Fock-space relativistic coupled-cluster calculation of the clock properties in two-valence Al⁺ ion.

The recent advances in the development of new and improved frequency and time standards in optical domain provides a road map to study fundamental as well as technological applications. To mention some important applications, probing physics beyond the standard model of particle physics, searching for the variation in the fundamental constants, navigation systems, and the basis for the redefinition of the second [1 - 4]. The group-13 ions are identified as the promising candidates for the accurate optical clocks as they are expected to have a low fractional frequency shift [5,6]. For example, the fractional frequency shift for ¹S₀ – ³P₀ clock transition in Al⁺ is reported to be 9.4×10^-19 [7]. Since the direct measurement of black-body radiation shift is nontrivial, the accurate data from high precision atomic structure calculations are important in developing the new optical frequency standards. Considering the two-valence nature of Al⁺, accurate calculation of the properties, however, requires the inclusion of electron correlation effects to the highest level of accuracy.

In this work, we have developed a Fock-space relativistic coupled-cluster theory based method for the properties calculation of two-valence atoms and ions. We have then employed this method to compute the excitation energies, hyperfine structure constants, oscillator strength, and the lifetime of the ³P^o₀ clock state for Al⁺ ion [8].

References

[1] S. G. Karshenboim and E Peik, Astro., Clocks and Fundamental Const, (Springer, NewYork, 2010).

[2] M. S. Grewal, et al. Global Navigation Satellite Systems, Inertial Navig, and Int. (Wiley, New York, 2013).

[3] M. S. Safronova, et al. Rev. Mod. Phys. 90, 025008 (2018).

[4] F. Riehle, et al. Metrologia 55, 188 (2018).

[5] M. S. Safronova, et al. Phys. Rev. Lett. 107, 143006 (2011).

[6] Z. Zuhrianda, et al. Phys. Rev. A 85, 022513 (2012).

[7] S. M. Brewer, et al. Phys. Rev. Lett. 123, 033201 (2019).

[8] Ravi Kumar, et al. Phys. Rev. A 103, 022801 (2021).