# Measurements of the branching ratios for $6P_{1/2}$ decays in $^{138}$Ba$^+$

## TL;DR

This paper precisely measures the branching ratios of $6P_{1/2}$ decays in $^{138}$Ba$^+$, resolving previous discrepancies and refining the lifetime and matrix element estimates through experimental and theoretical analysis.

## Contribution

The study provides the most accurate measurement of the $6P_{1/2}$ decay branching ratio in $^{138}$Ba$^+$ and clarifies discrepancies with prior results, improving theoretical estimates.

## Key findings

- Measured decay probability $p=0.268177$ with detailed systematic analysis.
- Resolved a $12\sigma$ discrepancy with previous measurements.
- Refined the $6P_{1/2}$ lifetime to 7.855 ns.

## Abstract

Measurement of the branching ratios for $6P_{1/2}$ decays to $6S_{1/2}$ and $5D_{3/2}$ in $^{138}$Ba$^+$ are reported with the decay probability from $6P_{1/2}$ to $5D_{3/2}$ measured to be $p=0.268177\pm(37)_\mathrm{stat}-(20)_\mathrm{sys}$. This result differs from a recent report by $12\sigma$. A detailed account of systematics is given and the likely source of the discrepancy is identified. The new value of the branching ratio is combined with a previous experimental results to give a new estimate of $\tau=7.855(10)\,\mathrm{ns}$ for the $6P_{1/2}$ lifetime. In addition, ratios of matrix elements calculated from theory are combined with experimental results to provide improved theoretical estimates of the $6P_{3/2}$ lifetime and the associated matrix elements.