Several recent proposals to measure α-variation use highly-charged ions, in which the effects of a possible variation are enhanced [1]. These systems include potential new clocks that are predicted to have extraordinarily high accuracy [1-4]. In systems where the transitions are available due to level crossings, the clocks can have extremely high sensitivity to variation of the fine-structure constant α, potentially improving current limits on time-variation of α by up to two orders-of-magnitude.

The experimental spectroscopy of one such candidate, the Ir17+ ion which has two holes in the otherwise closed 4f14 5s2 valence shells, has shown that current theoretical methods have severe limitations in accurately describing the spectrum [5]. That study included (along with the experimental spectrum) the results of several calculations including different variants of configuration interaction (CI), multiconfigurational Dirac-Fock, and Fock-space coupled cluster. None of the theories tested were able to unambiguously identify the entire observed spectrum. Furthermore many existing methods of calculation – such as the combined configuration interaction and many-body perturbation theory (CI+MBPT), correlation potential methods, and coupled-cluster methods – are designed to work well in one or two-valence-electron atoms and particularly in near-neutral systems.

We have developed an ab initio method of calculating atomic spectra and properties in complicated systems, such as HCIs and particularly where electron-holes play an important role. Based on the CI+MBPT method [6], we have implemented Wick contractions numerically in AMBiT allowing the inclusion of configurations with arbitrary numbers of valence holes and electrons. As a first test case, we have performed calculations of spectra and sensitivity to α-variation for the Hg+ ion, where the clock transition 6s to 5d−1 6s2 has been compared with an Al+ clock to get the best current limit on time-variation of α [7]. We present results of the full CI+MBPT method with holes, and updated limits on time-variation of α based on the existing experiment [8].

The enhanced sensitivity to α-variation of highly-charged ions is also exploited in astrophysical measurements of metal lines in the spectra of white-dwarf stars [9]. These are used to probe the dependence of α on a strong gravitational field. While the FeV and NiV ions used in this study are less highly-charged, many of the limitations in the accuracy of calculations are common to the clock HCIs.

References

[1] J. C. Berengut, V. A. Dzuba, and V. V. Flambaum, Enhanced laboratory sensitivity to variation of the fine-structure constant using highly charged ions, Phys. Rev. Lett. 105, 120801 (2010).

[2] J. C. Berengut, V. A. Dzuba, V. V. Flambaum, and A. Ong, Hole Transitions in Multiply-Charged Ions for Precision Laser Spectroscopy and Searching for α-variation, Phys. Rev. Lett. 106, 210802 (2011).

[3] A. Derevianko, V. A. Dzuba, and V. V. Flambaum, Highly-Charged Ions as a Basis of Optical Atomic Clockwork of Exceptional Accuracy, Phys. Rev. Lett. 109, 180801 (2012).

[4] J. C. Berengut, V. A. Dzuba, V. V. Flambaum, and A. Ong, Optical transitions in highly-charged californium ions with high sensitivity to variation of the fine-structure constant, Phys. Rev. Lett. 109, 070802 (2012).

[5] A. Windberger et al., Identification of the Predicted 5s–4 f Level Crossing Optical Lines with Applications ?to Metrology and Searches for the Variation of Fundamental Constants, Phys. Rev. Lett. 114, 150801 (2015).

[6] V. A. Dzuba, V. V. Flambaum and M. G. Kozlov, Combination of the Many-body Perturbation Theory with the Configuration-Interaction Method, Phys. Rev. A 54, 3948 (1996)

[7] T. Rosenband et al., Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks; Metrology at the 17th Decimal Place, Science 319, 1808 (2008).

[8] J. C. Berengut, Particle-hole configuration interaction and many-body perturbation theory: Application to Hg+, Phys. Rev. A, 94, 012502 (2016).

[9] J. C. Berengut, V. V. Flambaum, A. Ong, J. K. Webb, J. D. Barrow, M. A. Barstow, S. P. Preval, and J. B. Holberg, Limits on the Dependence of the Fine-Structure Constant on Gravitational Potential from White-Dwarf Spectra, Phys. Rev. Lett. 111, 010801 (2013).