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Long-lived ionic quantum states known as metastable electronic states inhighly-charged ions (HCIs) are of great interest in fundamental physics.Especially, it generates transitions with very narrow natural linewidth whichis a promising candidate for use in the next generation HCI atomic clocks toreach an accuracy below $10^{-19}$. A recent experiment reported in[Nature,581(7806) 2020], used Penning trap mass spectrometry to measure theenergy of an extremely long-lived metastable electronic state, thus openingdoors to search for HCI clock transitions. Building upon prior research, thisstudy introduces an experimental proposal with the goal of measuring lifetimesof the metastable states beyond seconds. Our approach employs a sequentialpulse-and-phase measurement scheme, allowing for direct observations of thedecay processes from metastable electronic states through single-ion massspectrometry in a Penning trap. This measurement poses a significant challengeto conventional techniques like fluorescence detection. To demonstrate theeffectiveness of this method, we conducted a comprehensive simulation underreal experimental conditions, yielding promising results in a specificscenario. Two suitable candidates are proposed for testing this method, and thestate-of-the-art MCDHF theory are employed for accurate energy levels andtransition rate calculations. Some future prospects in the experimentaldeterminations of a wide range of energy and lifetimes of long-lived metastableelectronic states, probing hyperfine and magnetic quenching effects onhigh-order forbidden transitions and search for highly quality HCI clocktransitions are discussed.

Experimental Access to Observing Decay from Extremely Long-Lived Metastable Electronic States via Penning Trap Spectrometry