1 Introduction

The discussion on whether decay rate of a nucleus is its fundamental constant or it can be manipulated by external means goes back to the beginning of the last century, when the discovery of radioactivity went hand-in-hand with the first attempts to alter its properties [1,2,3]. The motivations for finding ways to change nuclear rates are manyfold. Indeed, if such alchemy was possible, the impact on our daily life would be immense. One could then dream about production and enrichment of low-abundance elements or about changing waste composition, as well as about many other applications in astronomy, geology, biology, medicine, chemistry, etc.

However, in numerous experiments on atoms, aiming at modifying nuclear decay probabilities by varying temperature, pressure, electric and magnetic fields, chemical environments, acceleration and other parameters, only tiny modifications of below about 1% were observed, which were attributed to changes of the electron density at the nucleus.

A perturbation of the orbital electron capture (EC) rate by implanting atoms in different media was addressed by Segrè in 1947 [4]. This has independently been suggested also by Daudel [5], who in addition indicated that internal conversion (IC) de-excitation of nuclear isomeric states can as well be affected. Soon after, Segré and Wiegand found small changes in the EC probability of \(^7\)Be by comparing its half-life in a pure metal sample and in BeO or BeF\(_2\) compounds [6]. In this context, \(^7\)Be is probably the most intensively studied case, see e.g.  [7,8,9,10,11]. Apart from basic understanding of radioactivity, it is valuable for solar physics, where the EC decay of \(^7\)Be, ionised in solar plasmas [12, 13], affects the electron neutrino flux [14, 15].

A huge number of implantation experiments have been conducted to date. Although light atoms are the best-suited probes, effects were also found in heavy atoms up to \(^{235m}\)U [16]. It is impossible to mention here all studies accomplished. The interested reader is referred to reviews [17, 18] and references cited therein.

It is clear that the largest modifications of electron densities are achieved in highly charged ions (HCI). This is obviously true for fully-ionised atoms, where the electron density at the nucleus is just zero and all decays involving bound electrons are disabled. Extensive systematic studies of decays of HCIs became possible in the 1990 s with the advent of heavy-ion storage rings coupled to radioactive-ion beam facilities [19]. We note that exciting plans exist for measuring radioactive decays of HCIs in electron-ion beam traps (EBIT) [20,21,22]. First results on charge-bred \(^{124}\)In and \(^{124}\)Cs were reported [23].

Stellar nucleosynthesis is one of the major motivations for decay studies of HCIs. It proceeds in environments characterised by huge densities and temperatures [24, 25]. Beta decay (\(\beta \)-decay) alters the proton number and thus plays a decisive role in all nucleosynthesis processes [26,27,28]. The main routes, responsible for the synthesis of about 99% of chemical elements heavier than iron, are the slow (s) and rapid (r) neutron capture processes. The respective thermal energies at the corresponding sites reach several keV to about hundred keV. In such violent conditions, involved nuclei are highly ionised and their decay properties can differ from the ones established in neutral atoms [29,30,31,32].

Another important motivation is to understand the coupling of the atomic and nuclear degrees of freedom [33,34,35,36]. Here, the HCIs offer the possibility to investigate decays of systems with involved leptons being in a well-defined quantum-mechanical state. For example, the parent nuclides can be prepared as bare, hydrogen- (H-like), helium- (He-like), or lithium-like (Li-like) ions. In this way, the complicated interactions of the many bound electrons in atoms, like partial screening of the nuclear charge by the electron cloud, can be treated exactly in few-electron systems [37].

In this work, we review experimental results on the radioactive decays of HCIs obtained at heavy-ion storage rings to date and give an outlook on future research. In 2011, a compilation of then available results has been published in [38]. It is updated here.

2 Beams of highly charged radioactive ions

The prerequisite for decay studies of radioactive HCIs is their production in a nuclear reaction and in a (high) atomic charge state of interest, separation from inevitable contaminants, and injection and storage in an ultra-high vacuum environment of a storage ring [39].

Fig. 1
figure 1

Calculated with the GLOBAL code equilibrium charge state distributions of different projectiles emerging the \(^9\)Be metal foil at 400 AMeV exit energy [40]. The figure is adopted from [41]

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There are two complementary methods to produce radioactive ions in high atomic charge states. One of them is the Isotope Separation On-Line (ISOL), which delivers, except for some chemical elements, intense beams of low charged (typically \(q=1+\)) radioactive ions [42]. Thick targets are utilised, in which high-energy light projectiles lead to creation of short-lived nuclei through target spallation or fission nuclear reactions [43]. Diffused to an ion source particles are extracted at low energies. The ISOL beams have small emittances and are thus well suited for charge breeding in an Electron Beam Ion Source/Trap (EBIS/T) [44,45,46]. The resulting HCIs have low kinetic energies ideal for their subsequent incarceration in an ion trap [47,48,49]. The overall HCI production chain can be as fast as a few tens of milliseconds. This is the basic procedure utilised for decay spectroscopy in traps mentioned in Sect. 1 as well as in low-energy storage rings, which are being considered at ISOL facilities, see Sect. 7.

Another approach is the in-flight production and separation of exotic nuclei. This method is presently employed at all operating heavy-ion storage ring facilities, that are discussed in Sect. 3. All of them are coupled to in-flight fragment separators [50, 51]. Different nuclear reactions can be utilised for production of radioactive nuclei in various regions of the nuclidic chart. In our context, fragmentation of relativistic heavy primary beams and fission of uranium beams on thin targets of light elements are the most commonly used nuclear reactions [43, 52]. Projectiles at relativistic energies of about 100–600 MeV/u are typically employed.

Fig. 2
figure 2

Schematic illustration of the secondary-ion beam facility at GSI. The heavy-ion synchrotron SIS receives beams from the linear accelerator UNILAC. Secondary ions are produced either in the production target in front of the in-flight fragment separator FRS or in the direct transfer line in the stripper-foil station. Two stages of magnetic rigidity analysis and energy loss degrader positions in the FRS are indicated. The main components in the storage ring ESR, including the extraction towards HITRAP, are labeled. Shown also is the location of the recently installed low-energy storage ring CRYRING@ESR with its local ion source and injection line. The figure is updated from [64]

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HCIs are produced through stripping of bound electrons by sending energetic fragments through matter [40, 52, 53]. Here, the production target is simultaneously used for the electron stripping. Calculated equilibrium charge state fractions, the ones independent from the initial charge state of the projectile entering the matter, as a function of proton number (Z) are plotted in Fig. 1 for fragments leaving \(^9\)Be target at 400 AMeV energy. By choosing a proper stripper material as well as its thickness, one may enhance population of a specific charge state [54,55,56,57].

Distinct from the ISOL beams, the in-flight ones have broad momentum distributions of a few percent [52, 58, 59]. The fragments are transported by a fragment separator, typically an achromatic device [60], from the target to the experiment, which in our case is the injection into a storage ring. The separator has planes with large dispersion, which are used for magnetic rigidity \(B\rho =mv\gamma /q\) analysis. Here B is the magnetic flux density, \(\rho \) bending radius, and m, v, q, and \(\gamma \) are the mass, velocity, charge, and relativistic Lorentz factor of the ion, respectively. The high kinetic energies of the fragments allow for adding special solid degraders [60, 61]. Since the energy loss (\(\Delta E\)) is charge dependent, the \(B\rho -\Delta E - B\rho \) analysis enables high purification power, such that mono-isotopic beams can be prepared. It is also possible to use different charge states in the first and second \(B\rho \) stages and the degrader for changing the charge state distribution in between [62, 63].

3 Heavy-ion storage ring facilities

There are three heavy-ion storage ring facilities in operation today [51, 64].

The radioactive ion beam facility at GSI in Darmstadt is a combination of the high-energy heavy-ion synchrotron SIS [65], the in-flight fragment separator FRS [61], and the cooler-storage ring ESR [66]. Except for poisonous source materials like Be, Cd, Tl etc, intense beams of any (semi-)stable nuclide from protons up to uranium can be accelerated by the SIS to the maximum magnetic rigidity \(B\rho =18\) Tm. The ESR can vary the energy of the stored beam within 3 Tm \(\le \) B\(\rho \) \(\le \)10 Tm. Decelerated beams can either be ejected towards a dedicated low-energy storage ring CRYRING@ESR, which has recently been commissioned [67, 68], or towards the trapping facility, HITRAP [69]. The GSI facility is schematically illustrated in Fig. 2.

The flight time of secondary beams from the target through the FRS until the exit of the separator is a few hundred nanoseconds. This sets the minimal lifetimes of nuclei that can be addressed in the ESR, where the time required for the measurement itself needs to be considered in addition. By employing only the \(B\rho \) analysis, cocktail beams can efficiently be transmitted to the ESR, which is frequently used for broadband mass measurements [59]. The \(B\rho - \Delta E - B\rho \) separation is used to prepare mono-isotopic beams either for lifetime spectroscopy discussed here or for the in-ring reaction studies  [70,71,72,73,74,75]. In addition, radioactive HCIs can be produced in the direct SIS-ESR beam-line bypassing the FRS [76,77,78], which is often overbooked with non-ring experiments.

The concept of the Heavy Ion Research Facility in Lanzhou (HIRFL) [79, 80] is very similar to the one of GSI. The core of the high energy part of HIRFL is the main cooler-storage ring CSRm, which functions as a heavy-ion synchrotron with a maximum \(B\rho =11\) Tm. The fragment separator, the second radioactive ion beam line in Lanzhou, RIBLL2, operates as a pure \(B\rho \) analyser to transmit cocktail beams of radionuclides to the experimental cooler-storage ring CSRe [81]. The CSRe has a maximum magnetic rigidity \(B\rho =8.4\) Tm. The present accelerator chain allows efficient acceleration of beams up to about xenon, which limits the range of secondary systems to be studied. The situation will dramatically improve with the installation of a new linear accelerator as a primary injector of the CSRm [82].

Of utmost importance for lifetime measurements in storage rings is the ability to cool hot secondary beams [83]. Three cooling methods are utilised in storage rings. The electron [84] and stochastic [85] methods are applicable to any types of stored ions and are routinely used [86,87,88,89]. A significant progress has been achieved in laser cooling, though it can only be utilised for a limited number of ions [90,91,92]. Moreover, beam cooling facilitates broad and rapidly developing research programs in atomic and nuclear physics. These cannot be covered here and the reader is referred to reviews [93,94,95,96,97,98,99,100,101,102,103] and references cited therein.

The driver accelerators at GSI and HIRFL are synchrotrons, which are pulsed machines. Therefore, the beam transmission chain to the storage ring is a synchronised bunch-to-bunch procedure. The facility at RIKEN Nishina Center for Accelerator-Based Science is built on a very different principle. The storage ring, Rare-RI Ring (R3) [104], is basically a weak focusing synchrotron. It is composed only of dipole magnets and is run solely in isochronous optics at a fixed rigidity of 5.5 Tm, see Sect. 4.1. The driver accelerator is a superconducting cyclotron, which as of today delivers the most intense primary beams worldwide and as a consequence gives access to the most exotic nuclides. It is therefore attractive to store them in a ring. However, due to the (quasi-)DC characteristics of the cyclotron beams, the injection and investigation of only individual particles one by one is possible [105,106,107]. Apart from the highest intensities, the strongest advantage of the setup is that each particle is identified within the large-acceptance BigRIPS fragment separator [108] and only the ones of interest generate a valid trigger for the injection into the R3 [109]. No cooling is presently available. Although lifetime measurements of HCIs were not attempted yet, non-destructive diagnostic is being developed [110, 111], see Sect. 4.1, which will enable such research in the future.

Fig. 3
figure 3

Schottky diagnostics at the ESR. Left: Two pairs of copper plates (capacitive arrangement) installed directly inside the ESR vacuum pipe [112]. Middle: First generation of resonant Schottky detector with the resonator cavity on air [113]. The cavity is screwed together around the ceramic gap. In the photo, the halves of the cavity are driven apart such that the ceramic gap (white) can be seen. Right: The recently installed fully-UHV resonant Schottky detector [114]. Photos: P. Petri, M.S. Sanjari, GSI, Darmstadt

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4 Time-resolved storage ring mass spectrometry

The measurements of nuclear decays rely on the storage ring mass spectrometry (SRMS). Its basic principle lies in the fact that the mass-over-charge ratio (m/q) of a particle changes in the decay, which can be detected through time-resolved and intensity-resoved SRMS. In the following, we briefly discuss the basics of the SRMS.

Fig. 4
figure 4

Time-resolved Schottky frequency spectra of stored isobars with \(A = 175\) measured in the ESR. Data are displayed at the 30th harmonic of the mean revolution frequency of about 2 MHz, that is why the offset of 59,950 kHz is subtracted. Three H-like \(^{175}\)W\(^{73+}\) ions (at \(f\approx 8.4\) kHz) are produced via radioactive decays. One of them is from the EC decay of a single He-like \(^{175}\)Re\(^{73+}\) ion (at \(f\approx 8.1\) kHz) about 3 min after the measurement start, which is the time of the ion injection. The other two ions are products of the three-body \(\beta ^+_c\)-decay of H-like \(^{175}\)Re\(^{74+}\) ions (at \(f\approx 154.0\) kHz) at about 2 and 10 min. The charge state remains the same in the EC decay and only a small \(\Delta f \approx 300\) Hz is observed, which directly corresponds to the decay Q-value. The atomic charge state is altered by one unit in the \(\beta ^+_c\) decay, which yields a much larger \(\Delta f \approx 140\) kHz. Note the break in the frequency scale. The figure is adopted from [41]

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4.1 Conventional storage ring mass spectrometry

In first-order approximation, the relative revolution frequency deviation \(\Delta f/f\) of the stored ions can be related to the relative difference \(\Delta (m/q)/(m/q)\) and the velocity spread \(\Delta v/v\) via the following expression [115,116,117,118]:

$$\begin{aligned} \frac{\Delta {f}}{f} = -\frac{1}{\gamma _t^2}\frac{\Delta (m/q)}{(m/q)}+\Bigl (1-\frac{\gamma ^2}{\gamma _t^2}\Bigr )\frac{\Delta {v}}{v}, \end{aligned}$$
(1)

where \(\gamma \) is the relativistic Lorentz factor and \(\gamma _t\) the machine parameter termed transition energy. The latter quantity is connected to the momentum compaction factor \(\alpha _p\) as \(\alpha _p=1/\gamma _t^2\), which describes the relative change of the orbit length caused by a relative change of magnetic rigidity. \(\alpha _p\) is supposed to be constant for a given ion-optical setting of the ring [119, 120].

According to Eq. (1), the revolution frequency is the measure of the particle mass-over-charge ratio if the second term on the right-hand side is made negligible. However, the velocity spread of secondary particles produced in a nuclear reaction is huge and is typically larger than the acceptance of the transport beam lines and the injection into the storage ring.

In the conventional Schottky mass spectrometry (SMS)  [121], the velocity spread of the stored ions is reduced by stochastic and/or electron cooling [122], reaching–for particle intensities of below about 1000 ions–values as small as \(\approx 10^{-7}\) [123]. Thus the second term in Eq. (1) can be neglected.

Nuclides with lifetimes exceeding the cooling process, which takes at least several seconds, can be addressed by the conventional SMS.

The revolution frequencies are then measured by non-destructive Schottky diagnostics. The development of Schottky detectors in the ESR is illustrated in Fig. 3. A relativistic particle revolves in a storage ring with a high frequency of a few hundred kHz to a few MHz. Being charged, it periodically induces an electric current on the electrodes of a Schottky detector. The output of the detector, which is dominated by thermal noise, is Fourier analysed, which makes repeating signals visible. The obtained power spectrum contains frequency peaks ordered according to m/q values of the stored ions, see Eq. (1). This is routinely used for precision mass measurements [124,125,126,127,128,129,130], where the spectrum is calibrated by the unavoidably present nuclei with well-known masses. Furthermore, the area of a frequency peak is directly proportional to the number of stored particles. By tracing the evolution of peak areas, the corresponding half-lives can be determined. This is the basis of the time-resolved SMS [131].

The first generation of the ESR Schottky detector is illustrated in the left panel of Fig. 3. A sum signal from a pair of oppositely placed capacitive copper plates is typically used [112]. A single stored ion with charge \(q>30\) can be detected within about 30 s. The simultaneously measured bandwidth covers the entire ESR acceptance [126]. An example of the measured decays in the ESR is shown in Fig. 4.

The need for a faster detector led to a development of a pill-box cavity resonator [113], see the middle panel in Fig. 3. The cavity was placed on air with a ceramic gap separating it from the ultra-high vacuum (UHV) of the ring. The detection sensitivity was enhanced such that the frequency of a single ion could now be measured within a few ten milliseconds [132]. The inevitably smaller bandwidth of the detector allows for covering only 1/3 of the ESR aperture. To scan through the ring acceptance, the resonance frequency of the cavity can be varied by moving copper blocks in/out of its working volume. An identical detector is installed in the CSRe [133, 134] and, adjusted to its specific parameters, a similar one has been built for the R3 [110, 111].

Fig. 5
figure 5

Time-resolved Schottky frequency spectra of two H-like \(^{142}\)Pm\(^{60+}\) ions stored and electron-cooled in the ESR. Displayed is the 124th harmonic of the mean revolution frequency. Data were acquired with the resonant cavity-based Schottky detector [113], see Fig. 3 (Middle). The time- and frequency-resolutions are 32 ms and 31.25 Hz, respectively. Both parent H-like \(^{142}\)Pm\(^{60+}\) ions decay by EC to fully-ionised \(^{142}\)Nd\(^{60+}\) daughter nuclei, accompanied by the emission of an electron neutrino \(\nu _e\). Yellow arrows indicate the true decay times, as unambiguously identified by a decrease of the intensity of the trace corresponding to the parent ions and the simultaneous onset of the trace of the recoiling daughter ion. The latter starts at a revolution frequency shifted by \(\delta f\) with respect to the frequency after completion of electron cooling, which reflects the projection of the recoil velocity onto the beam direction axis immediately after the decay. The figure is adopted from [132]

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Figure 5 shows spectra taken with the new detector illustrating two EC decays of \(^{142}\)Pm\(^{60+}\) ions [132]. Both decays have specific features associated with the kinematics of the decay. The electron cooling is always on and forces the ions to the revolution frequencies defined by their m/q ratios. As discussed in Sect. 5.1, in the two-body EC decay, the energy is shared between the emitted neutrino and the recoiling daughter ion. The recoil causes a velocity mismatch, which is quickly removed by the electron cooling. This is seen by characteristic tails in Fig. 5, where the daughter nuclei require a few hundred milliseconds before they are cooled to the correct velocity, that is revolution frequency. In the first decay in Fig. 5, the electron neutrino is emitted in the backward direction. The resulting higher velocity of the daughter ion is then reduced by the cooling process, which is manifested by the right-hand side cooling tail. Vice versa, in the second decay the neutrino is emitted in the forward direction and the slower daughter ion needs to be accelerated. Since the storage ring has non-integer tune values [101], the transverse components of the recoil are averaged away after a few revolutions. This means that the lengths of the cooling tails reflect the projections of the recoiling momenta on the beam direction axis, which, combined with the fact that the emitted neutrino is ‘monochromatic’, gives information on the neutrino emission angle.

In the conventional isochronous mass spectrometry (IMS)  [118, 135], the ring is tuned in a special ion-optical mode. The very principle of this mode is to send a faster ion of a given ion species onto a longer orbit while a slower ion of the same ion species onto a shorter orbit, such that the velocity spread is compensated by the lengths of the closed orbits. In this mode, the Lorentz factor of the ions \(\gamma =\gamma _t\), see Eq. (1). The revolution times are measured by a time-of-flight detector. A thin foil (\(\approx 10\) \(\mu \)g/cm\(^2\)) is inserted into the ring aperture and is punched through by stored ions at each revolution [136,137,138,139,140]. Secondary electrons released from the foil provide precise timing stamps, which are then used to determine the corresponding frequencies [141, 142]. Ions can accomplish several thousand revolutions before they are lost from the ring either due to the energy loss or charge-exchange reactions in the foil. The method has been primarily developed for precision mass measurements [143,144,145,146,147,148,149,150,151,152,153,154,155,156,157]. The fragments do not require cooling. The overall measurement takes a few hundred microseconds, which is ideally suited for addressing short-lived nuclei. However, with respect to lifetime measurements, there is an upper limit of a few \(\mu \)s.

4.2 \(B\rho \)-defined isochronous mass spectrometry

Due to the large velocity spread of stored ions, the condition \(\gamma =\gamma _t\) is fulfilled only in a small range of m/q values, termed isochronous window. Outside of it, the mass resolving power and–in turn–the sensitivity deteriorate rapidly [50, 158]. However, if the velocity or magnetic rigidity of each particle is known, high resolving power can be extended beyond this window [159]. This has been verified at the ESR, where, in the so-called \(B\rho \)-tagging regime, the rigidities of all particles were limited in the dispersive plane of the FRS by mechanical slits to about \(10^{-4}\) [160]. The transmission was dramatically reduced, but the mass resolving power has increased and remained constant over the entire ESR acceptance, where at the edges of the acceptance the improvement by up to a factor of 8 was achieved. Several measurements have been conducted [161, 162].

A different approach has been realised at the CSRe. Here, two ToF detectors were installed about 18 m apart in a straight section [163]. Each stored particle causes two trains of timing signals in the detectors, which are then used to determine the frequency and the velocity of each ion [164, 165]. By assuming that the particles with the same \(B\rho \) have the same mean C, a universal calibration curve can be constructed. As a result, a high mass resolving power of about 400’000 has been achieved. Furthermore, it is about constant over the entire CSRe acceptance. The widths of the frequency peaks correspond to about 5 keV/q (FWHM) [166], which means that the mass of a single ion can be determined with this precision. It is worth emphasising that the overall measurement requires merely 200 \(\mu \)s. A striking confirmation of the power of the method has been delivered through measurements of the masses of \(^{70}\)Kr and \(^{75}\)Sr, which were produced with rates of below 2 particles per week [167,168,169]. This technique was termed \(B\rho \)-defined IMS or \(B\rho \)-IMS.

At the R3, the measurement of particle velocities is realised by using standard detectors within the Big-RIPS fragment separator. The results of the first mass measurements have been reported in 2022 [107].

4.3 Combined isochronous + Schottky mass spectrometry

As has been discussed above, non-destructive Schottky detection is ideally suited to study exotic nuclear decays of HCIs and, indeed, it has successfully been applied to investigate long-lived (\(T_{1/2} \gg 1\) s) systems, see Sect. 5. It has, however, been realised, that in order to access shorter-lived species new methods would be needed.

For instance, one could attempt to accelerate the cooling process. For this purpose stochastic and electron cooling were combined. In this procedure, the fast stochastic pre-cooling reduced the momentum spread to about \(10^{-4}\) within about a second. The subsequent electron cooling was then much quicker than usual and the half-life of isomeric state in \(^{207}\)Tl\(^{81+}\) with \(T_{1/2}=1.33(11)\) s [170] could be measured [171, 172]. No further significant decrease in the measurement time was achieved, and apart from employing it in the single-particle decay spectroscopy, see Sect. 5.1.3, this approach was no longer followed.

With the development of the new-generation of Schottky detectors[113], that enabled frequency measurement of a single stored ion within a very few ten milliseconds [132, 173], it has been proposed to abandon cooling and pursue lifetime measurements in the isochronous mode [174]. Such combined Schottky+isochronous mass spectrometry (S+IMS) would comprise the advantages of both techniques. Following a proof-of-principle demonstration at the ESR [175], the S+IMS has been applied in the CSRe to measure half-lives of \(^{49}\)Cr\(^{24+}\) and \(^{53}\)Fe\(^{26+}\) [176], see Table 1.

To further increase the sensitivity of the Schottky detector, the ceramic gap has been removed and the cavity became a part of the beam pipe, fully integrated into the ring UHV [114], see the right panel of Fig. 3. The technique has been verified in the ESR and successfully employed to measure the two-photon de-excitation of the first exited \(0^+\) state in \(^{72}\)Ge [177], see Sect. 5.2. Through the development of the S+IMS, simultaneous broad-band mass and lifetime measurements can now be aimed at [178].

5 Experimental results

Most of the lifetime results to date were obtained with the conventional time-resolved Schottky mass spectrometry, see Sect. 4.1. It is important to emphasise that such measurements provide redundant information, since typically both, the decay of the parent ions and the growth of the number of daughter ions, are simultaneously observed. In the case of a large relative change of the magnetic rigidity in the decay, the daughter ions might leave the storage ring acceptance. In such cases, the daughter ions can be measured with in-ring particle detectors [179,180,181].

Employing internal gas-jet targets [182, 183] facilitates atomic charge-exchange reactions, which can be used in combination with particle detectors to count the number of the produced daughter or remaining parent ions. This is essential for cases when the difference between the mass-over-charge ratios of parent and daughter ions is too small to be resolved by revolution frequency, see Sect. 5.1.2.

A careful consideration of ion losses due to atomic charge-changing reactions is necessary. The rings are operated at UHV conditions (\(10^{-10}\)–\(10^{-12}\) mbar). Dependent on the ion species, if not limited by the radioactive decay time, the storage times can reach several hours. Collisions with the residual gas atoms and molecules as well as the recombination with the cooler electrons are the main loss mechanisms [184, 185]. Furthermore, resonances in the machine can lead to unwanted losses.

Up to date results on radioactive decays of HCIs measured in heavy-ion storage rings are listed in Table 1.

Table 1 Half-lives of HCIs in ground and isomeric (m) states measured in storage rings. Listed are the investigated ion species, the measured or proposed decay mode, the measured half-life in the rest frame of ions (\(T_{1/2}(\textrm{exp})\)), half-lives for neutral atoms \(T_{1/2}(\mathrm lit.)\) are taken from NNDC  [170], and NUBASE [172] evaluations the employed measurement technique, storage ring facility, and the reference to the original work, respectively. An asterisk in last column indicates a new information as compared to the table published in [38]
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5.1 Beta decay

Measurements of weak decays in HCIs were among the main scientific motivations for the construction of the ESR [19].

The nuclear \(\beta \)-decay can be expressed as: \(n + \nu _e \leftrightarrow p + e^-\), where p, n, \(e^-\) and \(\nu _e\) indicate proton, neutron, electron and electron-neutrino, respectively. By taking into account particle-antiparticle symmetry, the following weak decays can be distinguished:

$$\begin{aligned}{} & {} n\rightarrow p+e^- + \bar{\nu }_e~~-\text{ continuum }~\beta ^-\text{-decay }~(\beta ^-_c)\\{} & {} n+\nu _e \rightarrow p+e^-_b~~-\text{ bound-state }~\beta ^-\text{-decay }~(\beta _b)\\{} & {} p\rightarrow n + e^+ + \nu _e~~-\text{ continuum }~\beta ^+\text{-decay }~(\beta ^+_c)\\{} & {} p+e^-_b \rightarrow n + \nu _e~~-\text{ orbital } \text{ electron } \text{ capture } \text{(EC) }\\{} & {} p+e^- \rightarrow n + \nu _e~~-\text{ free } \text{ electron } \text{ capture } \text{(free } \text{ EC) } \end{aligned}$$

Capture of free electrons is common in stellar plasmas, as e.g. \(^7\)Be nuclei in the Sun dominantly decay by the free electron capture from solar plasma [12, 13].

5.1.1 Continuum beta decay

In the continuum \(\beta ^+_c\)/\(\beta ^-_c\) decays, the energy and momentum are shared between the three particles in the final state, namely the emitted positron/electron, neutrino/antineutrino and the recoiling daughter nucleus. Fully-ionised \(^{19}\)Ne\(^{10+}\) ions were used in the first experiments at the FRS-ESR facility, during which the \(\beta ^+_c\) rate could be measured [39]. Short after, dedicated measurements of \(\beta ^+_c\) rates of fully-ionised \(^{52,53}\)Fe\(^{26+}\) nuclei were conducted [186]. In these first experiments, the feasibility of decay measurements in the ESR was confirmed, thereby enabling a first comparison of the calculated and measured \(\beta ^+\) decay rates for fully-ionised nuclei. Continuum \(\beta ^+_c\) and \(\beta ^-_c\) decays were intensively studied in the ESR by employing the time-resolved SMS. The first application of the combined S+IMS technique was done at the CSRe, where \(\beta ^+_c\) rates of \(^{49}\)Cr\(^{24+}\) and \(^{53}\)Fe\(^{26+}\) were determined [176].

5.1.2 Bound state beta decay

Bound-state beta decay [187, 188] is a nuclear weak decay in which one of the neutrons n in the nucleus is transmuted into a proton p accompanied by the emission of an electron and an electron antineutrino. However, different from an ordinary continuum \(\beta ^-\) decay mode, the electron is not emitted to the continuum but occupies one of the bound orbitals. Thus, there are two particles in the final state which share the decay Q-value. Two-body \(\beta \)-decays, EC and \(\beta _b\)-decay, are the time-reverse of each other. Similarly to the EC-decay in which the electron from any shell can be captured, the created electron in the bound-state \(\beta ^-\)-decay can occupy different shells in the daughter atom. The scaling of the probabilities to capture (generate) s-electron from (in) electron shells with different principal quantum number n is roughly \(1/n^3\) [189]. Since the inner orbitals in neutral atoms are Pauli-blocked, \(\beta _b\)-decay is restricted to very weakly bound electron states of the daughter atom and is, therefore, only a marginal decay branch of neutral atoms.

Although the existence of the \(\beta _b\)-decay was predicted in the 1940 s [187], it took several decades until it has experimentally been verified. All results on the \(\beta _b\)-decay come from the ESR.

Neutral \(^{163}\)Dy atoms are stable and decay with half-life of about 50 days if fully ionised. This was one of the very first measurements conducted in the ESR [190]. The obtained result impacted our understanding of the s-process flow, where \(^{163}\)Dy becomes a branching point nucleus, contributing to the creation of \(^{164}\)Er. In turn, the observed abundance of \(^{164}\)Er can be used to infer the ionisation degree of \(^{163}\)Dy and the corresponding environment temperature [41].

In a subsequent study, the \(\beta _b\)-decay of fully-ionised \(^{187}\)Re has been measured [191]. Neutral \(^{187}\)Re atoms have a very long half-life of 42 Gy [170, 172]. However, the increased decay Q-value, if all bound electrons are removed in \(^{187}\)Re\(^{75+}\) ions, enables the decay to the first exited state in \(^{187}\)Os nucleus at \(E^*= 9.8\) keV thereby reducing the half-life to merely 33 years. This result made a dramatic consequence for a possible application of the \(^{187}\)Re/\(^{187}\)Os pair as a nuclear cosmo-chronometer, turning it instead into a cosmo-thermometer [192].

The Q-values of the \(\beta _b\)-decays of \(^{163}\)Dy and \(^{187}\)Re are so small that the daughter ions cannot be resolved from the corresponding parent ions. To detect the bred H-like daughter ions an internal gas target has been utilised to strip the bound electron. The resulting bare nuclei have significantly different orbits and can be intercepted by particle detectors installed after a bending magnet downstream the target [101].

Fig. 6
figure 6

Illustration of the the bound-state beta-decay of fully-ionised \(^{206}\)Tl\(^{81+}\) measured in the ESR [193, 194]. The colour code represents logarithm of Schottky power in arbitrary units. Similar to Fig. 4, the data were measured at 30th harmonic of the revolution frequency. The isomeric state of thallium, labelled with m, decays by internal transitions to the ground state. The ground state decays via \(\beta _b\) decay to H-like \(^{206}\)Pb\(^{81+}\) ions. The decay Q-value is large enough to enable all ion species to be directly resolved. The parallel changes in the revolution frequencies are due to random fluctuations of the magnetic fields of the ESR. Figure taken from [41]

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The first direct observation of the bound-state \(\beta \)-decay was performed on the examples of fully-ionised \(^{206,207}\)Tl\(^{81+}\) nuclei, see Fig. 6. These systems have a sufficiently large decay Q-value (\(>1\) MeV), which allows for direct resolving of the parent and daughter ions by their revolution frequencies via SMS [193]. Furthermore, such large Q-values imply that the \(\beta _c^-\)-decay is also allowed. This enabled the first measurements of the \(\beta ^-_b/\beta ^-_c\) ratios [193, 194] in analogy to well studied EC/\(\beta _c^+\) branching ratios [189]. Therefrom obtained ratios are in fair agreement with theoretical estimations [30].

In spite of the successful investigations of \(\beta _b\)-decays, the most impactful case proposed before the construction of the ESR [195], namely the decay of \(^{205}\)Tl\(^{81+}\) nuclei, remained unmeasured. The knowledge of the decay rate is essential for the conclusion on the s-process clockworks in the Hg-Bi region, where especially the destruction/survival of long-lived \(^{205}\)Pb is affected [196]. Furthermore, there have been proposals to utilise \(^{205}\)Tl as a detector for solar pp-neutrinos [197,198,199], where the transition strength defines the neutrino capture probability. Although \(^{205}\)Tl is stable and abundant on Earth, it is poisonous and for safety reasons its use in a source was excluded. The case was revived every time an upgrade of the GSI facility was undertaken. However, the production of a sufficient amount of secondary \(^{205}\)Tl\(^{81+}\) nuclei was not possible for decades. An expected half-life can lie in the range from about 50 days to about 400 days [31, 32, 200, 201]. Therefore, \(10^6-10^7\) ions need to be produced and stored for several hours. In 2020 the experiment has finally been accomplished. Enriched \(^{206}\)Pb beam was used to produce \(^{205}\)Tl\(^{81+}\) ions. A challenging complication arises from a much higher production of the \(^{205}\)Pb\(^{81+}\) ions, which are the daughters of the \(\beta _b\)-decay of interest. Efficient production, purification, accumulation as well as the storage of up to 10 h could be achieved. The analysis is in its final stage and will be published soon.

5.1.3 Orbital electron capture

On the neutron-deficient side of the nuclidic chart, the two-body beta decay mode is the orbital electron capture [189]. It is obvious that EC is disabled in fully-ionised nuclei. The number of measured EC decays in highly-charged ions is limited and all results stem from the ESR, see Table 1.

The EC decays of H- and He-like ions were measured in \(^{122}_{~53}\)I, \(^{140}_{~59}\)Pr, and \(^{142}_{~61}\)Pm ions [202,203,204]. Also the corresponding \(\beta _c^+\) in the fully-ionised nuclei were obtained. A striking result was observed that H-like \(^{140}\)Pr\(^{58+}\) and \(^{142}\)Pm\(^{60+}\) ions decay through an allowed \(1^+\rightarrow 0^+\) Gamow-Teller transition by a factor \(\sim \)1.5 faster than the corresponding He-like \(^{140}\)Pr\(^{57+}\) and \(^{142}\)Pm\(^{59+}\) ions, and even than neutral atoms. Although at first glance counterintuitive, this result could be explained by the conservation of the total angular momentum and by the fact that the ions in the ESR are stored in the ground hyperfine state [205,206,207,208]. Similar results were seen in muon capture [209] and were discussed for EC [34]. One of the consequences is that the neutrino emission direction is strictly opposite of the direction of the spin of the parent nucleus, see the discussion in relation to Fig. 5.

To verify the theoretical explanation, the Gamow-Teller \(1^+\rightarrow 2^+\) decay of H-like \(^{122}_{~53}\)I\(^{52+}\) ions has been studied [204]. According to the proposed selection rules, this decay shall be disabled. Indeed a slower decay has been measured. A definite conclusion though was not possible, since the decay strength is split over numerous states in the daughter nucleus [170].

Substantial research has been devoted to the verification of a surprising observation of modulated EC decay of in H-like \(^{122}\)I\(^{52+}\), \(^{140}\)Pr\(^{58+}\) and \(^{142}\)Pm\(^{60+}\) ions [210, 211]. These measurements were conducted with the so-called “single-ion decay spectroscopy”, which aimed at a continuous observation of each stored ion. Precise decay times were seen as well-defined jumps of intensities corresponding to individual ions from the parent frequency to daughter frequency. Several thousands of such EC decay times were collected in several experiments. Although the periodic modulations with several second periods were not reproduced, these experiments were the motivation for the development of the highest-sensitivity Schottky detectors, see Sect. 4.1. In the latest experiment, a pure exponential decay of \(^{142}\)Pm\(^{60+}\) ions was obtained with a high statistical confidence [173]. A detailed discussion of this research can be found in [212].

5.2 Nuclear isomers

Isomers are long-lived nuclear states [213,214,215]. Such states have quantum numbers, which hinder transition to the corresponding low-lying states. Isomers can de-excite either through electromagnetic channels, that is via internal conversion (IC), emission of a \(\gamma \)-quantum (IT), or, if the excitation energy exceeds 1.022 MeV, via the creation of an electron-positron pair, through weak channels, that is via \(\beta \)-decay, see Eq. (), or through strong interaction, that is by emission of nucleons, \(\alpha \)-particles or fission. Conventionally, isomeric states are studied by utilising various spectroscopic methods. Of particular interest here is that highly charged ions offer a way to isolate specific decay channels.

We note, that prompt decays of excited states in HCIs can be measured at in-flight spectrometers. In such experiments, a new decay channel, namely the Bound Internal Conversion (BIC) was discovered [216,217,218]. Similar to the \(\beta ^-_b\)-decay, in this IC-decay mode the conversion electron is not emitted to the continuum but transferred to a different atomic level [219].

In fully ionised nuclei, all bound electrons are removed and the de-excitation through IC is impossible. In this way the partial (\(\beta ^+\)+\(\gamma \))-decay rate can be measured, which offers an independent approach to obtain conversion coefficients. In the first experiments, long-lived isomers in \(^{52}\)Mn and \(^{53}\)Fe were investigated [186] Afterwards, conversion coefficients were obtained for \(^{144m}\)Tb, \(^{149m}\)Dy and \(^{151m}\)Er isomeric states through measuring the pure IT channel in the corresponding fully-ionised nuclei [220]. Such measurements allow for addressing weak gamma decay branches.

A spectacular application of time-resolved SMS is to search for long-lived rarely produced isomers. Indeed, new isomeric states are frequently found in campaigns on broad-band mass measurements. However, assumed here are isomeric half-lives in the order of minutes, hours or longer and production rates of one particle per hour, day, week or even smaller. Here, the ultimate sensitivity to single stored ions allows for the detection and identification of every produced rare ion. Searches for such exotic isomeric states with conventional \(\gamma \)-spectroscopy are very complicated. In a dedicated experiment, several high-K isomers in neutron-rich nuclides in the Hf-Os region were discovered [221,222,223] and their properties, like excitation energy and lifetime, were determined. The latter can then be used to specifically design a spectroscopic experiment to investigate such isomers. As an example, the isomeric state in \(^{187}\)Ta has been first discovered in the ESR and then thoroughly studied at the KISS facility in RIKEN [224,225,226].

In the last few years, the advancement in the speed and sensitivity of the newest Schottky detectors together with the development of the combined S+IMS technique provided access to nuclear lifetimes in the millisecond range. For benchmarking the power of the technique, \(^{72}\)Ge has been selected. The ground and first excited states in this nucleus are both \(0^+\) [170]. In a fully-ionised nucleus, the IC and IT decay channels are disabled and the isomer is forced to decay via a second-order 2\(\gamma \)-decay. The successful measurement has been conducted in 2021 and is being analysed now [177]. The results are not yet disclosed by the collaboration but are expected soon to be reported.

Last but not least, although the measurement duration in the IMS is very short, decays of \(\mu \)s isomers are sometimes possible to detect. Here, the large losses due to interactions of the ions with the ToF-detector foil need to be taken into account [227]. For instance, the decays of isomers in \(^{133}\)Sb [228] and \(^{94}\)Ru [229] were measured in the ESR and CSRe, respectively. The former nucleus is just one proton above the doubly-magic \(^{132}\)Sn and the ESR result was useful for constraining shell-model predictions in this region. In the case of \(^{94}\)Ru, the change of the revolution frequency due to the decay could be observed directly in the measured revolution time stamps, see Sect. 4.1.

So far obtained half-lives for isomeric states are listed in Table 1, where the assumed decay channels are indicated.

6 Future experiments

The rich harvest of measured half-lives presented in Table 1 shows the past successes. However, the perspectives for future measurements are as well exciting. It is important to emphasise that half-life measurements are planned at all three facilities in operation.

New experimental capabilities are coupled to advances in detector development. The major goal in the context of lifetime measurements is the ability to non-destructively determine the velocity of each stored particle in the isochronous mode. Such determination will enable all advantages of the \(B\rho \)-defined IMS, see Sect. 4.2. The corresponding approach is to construct transverse Schottky detectors to measure the position of each particle in a dispersive location of the ring [230,231,232]. This will provide the particle magnetic rigidity, from which the velocity can straightforwardly be deduced. The first prototype of such detector is being installed in the R3.

Fig. 7
figure 7

Cartoon representation of the EC decay of H-like \(^{111}\)Sn\(^{49+}\) ions decaying through allowed Gamow-Teller transition to the ground state of fully-ionised \(^{111}\)In\(^{49+}\) nuclei. In the initial state (i), the nuclear and single electron spins can couple to the total angular momenta \(F_i=3\) and \(F_i=4\). Both nuclei have positive magnetic moments [170]. After a short time, only the \(F_i=3\) hyperfine ground state is populated. No repopulation of upper hyperfine states has been observed in the ESR [244]. In the final state (f), the states are \(F_f=4\) and \(F_f=5\). Therefore, no \(F_i=F_f\) transition is available and hence the EC decay is hindered. Taken from [247]. Courtesy Ragandeep Singh Sidhu

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An important goal of the future measurements is a broad-band determination of yet unknown \(\beta \)-decay half-lives. Of interest here are neutron-rich nuclei, especially those relevant to the r-process. There are indications that forbidden \(\beta \)-decays may become dominant, thus altering theoretical predictions [233, 234]. An additional channel, \(\beta \)-delayed single-neutron (\(P_{1n}\)) or multiple-neutron (\(P_{xn}\)) emission, becomes energetically allowed in such systems [235]. Proposals to employ the combined S+IMS with telescope detectors to measure \(P_{n}\) values have been prepared for the ESR [236, 237].

On the neutron-deficient side of the nuclidic chart, the production of nuclides beyond the proton drip-line is feasible. Taken the speed of the S+IMS, investigations of direct proton and/or \(\beta \)-delayed proton emission may become possible [238].

Although proposed more than 10 years ago, measurements of possible modifications of \(\alpha \)-decay rates in HCIs are still pending. Small changes of the rates are expected because of the reduction of the Coulomb barrier due to the missing screening effect of the electrons [239,240,241,242].

Regarding EC decays, the presently available measurement of the decay of H-like \(^{122}\)I [204] is yet insufficient to firmly confirm the theoretical explanation of the decay rates in H-like and He-like \(^{140}\)Pr and \(^{142}\)Pm. An ideal test candidate would be \(^{111}\)Sn [243], decaying by allowed Gamow-Teller transition \(7/2^+\rightarrow 9/2^+\) to the ground state of \(^{111}\)In, see Fig. 7. If the assumption of the disabled repopulation of hyperfine states in the storage ring is correct [244], the ground hyperfine state in H-like \(^{111}\)Sn has the total angular momentum \(F=3\). However, such F state is not available in the daughter ion and thus the allowed \(\Delta I = +1\) EC decay is not possible. We note that the magnetic moments of both nuclei are positive [170]. In the case of \(^{64}\)Cu it is negative [170] and thus the ordering of hyperfine states is inverted, which leads to the disabled \(\Delta I = -1\) decays [245]. If experimentally confirmed, it will be possible to use different combinations of states in parent and daughter nuclei to address, e.g. weak decay branches or forbidden decays, etc.

A special case is \(^{7}\)Be, which was briefly discussed in Sect. 1. The EC decay of the \(3/2^-\) ground state to the \(1/2^-\) first excited state in \(^7\)Li depends on the population of hyperfine states in \(^{7}\)Be [246]. The tiny hyperfine splitting might be used to probe the re-population probability in the storage ring.

EC decays of Li-like systems shall show similar dependence on the total angular momenta as the H-like ions. Predictions of such decays have been made and await experimental confirmation [248].

Search for long-lived rare isomers will continue. The immediate goal here is to study \(^{188}\)Hf where an exotic K-isomer with an exceptionally long lifetime with respect to photon decay is predicted to exist [215].

The fast S+IMS enabled half-life measurements in the millisecond range. Further measurements of known as well as yet unknown \(0^+\rightarrow 0^+\) decays are proposed at the ESR [249]. Furthermore, an exotic bound electron-positron pair decay will be addressed [250]. This decay mode is energetically open in \(^{194}\)Pb where the excitation energy of the first excited \(0^+\) state [170] combined with the binding energy of the K-orbital [251] gives about 10  keV excess energy, which is carried away by monochromatic positrons.

Further exotic decay modes are the time-reverse of IC, termed Nuclear Excitation by (free) Electron Capture (NE(free)EC), and of BIC, termed Nuclear Excitation by Electron Transition (NEET). A large deviation was observed between the NEEC measured through depletion of the isomer in \(^{93}\)Mo [252] and theoretical predictions [253]. It turns out that it is crucial whether electrons are considered to be free or bound in a target atoms [254, 255]. Several prepared proposals suggest various approaches to measure both NE(target)EC and NE(free)EC at the ESR and/or CRYRING@ESR [68, 256, 257].

Last but not least, the isomeric state in \(^{229}\)Th is in the focus of numerous experimental and theoretical investigations [258,259,260]. It is predicted that transition rates in highly charged \(^{229}\)Th ions may change dramatically due to the nuclear hyperfine interaction [261]. The versatile instrumentation, facilities (ESR, CRYRING@ESR, HITRAP), and variety of targets and probes offer promising prospects for studies on \(^{229}\)Th and other low-lying isomers [262,263,264].

7 Outlook

The presently running storage ring machines will continue research programs on half-life measurements of radioactive HCIs. However, there are several new storage ring projects launched worldwide.

At the future Facility for Antiproton and Ion Research (FAIR), which is in construction at the GSI site in Darmstadt [265], two new storage rings are planned. The first one, Collector Ring (CR), is a dedicated facility to be operated in isochronous mode [266]. It will profit from excellent design transmission from the new high-acceptance fragment separator Super-FRS [267]. Particle detectors for \(P_n\) determination, a double-ToF setup, and multiple Schottky detectors will be installed thus enabling \(B\rho \)-defined IMS, S+IMS as well as the combination of both. Since only one ion is needed to obtain its mass and lifetime, this will be the facility, where the basic properties of the most exotic nuclei will be measured. The second ring is the High-Energy Storage Ring (HESR) [268]. Accumulation and long storage times of stochastically cooled ion beams will be possible in the HESR [269]. Counting on high intensities of secondary beams from Super-FRS and CR, dedicated measurements of rare decay channels and long half-lives are aimed at [178].

Another future complex in construction is the High Intensity Heavy-ion Accelerator Facility in China [270]. A 15 Tm spectrometer ring SRing [271] will be built behind a synchrotron, connected by the fragment separator HFRS. The multi-purpose SRing will be equipped with electron, stochastic and laser cooling capabilities, various detector and spectrometer setups, and internal targets. A special care is devoted to high quality isochronous ion-optical mode [272]. Further in the future, it is planned to upgrade the facility by adding a 45 Tm superconducting MRing [273, 274], which will form a special configuration with the SRing for interaction of two co-propagating beams.

In addition to the projects in construction, there are a few ones in the discussion phase. The first one is the dedicated low-energy storage ting at ISOLDE at CERN [246]. Measurements of \(\beta \)-decays of HCIs is one of the proposed physics cases there. One of the key nuclei is the H-like \(^{7}\)Be, which decay probability was still not feasible to measure elsewhere. Other low-energy storage rings in discussion are the ones at LANL [275] and TRIUMF [276]. These rings will be coupled to free-neutron targets primarily for challenging neutron-induced reaction measurements [277, 278], though some yet unspecified decay measurements are not excluded. Last but not least, a multi-purpose storage ring project DERICA is being considered at JINR in Dubna [279]