Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multipole transition amplitudes and radiative decay rates in neutral cadmium

P. J. Robert, S. Manzoor, M. Chiarotti, N. Poli

TL;DR

This work provides a comprehensive ab initio treatment of neutral cadmium (Cd I) transitions, deriving general analytic expressions for electric and magnetic multipole matrix elements of arbitrary order and applying them to compute forbidden as well as allowed transitions. By combining Configuration Interaction with Many-Body Perturbation Theory (CI+MBPT) within the AMBiT framework, the authors calculate E1, E2, E3, M1, and M2 transition elements, determine radiative decay rates and lifetimes, and evaluate the long-range C6 dispersion coefficient. The study reports energy levels in close agreement with experimental data (average deviation ~$0.3\%$) and provides detailed data for bosonic and fermionic cadmium isotopes, including clock-transition considerations and two-photon decay pathways. Additionally, the work yields a consistent $C_6$ value ($395$ a.u.) and establishes a robust benchmark for future cadmium-based precision spectroscopy, optical clocks, and cold-collision experiments. Overall, the paper demonstrates that CI+MBPT on standard hardware can deliver high-precision atomic-structure data for complex atoms like Cd I, with broad relevance to metrology and quantum technology.

Abstract

We present a comprehensive study of the electronic transitions in neutral cadmium (Cd I) with a focus on forbidden transitions, motivated by recent advances in laser technology and the growing relevance of cadmium in quantum gas research, precision metrology, and atom trapping. General analytic expressions are derived for transition matrix elements of all multipolar orders, formulated to be applicable for experimental use. Using configuration interaction combined with many-body perturbation theory, we calculate not only the previously reported contributions from electric dipole (E1) transitions, but also the electric quadrupole (E2), electric octupole (E3), magnetic dipole (M1), and magnetic quadrupole transitions (M2) that have not yet been investigated for cadmium. These matrix elements are then employed to determine the lifetimes of key excited states, particularly those pertinent to laser cooling and optical frequency standards, and to evaluate the long-range dispersion coefficient C6. The linewidths of the strongest transitions, along with the atomic energy levels, are compared with available experimental data to validate the accuracy of the simulations. Overall, the results are in good agreement, with the calculated energy levels exhibiting an average relative deviation of 0.3% from experiments. These values serve as benchmarks for both bosonic and fermionic isotopes, providing a foundation for future experimental and theoretical work in cadmium-based precision spectroscopy and cold-collision studies.

Multipole transition amplitudes and radiative decay rates in neutral cadmium

TL;DR

This work provides a comprehensive ab initio treatment of neutral cadmium (Cd I) transitions, deriving general analytic expressions for electric and magnetic multipole matrix elements of arbitrary order and applying them to compute forbidden as well as allowed transitions. By combining Configuration Interaction with Many-Body Perturbation Theory (CI+MBPT) within the AMBiT framework, the authors calculate E1, E2, E3, M1, and M2 transition elements, determine radiative decay rates and lifetimes, and evaluate the long-range C6 dispersion coefficient. The study reports energy levels in close agreement with experimental data (average deviation ~) and provides detailed data for bosonic and fermionic cadmium isotopes, including clock-transition considerations and two-photon decay pathways. Additionally, the work yields a consistent value ( a.u.) and establishes a robust benchmark for future cadmium-based precision spectroscopy, optical clocks, and cold-collision experiments. Overall, the paper demonstrates that CI+MBPT on standard hardware can deliver high-precision atomic-structure data for complex atoms like Cd I, with broad relevance to metrology and quantum technology.

Abstract

We present a comprehensive study of the electronic transitions in neutral cadmium (Cd I) with a focus on forbidden transitions, motivated by recent advances in laser technology and the growing relevance of cadmium in quantum gas research, precision metrology, and atom trapping. General analytic expressions are derived for transition matrix elements of all multipolar orders, formulated to be applicable for experimental use. Using configuration interaction combined with many-body perturbation theory, we calculate not only the previously reported contributions from electric dipole (E1) transitions, but also the electric quadrupole (E2), electric octupole (E3), magnetic dipole (M1), and magnetic quadrupole transitions (M2) that have not yet been investigated for cadmium. These matrix elements are then employed to determine the lifetimes of key excited states, particularly those pertinent to laser cooling and optical frequency standards, and to evaluate the long-range dispersion coefficient C6. The linewidths of the strongest transitions, along with the atomic energy levels, are compared with available experimental data to validate the accuracy of the simulations. Overall, the results are in good agreement, with the calculated energy levels exhibiting an average relative deviation of 0.3% from experiments. These values serve as benchmarks for both bosonic and fermionic isotopes, providing a foundation for future experimental and theoretical work in cadmium-based precision spectroscopy and cold-collision studies.

Paper Structure

This paper contains 14 sections, 16 equations, 1 figure, 8 tables.

Table of Contents

  1. Introduction
  2. CI+MBPT framework
  3. Theory
  4. AMBiT
  5. Reduced matrix elements
  6. Theory and selection rules
  7. Level Structure
  8. Multipole Matrix Elements
  9. Radiative decay rates
  10. Theory
  11. Results
  12. Transitions to metastable $^3$P$^o_0$ and $^3$P$^o_2$ states
  13. C6 long-range dispersion coefficient
  14. Conclusion

Figures (1)

  • Figure 1: Simplified energy-level structure of neutral cadmium (Cd I) and its principal optical transitions relevant to laser-cooling and spectroscopic applications. Wavelenghs and natural linewidths $\Gamma/2\pi$ of the transitions are also reported. The different $^3$D$_\mathrm{J}$ and $^3$P$_\mathrm{J}$ levels are not drawn to scale; they have been separated for readability.