# Theoretical laser cooling feasibility study of ZrH molecule at the fine structure level

## TL;DR

This paper studies whether the ZrH molecule can be laser cooled by analyzing its electronic and vibrational properties.

## Contribution

The study provides a detailed theoretical analysis of ZrH's electronic structure and transition properties for laser cooling feasibility.

## Key findings

- The radiative lifetimes of ZrH transitions are too long for direct laser cooling.
- Electronic and vibrational properties of ZrH were calculated using advanced quantum methods.
- Franck-Condon factors and Einstein coefficients were determined for relevant electronic transitions.

## Abstract

A theoretical electronic structure calculation of the ZrH molecule is conducted via ab initio Complete Active Space Self-Consistent Field and the Multireference Configuration Interaction with Davidson correction calculation (CASSCF/MRCI + Q). The adiabatic potential energy curves (PECs) for the 53 low-lying electronic states in the representations of 2s+1Λ(+/−) and Ω(+/−) for ZrH molecule have been investigated along with the internuclear distance Re, the harmonic frequency ωe, the dipole moment μ, the rotational constant Be and the electronic transition energy with respect to the ground state Te. are calculated. By using the canonical function approach, the vibrational energy Ev, the rotational constants Bv, the centrifugal constants Dv, and the turning points Rmin and Rmax have been calculated up to the vibrational level v = 18. Based on the investigated data, the Franck−Condon factors, the Einstein coefficient, the radiative lifetimes, and the vibrational branching ratio for the transitions X2Δ3/2 - (1)4Φ3/2, X2Δ3/2 - (1)4Φ5/2, X2Δ3/2 - (1)2Π3/2 have been calculated. The large value of the radiative lifetimes in (ms) for these transitions proves that this molecule is not a good candidate for direct laser cooling.