Radioactive Decay of Highly Charged Ions

Most forms of nuclear decay involve only the bound protons and neutrons that constitute the atomic nucleus, and require little-to-no interactions with the electrons that typically surround them. However, some common modes of electroweak decay such as orbital electron capture (EC) and internal electron conversion (IC), proceed through an interaction between the nucleus and bound electrons within the constituent atom. Additionally, for radioactive decay modes that emit charged leptons ($\beta^+$/$\beta^-$ decay which emit positrons/electrons, respectively), interactions with the surrounding electron cloud of the atom can change the energy and shape of the observed particle-emission momentum distributions. As a result, these respective decay modes are not only influenced by the structure of the initial and final states in the nucleus, but can also depend strongly on the atomic charge state [1]. These effects, particularly for EC and IC, become increasingly more significant as the atom is ionized closer to electron shells with the largest spatial overlap with the nucleus ($K$ and $L$ shell). In general, very few experimental studies have been performed on the decay of highly charged ions (HCIs), largely due to significant technical obstacles of creating and storing radioactive nuclides at high atomic charge states.

From a fundamental physics standpoint, these measurements are motivated by:
1) Investigating nucleosynthesis under extreme astrophysical environments which are hot enough to partially or fully strip atoms of their bound electrons, and
2) Tests of the electroweak interaction under varying atomic conditions.

Due to the typically short decay half-lives of the radioactive nuclides of interest ($T_{1/2}\approx10^{-3}-10^{3}$~s), they must be produced, purified, and delivered to the respective experimental setups in a short amount of time. The Isotope Separator and Accelerator (ISAC) facility at TRIUMF in Vancouver, Canada, employs a high-intensity (up to 100 $\mu$A) beam of 500~MeV protons to produce radioactive ion beams (RIBs) using the isotope separation on-line (ISOL) technique. ISAC is currently able to provide a wide variety of RIBs via spallation and fission reactions through the use of several different production target and ion-source combinations. For the decay studies described in this article, the mass-selected continuous beam of radioactive singly charged ions (SCIs) is delivered at low energies to TRIUMF's Ion Trap for Atomic and Nuclear Science (TITAN). The EI group at CSM utilizes the unique capabilities of our decay-spectroscopy device with TITAN at TRIUMF. Our goal over the next several years is to investigate the effects of high charge states on various forms of electroweak decay.

Study of HCIs in Extreme Astrophysical Scenarios

The hindrance or full blocking of the EC decay mode can occur in several astrophysical environments that are hot enough to fully (or partially) ionize the radioactive atoms. Perhaps the most prominent case is that of $^{7}$Be in the core of the sun, where temperatures can exceed $1.5\times10^7$~K ($\sim1.3$~keV) which is hot enough to fully ionize beryllium. Since the $^{7}$Be decay is an integral step of the {\it pp-II} chain for hydrogen burning in the sun, the alteration of its half-life through ionization is a particularly relevant topic for determining how stars burn. Since the final state in EC decay has only two bodies (recoil nucleus and neutrino), the rate at which these nuclei decay is also particularly important for understanding the solar neutrino spectrum. The terrestrial half-life for $^{7}$Be is $T_{1/2}=53.3$~days. However, since the only mode of radioactive decay is through electron capture, a fully ionized $^{7}$Be$^{4+}$ can effectively become stable\footnote{In practice, the electron densities in the sun are high enough that $^{7}$Be$^{4+}$ can capture a free electron from the surrounding plasma and still undergo radioactive decay, as evidenced by the observation of the two lines in the solar neutrino spectrum at 861~keV and 384~keV.}. For higher-energy scenarios in the cosmos, such as the acceleration of material by supernovae (SN) explosions to relativistic energies ($>$200~MeV/$u$) of galactic cosmic-ray particles, even heavy atomic systems with large numbers of bound electrons can be fully ionized. Through this method, relatively short-lived isotopes such as $^{37}$Ar (t$_{1/2}$= 35~days) and $^{51}$Cr (t$_{1/2}$= 27.7~days) which are produced by cosmic-ray spallation reactions on the SN ejecta can become long-lived ($\approx10^6$~years) due to the suppression of their EC decay mode. As the lifetimes of these nuclides become increasingly longer, they can provide more complete information on distant astrophysical phenomena as they are detected by earth-bound satellites collecting cosmic-ray particle. If a weak decay branch exists in these cosmic isotopes besides the dominant EC-branch, the removal of all electrons leads to a long partial stellar half-life governed only by the decay of the weak branch. Prominent examples are $^{54}$Mn (EC, $\beta^+$/$\beta^-$), $^{56}$Ni (EC, $\beta^+$), and $^{59}$Ni (EC, $\beta^+$). Several measurements of these weak decay branches have been performed under terrestrial conditions, mainly via $\beta^\pm$- or $\gamma$-spectroscopy but very few (or none) have been performed under these proper astrophysical conditions. Under those conditions, the EC lifetimes do not become significantly affected until the atom is nearly fully stripped of its bound electrons. In fact, in most cases, orbital EC is only strongly influenced by the density of electrons in the $K$ and $L$ atomic shells. A simplified view can be described as follows:

• No orbital electrons (bare nucleus): the isotope is stable unless free electrons are captured or other decay modes are possible (see $^7$Be$^{4+}$ in the sun).
• One $s$-electron (H-like state): a single electron in the $K$ shell can be captured. Since only half of the $K$ shell is occupied, the decay half-life should be twice as long.
• Two orbital $s$-electrons (He-like state): both electrons are in the $K$ shell. The decay rate roughly corresponds to the terrestrial rate, but without contributions from $L$-shell capture (proportional to $n^{-3}$).

However, this picture is not universally true. It was shown in storage ring measurements at GSI Darmstadt that for H- and He-like $^{122}$I$^{52+,51+}$, $^{140}$Pr$^{58+,57+}$, and $^{142}$Pm$^{60+,59+}$ ions that these simple assumptions do not hold for HCIs. In all three cases, the He-like ions decay with the predicted half-life of $\frac{9}{8}$$\cdott_{1/2}(terr.), while the behaviour of the H-like ions is strongly dependent on the hyperfine structures of the initial and final nucleus. For ^{140}Pr^{58+} and ^{142}Pm^{60+}, the measured half-life became even shorter than the terrestrial half-life: \frac{9}{10}$$\cdot$t$_{1/2}$(terr.), and not twice as long as in the simplified picture. An explanation for the observed deviation in allowed transitions has been presented, and states that the conservation of total angular momentum in the nucleus-lepton system has to be taken into account. This is necessary since only certain spin orientations of the nucleus and of the captured electron can contribute to the allowed decay. The suppression or enhancement for a single-electron ion depends on the populated hyperfine state. In all three of the previously investigate cases, the dominant EC branch were $1^+\rightarrow0^+$ ground-state to ground-state transitions. As a result of these interesting results and their subsequent theoretical interpretation, continued experimental investigations into these systems are required to better understand the behaviour of HCIs in the cosmos. We are currently working to expand our program towards the goal of measuring the effects of high atomic charge states on the properties of electroweak decay, including internal conversion, electron capture, and electronic screening.

Selective Blocking of Radioactive Decay Modes to Expose Second Order Processes

To first order, excited nuclear states release energy via single $\gamma$ emission with possible IC and internal pair creation (IPC) in competition. Other modes of internal nuclear decay are rare and difficult to study as they involve the inclusion of higher-order processes in electroweak decay theory, and are thus significantly less likely. Particularly of note is the nuclear two-photon (2$\gamma$) decay, a second order electroweak process which has only been observed in a few cases. Due to the high level of competition in the decay modes, perhaps the best way to study this rare process is to avoid or suppress the other processes: one-photon emission, IPC and IC. To date, studies on two-photon decay have focused on cases in which the one-photon emission is forbidden or heavily suppressed. This typically occurs in cases where both the ground and first-excited states are $J^\pi=0^+$, since the $E0$ photon emission is forbidden. This is referred to as {\it non-competitive} 2$\gamma$ decay, and has only been observed in $^{16}$O~\cite{Kra87}, $^{40}$Ca~\cite{Sch84}, and $^{90}$Zr~\cite{Sch84,Muc89}. As with the EC-decay studies presented in the previous section, further case-selection criteria must also be applied before these measurements are possible. For instance, the only way to avoid IPC as a dominant mode of decay is to explore cases where it is energetically forbidden. However, even avoiding cases in which one-photon emission and IPC are present, decay from these excited $0^+$ states still occurs via IC with a much higher probability than 2$\gamma$ decay. A novel method to eliminate the highly competing $0^+\rightarrow0^+$ IC has therefore been devised to elucidate the rare $2\gamma$ process with no competition. The recently commissioned decay spectroscopy setup with the TITAN EBIT provides a unique environment for generating these conditions and observing such decays~\cite{Lea15}.