# High-precision calculations of the $1s^{2} 2s 2p$ $^1P_{1} \to 1s^{2} 2s^{2}$ $^1S_{0}$ spin-allowed $E1$ transition in C {\small III}

## TL;DR

This paper presents high-precision relativistic calculations of the $1s^{2} 2s 2p$ to $1s^{2} 2s^{2}$ transition in Be-like carbon, providing a reliable theoretical benchmark for experimental lifetime measurements.

## Contribution

The study develops and tests multiple correlation models within the MCDHF framework to accurately predict the transition line strength, including finite nuclear mass effects.

## Key findings

- Accurate transition energy and line strength values for Be-like carbon.
- Quantified uncertainties due to electron correlation effects.
- Benchmark data supporting high-precision lifetime measurements.

## Abstract

Large-scale relativistic calculations are performed for the transition energy and line strength of the $ 1s^{2} 2s 2p$ $^1P_{1} \,-\ 1s^{2} 2s^{2}$ $^1S_{0} $ transition in Be-like carbon. Based on the multiconfiguration Dirac-Hartree-Fock~(MCDHF) approach, different correlation models are developed to account for all major electron-electron correlation contributions. These correlation models are tested with various sets of the initial and the final state wave functions. The uncertainty of the predicted line strength due to missing correlation effects is estimated from the differences between the results obtained with those models. The finite nuclear mass effect is accurately calculated taking into account the energy, wave functions as well as operator contributions. As a result, a reliable theoretical benchmark of the $E1$ line strength is provided to support high precision lifetime measurement of the $ 1s^{2} 2s 2p$ $^1P_{1} $ state in Be-like carbon.