Lifetimes of the Metastable $6\mathrm{d}\, ^{2}\mathrm{D}_{5/2}$ and $6\mathrm{d}\, ^{2}\mathrm{D}_{3/2}$ States of Ra$^+$

TL;DR

This paper measures the lifetimes of metastable states in Ra$^+$ ions and validates a high-precision coupled-cluster computational method for heavy elements, aiding optical clock development and fundamental physics tests.

Contribution

It provides the first experimental lifetime measurements of Ra$^+$ metastable states and validates a coupled-cluster method for accurate predictions in heavy atoms.

Findings

Measured lifetimes: 303.8 ms and 642 ms for two states.

Validated coupled-cluster calculations agree with experimental data.

First tests of the method for transition properties in heavy elements.

Abstract

We report lifetime measurements of the metastable $6\mathrm{d}\, ^{2}\mathrm{D}_{5/2}$ and $6\mathrm{d}\, ^{2}\mathrm{D}_{3/2}$ states of Ra$^+$. The measured lifetimes, $\tau_{5} = $ 303.8(1.5) ms and $\tau_{3} = $ 642(9) ms, are important for optical frequency standards and for benchmarking high-precision relativistic atomic theory. Independent of the reported measurements, the D state lifetimes were calculated using the coupled-cluster single double triple method, in which the coupled-cluster equations for both core and valence triple excitations were solved iteratively. The method was designed for precise prediction of atomic properties, especially for heavy elements, where relativistic and correlation corrections become large, making their treatment more challenging. This Letter presents the first tests of the method for transition properties. Our prediction agrees with experimental values within the uncertainties. The ability to accurately predict the atomic properties of heavy elements is important for many applications, from tests of fundamental symmetries to the development of optical clocks.