d \mu$ and $d t \mu$ muonic ions

TL;DR

This paper calculates the total and binding energies of the weakly-bound (1,1)-states in muonic $d d b5$ and $d t b5$ ions with high numerical precision, providing the most accurate values for experimental comparisons.

Contribution

It provides the most precise numerical values for the (1,1)-state energies in muonic $d d b5$ and $d t b5$ ions, advancing the accuracy of theoretical predictions.

Findings

Binding energy of $d t b5$ ion's (1,1)-state: -0.66033003831(30) eV

Binding energy of $d d b5$ ion's (1,1)-state: -1.9749806166970(30) eV

Energies are sufficient for current and future experimental needs.

Abstract

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