An alternative approach to populate and study the $^{229}$Th nuclear clock isomer

A new approach to observe the radiative decay of the $^{229}$Th nuclear isomer, and to determine its energy and radiative lifetime, is presented. Situated at a uniquely low excitation energy, this nuclear state might be a key ingredient for the development of a nuclear clock, a nuclear laser and the search for time variations of the fundamental constants. The isomer's $\gamma$ decay towards the ground state will be studied with a high-resolution VUV spectrometer after its production by the $\beta$ decay of $^{229}$Ac. The novel production method presents a number of advantages asserting its competitive nature with respect to the commonly used $^{233}$U $\alpha$-decay recoil source. In this paper, a feasibility analysis of this new concept, and an experimental investigation of its key ingredients, using a pure $^{229}$Ac ion beam produced at the ISOLDE radioactive beam facility, is reported.

A new approach to observe the radiative decay of the 229 Th nuclear isomer, and to determine its energy and radiative lifetime, is presented. Situated at a uniquely low excitation energy, this nuclear state might be a key ingredient for the development of a nuclear clock, a nuclear laser and the search for time variations of the fundamental constants. The isomer's γ decay towards the ground state will be studied with a high-resolution VUV spectrometer after its production by the β decay of 229 Ac. The novel production method presents a number of advantages asserting its competitive nature with respect to the commonly used 233 U α-decay recoil source. In this paper, a feasibility analysis of this new concept, and an experimental investigation of its key ingredients, using a pure 229 Ac ion beam produced at the ISOLDE radioactive beam facility, is reported.

I. INTRODUCTION
In 1976, experimental evidence was reported pointing to a low-lying nuclear state in the 229 Th isotope at an excitation energy, E iso , below 100 eV [1]. Subsequent experiments lowered the predicted excitation energy of this 229 Th isomer down to the eV range, which is unique on the nuclear chart [2][3][4][5][6][7][8][9][10]. This exeptionally low excitation energy of the isomer initiated numerous research projects aimed at unveiling its characteristics. In the last decade, breakthrough experiments offered a proof of its existence, studied the isomer's nuclear moments and provided confirmation of an excitation energy in the VUV part of the spectrum (E iso < 18.3 eV) [11][12][13][14]. The available experimental data on the isomer in 229 Th are summarized in fig. 1. The main feature of this isomer, its low excitation energy, promises a range of future applications which rely on the extension of laser manipulation techniques from the electron shell towards the nuclear domain, more specifically: a direct VUV laser excitation of a nuclear transition could be within reach for the first time. In addition to the creation of a nuclear clock, matching or even exceeding the performance of present day atomic clocks, this isomeric nuclear state could be decisive in the development of the first nuclear laser and more fundamentally; in the study of the time dependence * Matthias.Verlinde@kuleuven.be of fundamental constants of nature [15][16][17][18][19].
Working towards a laser excitation of a nuclear transition, fulfilling the isomer's potential, requires, however, improvement in the precision and accuracy of both excitation-energy and unknown radiative-lifetime observables. The present-day accepted value places the isomer's excitation energy at E iso = 7.8 (5) eV. This value was obtained through indirect high-resolution γ-spectroscopy data of inter-and intraband transitions in ground-and isomeric state collective bands [11]. The large experimental uncertainty of 0.5 eV (corresponding to ≈ 10 nm or ≈ 120 THz) in combination with an expected narrow nuclear resonance of 10 −4 Hz, presents a practical stumbling block for the direct excitation of this nuclear transition using coherent light sources. Moreover, recent studies shed doubt on the accuracy of the current excitation energy [20]. To improve both the accuracy and the precision of the isomer's key observables, a variety of physics techniques are implemented, with one branch focusing on a direct measurement of the electromagnetic deexcitation of 229m Th embedded in a host material.
To study and detect the VUV photons originating from the 229m Th-229 Th transition, the α decay of 233 U (T 1/2 = 1.6 · 10 5 years) is frequently used to populate the isomer [11,13,21,22]. With a probability of ≈ 2% per α decay, 233 U decays to 229m Th, whose 84 keV recoil energy arXiv:1904.10245v1 [nucl-ex] 23 Apr 2019 is thermalized in a gas or solid host after which its decay products can be scrutinized. Due to the unusually low excitation energy, the electromagnetic environment where the isomer is finally situated, determines its decay mode. In case the thorium electrons have a free quantum state available at an energy equal to E iso above its current state, satisfying conservation of energy, the isomer's dominant decay channel is internal conversion (IC). A half-life of T 1/2 = 7 ± 1 µs was reported for this decay channel when the isomer was deposited on the surface of a Multi-Channel Plate (MCP) detector [13]. In the other case, nuclear γ decay will persist, albeit with a much longer lifetime, α IC = T 1/2,γ T 1/2,IC ≈ 10 9 [23]. This rare feature allows a certain freedom in tuning the environment to select the favored decay mode. However, at the same time, it requires sufficient understanding of the 229m Th electromagnetic environment.
In this paper, a novel approach to observe the radiative decay and to measure the radiative energy and lifetime of 229m Th is described. It is based on an alternative production method, whereby the isomer is populated via the β decay of 229 Ac, produced online. VUV spectroscopy is then performed after implantation of 229 Ac in a large band gap crystal (E bandgap > E iso , to block the IC channel), where it decays to 229m Th. In the next section, a detailed comparison between the aforementioned production methods will be presented, in line with the goals of the proposed experiment. The feasibility of the proposed experiment will then be outlined in section III. Three preparatory experiments have been conducted and reported in sections IV-V-VI-VII together with some preliminary results. First, the ability to produce an intense beams of actinium ions was verified at ISOLDE, CERN, for the first time (see section IV). Second, as a key performance indicator of 229 Ac for producing the isomer, an attempt was made to measure the true total feeding probability, 229 Ac− 229m Th (see section V-VI). Finally, the lattice positions of the 229 Ac atoms, after implantation in a CaF 2 host, were studied (see section VII).

II. THE β DECAY OF 229 Ac
To produce 229m Th via radioactive decay, three methods exist: α decay from the 233 U (T 1/2 = 1.6 · 10 5 years) mother nucleus, electron capture decay from 229 Pa (T 1/2 = 1.5 days) and β decay from 229 Ac (T 1/2 = 62.7 min). The 233 U source has been used extensively as means to produce the isomer, also when aiming at a direct decay measurement of the low-energy photons. However, some aspects of this production method can be brought forward as possible reasons for the absence of conclusive results. The 233 U radioactive decay produces energetic α particles (≈ 4.8 MeV). The background signal that these particles induce through radioluminescence in the host structure, is a strong competitor for the iso-meric decay signal, which is, additionally, hampered by the small ≈ 2% branching ratio [24]. Next, absorbing the 84 keV recoil energy of the 229m Th particles in the host material will cause local pockets of lattice damage close to the unknown point of arrival. As the large bandgap of the host crystal is essential for the radiative decay of the isomer to happen, this structural damage and the unknown stopping point of the isomer after implantation could induce new levels in the band gap, restricting the ability of the host to suppress the IC channel.
As an alternative to 233 U, 229 Pa and 229 Ac exist. Both isotopes suffer from low production yields, although renewed interest can be found in 229 Pa. Only recently, an efficient way of producing 229 Ac, online, was reported [25]. It enables to study 229m Th with intense beams of 229 Ac, for which the β decay presents a number of key advantages in comparison to the 233 U α decay. A summary of the decay characteristics of 229 Ac is given in fig. 1. The advantages can be listed as follows: • The online production in a UC x target via a laser ion source at ISOLDE, CERN, using a proven ionization scheme, will provide an intense and pure source of 229 Ac (section IV).
• From the point of the feeding probability, the literature branching ratio 229 Ac − 229m Th ≥ 14% anticipates an increase in the signal to background ratio by at least a factor of seven compared to 233 U (section V) [26].
• The β decay of 229 Ac provides an almost recoil free (E recoil ≈ 2 eV) 229m Th production, locking 229m Th in the place of implantation, establishing an unchanged band gap.
• The β particles, emerging after the 229 Ac decay, are likely to produce a significantly lower radioluminescence in comparison with the high stopping power α particles and the recoiling 229 Th nucleus, both emerging after 233 U decay.
• The 229 Ac half-life (T 1/2 = 62.7 min) opens a time window for annealing the host crystal after implantation, before radiation detection takes place (see section VII) [27].
The advantages of using 229 Ac β decay over 233 U α decay are explained in detail below. First, an indirect β-decay branching ratio of at least 14% towards the isomer in the 229 Th daughter has been experimentally determined [26]. This presents only a lower limit for the feeding probability towards the isomer, because, per β decay, a probability of 79% exists for the decay path to go towards the 229 Th isomer or ground state directly, indistinguishable in these data. The feeding probability should, therefore, lie in the region 14% < λ β,isomer < 93%. An experiment to determine this probability will be outlined in section V. Second, after the 229 Ac β decay, the 229 Th nuclei experience a maximum recoil energy of only 2.3 eV [28], which is around an order of magnitude smaller than the typical displacement energies in a crystal lattice . Therefore, it is expected that after implantation, both 229 Ac and its daughter 229 Th reside in the same position on the crystal lattice. This assumption drastically simplifies an accurate understanding of the electromagnetic environment of the isomer, as the 2.3 eV recoil energy does not induce any additional damage to the lattice. An experiment, aiming for an accurate determination of the isomer's position in the host's lattice, will be discussed in section VII. Third, when implanting 229 Ac in a crystal host, the emitted β particles will result in a lower radiatively-induced background. The β particle stopping power is around three orders of magnitude lower than that for α's and much lower than that of the recoiling nuclei. Finally, in case the aforementioned experiment shows an unfavorable lattice location of the isomeric nuclei, one where E bandgap > E iso is not fulfilled, the lifetime of the 229 Ac isotope allows for host annealing to be done after implantation. In this way, the probability of a favorable lattice site occupation can be increased [27]. In combination, these numbers present an increase of at least a factor seven of the signal-to-noise ratio in comparison to the conventional 233 U production method, potentially further enlarged by the unknown total feeding probability, as well as better control of the lattice occupation and a reduction of the radioluminescence background signal that will be quantified in the next section.  Figure 1. The known experimental data on the isomer, 229m Th, mentioned in section I, are shown alongside the most important parameters concerning the β decay of 229 Ac, mentioned in section II. The total feeding probabilities of the 229 Ac β − decay to both isomer and ground state are shown. The value for the radiative half-life of the isomer, T 1/2,radiative , is a theoretical prediction. The µexp and Qexp are the experimental magnetic-and quadrupole moments, respectively [14,20,23,26,29,30].

III. QUANTITATIVE ANALYSIS OF THE VUV SPECTROSCOPY CONCEPT
The proposed experiment to study 229m Th, produced online via 229 Ac, will consist of two main components. First of all, the 30 keV 229 Ac ion beam will be implanted in the bulk of a thin large-bandgap host crystal. The reduced thickness of the sample will minimize the background (see below), while, more importantly, the large band gap inhibits the IC decay channel of the isomer. Multiple options for the host crystal exist, such as CaF 2 , MgF 2 , Na 2 ThF 6 , LiCaAlF 6 , LiSrAlF 6 , YLIF 4 and more exotic, frozen noble gases [31,32]. For the purpose of this paper, CaF 2 is selected, presenting a band gap of 11.6-12.1 eV [33]. 229 Ac ions implanted in CaF 2 at 30 keV, have a projected range of 18.2 nm with a straggling of 3.5 nm.
Depending on the outcome of the implantation studies of 229 Ac in CaF 2 (see section VII), the implantation period of around two 229 Ac half-lives (≈ 2 hours), can be followed by in situ annealing procedures. In the second part of the experiment, the crystal will be moved to the spectrometer port, where the low energy photons of the 229m Th-229 Th transition will be studied by a VUV spectrometer (e.g. Resonance VM92). This device delivers a spectral resolution better than 1 nm with a 150 µm slit, standard grating of 1800 grooves/mm, f# number of 2.2 and a grating efficiency > 15% in combination with tailored entrance optics, cooled electronics and an MCPbased detection setup. A spectral resolution of 0.1 nm is within reach after decreasing the slit's dimensions, at the cost of efficiency. During detection, a second foil will be irradiated with the 229 Ac beam simultaneously to minimize duty cycle losses of the online beam time.
In order to quantify the expected signal strength at the 229m Th-229 Th photon energy, a detailed feasibility analysis can be done. Based on theoretical cross sections for 1.4 GeV protons impinging on a 238 UC x target at the ISOLDE facility of CERN, a 229 Ac ion beam intensity of 10 7 pps (see section IV) is estimated. In the aforementioned measuring cycle with a detection time of ±3 h, and an assumed 1 h radiative half-life of the isomer, approximately 3·10 5 VUV photons s −1 are to be expected from the isomeric decay, considering a conservative feeding of only 14% (this number represents an average over the 3 h of detection time). This number can be compared to the expected photon rates from 229m Th ions, produced by 233 U, recoiling from a thin foil (≈ 150 s −1 ), from a 1 cm 3 233 U-doped CaF 2 crystal (4·10 4 s −1 ) or using synchrotron radiation to excite 229 Th-doped crystals (10 6 s −1 ) [31]. The total VUV detection efficiency considers the geometrical efficiency of the entrance slit, the acceptance solid angle of the spectrometer, the efficiency of the grating and the quantum efficiency of the CCD camera setup, adding to a total efficiency of 0.003%. Taking this number into account, the isomer decay signal should correspond to a total of around 9 cps situated in the range 159(10) nm, see table I. The most significant background-signal contributions, detected in the MCP detector, are divided in three categories. First, the detection of primary radiation from the decay of 229 Ac and its daughters is minimized due to passive radiation shielding and the limited measuring time on each implantation foil. Second, the radioluminescence of the decay products of 229 Ac is to be considered. When fully stopped, the 5 MeV α particles emerging from the decay of 229 Th release a total of around 10 4 photons. By limiting the CaF 2 layer to a thickness of 50 nm, the α particles will only lose around 10 keV leading to a total detection rate smaller than 10 -4 cps at the detector during the decay cycle, predominantly in the spectral region above 200 nm. A similar story holds for the signal due to radioluminescence from the β particles, which, in the region below 200 nm, is predominantly owing to Cerenkov radiation. Only losing about 10 eV in the 50 nm implantation foil, this specific background rate should be below 10 -4 cps at the detector site [22,34]. Finally, the ISOLDE facility provides the opportunity to run the experiment with other actinium isotopes. In combination with the possibility to check the obtained signal with the lasers of the ISOLDE ion source on/off (see section IV), these extra measures should deliver key advantages in characterizing the background signal in a reproducible way.

IV. THE PRODUCTION OF 229 Ac AT ISOLDE, CERN
To allow for a high intensity, pure 229 Ac source, the described experiments take place at the ISOLDE facility in CERN, Geneva [35]. In this radioactive ion beam facility, protons at an energy of 1.4 GeV, and an average current of 2 µA, produced by CERNs PS-Booster proton accelerator, irradiate a thick (≈100 g/cm 2 ) 238 UC x target heated to about 2000 • C. The nuclear reaction products which arise from these energetic collisions are extracted from a hot target, predominantly in a neutral atomic state, via diffusion and effusion into an ionization cavity. Subsequently, they are ionized, mainly via laser resonant ionization [36], increasing the total yield and beam purity significantly. After laser ionization, the ions are extracted and accelerated to 30 kV, mass separated and sent to different experiments. Recently, a number of efficient laser ionization schemes for actinium isotopes are developed [25,37]. The two laser schemes used to produce actinium ions for the experiments discussed in sections V and VII are shown in fig. 2. Ionization with either 424.69 nm or 456.15 nm revealed similar ionization efficiency, resulting in a laser-ionized 227 Ac production rate of about 4 · 10 7 pps as measured at a Faraday cup in the focal plane of the separator. Based on a calculated cross section for the 229 Ac isotope, 1.2 ·10 8 particles/µA are produced in a typical 238 UC x target (the yield could be increased by an order of magnitude when using a 232 Th target [38]). Within conservative estimates, the laser ion source at ISOLDE, aiming for the known Ac laser ionization scheme of fig. 2, should be capable of producing 229 Ac beams of around 10 7 pps, delivered in a spot of diameter 4 mm. Due to suboptimal ion transport conditions, caused by technical problems in the ISOLDE separator, a production rate of about 10 6 particles s −1 was observed at the branching ratio setup (discussed in section V), for the specific isotope 229 Ac. Through the combination of the known Ac ionization scheme and the ISOLDE facility, it is possible to produce isotopicallypure, high-intensity beams of 229 Ac via laser resonant ionization techniques in an online facility, opening the door for the exploitation of the 229 Ac isotope as a viable source of the isomer in 229 Th.  The two laser-ionization schemes used for the first production of laser-ionized actinium ions at the RILIS laser ion source of ISOLDE, CERN [25,37]. The ionization efficiency for both auto-ionizing levels is similar.

V. BRANCHING RATIO MEASUREMENT
One key feature of the new approach to study the 229 Th isomer is its expected strong feeding in the decay of 229 Ac. To measure the unknown total branching ratio towards the isomer, a dedicated setup detecting the isomeric decay via its low-energy IC electrons in timedelayed coincidence with the β decay of the actinium mother nucleus has been developed, see fig. 3. Differentiating the low-energy internal conversion electrons stemming from the decay of the isomer from other low-energy electrons (e.g. β and γ radiation-induced secondary electrons and conversion electrons from higher lying states in 229 Th) is based on the time-dependence of the signal. Where the former shows an exponential decay with a half-life of 7 µs, the latter is of prompt nature within a time window of 500 ns. The experimentally determined half-life of 7 µs, however, is expected to be dependent on the chemical environment of the isomer, which will be different for the present experiment. The setup in fig. 3 consists of two components. First, the 229 Ac 1+ radioactive ion beam will be implanted in a suitable host material. This host is chosen such that after β-decay the chemical environment around the thorium dopant favors the IC decay channel of the isomer over the radiative one in order to take advantage of the shorter lifetime (α IC ≈ 10 9 ) of this channel and the efficient detection of low-energy electrons [23]. Internal conversion will take place if the electromagnetic environment allows the excitation of surrounding electrons with the isomeric energy E iso . This condition is easily fulfilled in metallic hosts, where a continuous distribution of electronic quantum states, referred to as Density of States (DOS), without any intermittent bandgap is available. Finally, the setup consists of a rotatable target holder with a thin metallic foil (25 µm) as implantation host material, which can be lifted, turned and positioned from the low-energy implantation site to a detection site where the time-delayed coincidences will be performed (see central part of fig. 3).
In order for the low-energy IC electrons to escape from the host material, the actinium dopant must be implanted close to the metal/host surface. To accomplish this, the highly energetic actinium ions, which are delivered to the implantation section of the setup, first encounter a deceleration electrode of parabolic shape which can decelerate the radioactive ion beam to a few hundreds of eV and focus it on the target to obtain a shallow implantation profile (see left and right fig. 3). The design has been optimized for an efficient deposition of actinium within a spot of 20 mm diameter on the target, using the SIMION electrostatic solver and ion trajectory simulator [39]. A typical beam with 30π mm mrad emittance and a Gaussian spatial distribution of 7 mm full-width-at-half-maximum at 30 keV energy passes a diaphragm with 20 mm inner diameter at the entrance to the setup. The voltage of the deceleration electrode (typically 1-3 kV below the target voltage) is tuned to obtain optimal focusing of the decelerated beam on the target. The simulation shows that with this conservative estimate of typical beam parameters at ISOLDE and a correctly aligned beam, efficiencies of 95% or higher at implantation energies of 100 eV are obtained. The magnitude of the deceleration electrode's dimensions and the large target size make the design less sensitive to deviations of the incoming actinium ion beam with respect to the central axis. Higher implantation energies decrease this sensitivity even further but reduce at the same time the detection efficiency of low-energy conversion electrons stemming from the isomeric decay as outlined in the next section.
After an implantation period of approximately one halflife, the target is rotated towards the detection section. β radiation emitted in the decay of 229 Ac is registered by a passivated implanted planar silicon detector (PIPS, Mirion 30X30500eb). γ radiation can be detected using a 70% relative efficiency high-purity germanium detector (Canberra HPGe 88045). IC electrons leaving the bulk of the target are accelerated by a 4 kV electrode and guided towards a channeltron detector (Sjuts KBL10RS). The germanium, silicon and channeltron detector signals are recorded on an event-by-event basis together with an absolute time stamp and the signals of time-to-amplitude converters. This time information will be used to discriminate between signals in the channeltron from secondary electrons produced by β-and γ radiation and direct β radiation. Secondary electrons created by β-and γ radiation are expected to produce a prompt timing signal in the electron detector, while the conversion electrons from isomeric decay will be detected as time-delayed coincidences, characterized by the µs lifetime of the isomer, with the direct β particles. Time-delayed coincidences between the low-energy electron-, β-and γ-signals allow to determine the direct and indirect isomeric state feeding, respectively. The conversion electron detector is designed to accept, at high efficiency, electrons that emerge from the target with a 2π solid angle distribution with a maximum energy of 8 eV. Because real IC electrons will show a lower maximum kinetic energy due to the work function of the metal, they will be more swiftly accelerated towards the channeltron upon leaving the target host and, thus, detected with an optimal efficiency. The design has been verified and optimized using electron trajectory simulations. IC electrons emerging from the target within a round spot of radius 10 mm are detected with a > 99% efficiency, allowing for a large implantation spot size on the target. The high-purity germanium detector has an estimated detection efficiency of 0.8% at an energy of 569 keV, while the PIPS detector accepts betas with a 40% geometrical efficiency. The total efficiency for detecting the low-energy electrons from the IC process are discussed in the next section.
The setup has been used in a test experiment at ISOLDE and the functionality of the newly developed components was verified. Two different targets, consisting of a thin niobium and gold layer grown on a Mylar film, have been used for implantation at 30, 5 and 2 keV. The choice of the host material and the implantation energies is motivated in the next section. Time spectra, created by gating on known γ-ray energies, feeding directly or indirectly the isomer, and on the low-energy electron detector signal, were investigated. Using the known 229 Ac decay scheme and the 6% total low-electron detection efficiency for 2 keV implantation in Nb (see next section), it can be concluded, with a 95% confidence level, that no 7 µs γ-electron decay signal was observed. Possible scenarios to explain this might be a different (shorter) half-life for internal conversion of the isomer, embedded in a metallic host material, or a different β-decay feeding pattern of the isomer as compared to literature.

VI. INTERNAL CONVERSION IN A METAL
In order to estimate the escape probability for the lowenergy IC electrons of interest, internal conversion is modeled in the bulk material, neglecting the surface effects of the first few monolayers. First, the energy of the isomeric decay E iso is transferred from the nucleus to an electron in an occupied bound state of the valence band if a suitable unoccupied electronic state is available. Next, this electron travels towards the surface of the bulk material while losing energy in scattering processes. Finally, upon arriving at the surface, the electron is released if it overcomes the surface potential barrier. Below, these three processes are treated independently.
In the present model, the converted electrons are characterized by their energy, E, expressed relative to the Fermi energy of the metal E F = 0. The occupied levels are, thus, characterized by E < 0. The energy distribution of valence-band quantum states is given by the local density of states at the dopant's location and is calculated using density functional theory (DFT) [40,41]. A projection on hydrogen s-wave functions selects the components with zero angular momentum, whereas higher angular momenta are neglected as their relative spatial overlap with the nucleus compared to s-states is negligible and, therefore, less significant in the internal conversion decay process. At 0 K, quantum states are occupied by electrons up to the Fermi energy level E F , higher energetic states remain unoccupied. Electrons, excited by the internal conversion process, move from an initially occupied state at energy E to an unoccupied final state at an energy E f = E + E iso . The expected effect of the internal conversion decay on the distribution of electron energies, obtained from DFT calculations, is shown for gold and niobium in fig. 4 (a). After excitation via internal con-version decay of the nucleus, a conversion electron travels from its initial position at depth h in the bulk material towards the surface and scatters elastically and inelastically. Inelastic scattering is characterized by the inelastic mean free path λ IMFP , which is a function of energy and can be approximated as universal for elementary metals [42]. The starting position is defined by the implantation energy. 229 Ac ions are implanted into the host at low energies of a few hundreds to a few thousands eV. At 100 eV implantation energy the mean implantation depth is around 1 nm for niobium with a lattice constant of 0.330 nm [43]. Typical implantation profiles were obtained with the binary collision approximation using the SRIM software package and are shown in fig. 4 (b) [44]. The probability of conversion electrons emitted isotropically at depth h with energy E, with respect to the Fermi level, to reach the surface is given by: with θ equal to the polar angle. This probability is shown in fig. 4 (c) for elementary metals. At the surface the electrons have to overcome the surface potential characterized by the metals work function, E WF . Electrons stemming from electronic states close to the Fermi energy gain enough energy during internal conversion, while electrons from the lower part of the DOS distribution remain bound in the bulk material. Only electrons with an energy E + E iso ≥ E WF can leave the bulk. The escape probability thus becomes: Consequently, a high efficiency is obtained for host materials with a low work function and a high density of states in the region between -E iso +E W F and the Fermi level of the DOS, as shown by the dark shaded regions in fig. 4 (a). Electrons stemming from the lower energy region of the energy distribution (light shaded in the figure) remain bound and are not detected. Low-energy implantation deposits actinium ions close to the surface, such that electrons can reach the boundary without being scattered but deep enough that distortions by the surface are avoided.
DFT calculations were used to search for a host material with a DOS that maximizes the number of available electrons capable of reaching the surface. From these simulations, η escape was computed as shown in table II, after implantation at 100 eV energy. The choice of a suitable host material for the branching ratio experiment not only depends on the electronic structure, but also on the contamination of the material at the surface and in 0cm 2cm 3cm 1cm z x 1 2 3 5 6 7 8 4 Figure 3. A schematic view of the setup for the measurement of the branching ratio with diaphragm (1), deceleration electrode (2) and target in implantation position (3), the HPGe detector (4), β detector (5), target in detection position (6), acceleration electrode for the low-energy electrons (7) and channeltron detector (8). The beam envelope (depicted in red) and the expected distributions at the diaphragm and the target (inset on the left and right, respectively) for typical beam characteristics are shown. The blue envelope corresponds to the escaping conversion electrons leaving the target foil for detection in the channeltron.
the bulk. The presence of contaminants in the bulk can change the electron kinetic energy distribution significantly, while an oxide layer at the surface additionally alters the work function. This oxide layer has to be thin enough, such that electrons can pass through it without experiencing losses and such that the workfunction is not significantly altered. A sample material with high purity should be chosen in order to be able to neglect their influence. Gold, as an inert element, is not exhibiting an oxide layer and is, additionally, available with high purity. However, at 100 eV implantation energy, its escape probability is limited to 4%. Based on these efficiencies and as a trade-off between a favorable electronic structure, a low expected oxidation rate and the availability of pure sample material, niobium has been chosen as additional target material. The expected escape efficiencies at different implantation energies for gold and niobium are shown in fig. 4

VII. CRYSTAL CHARACTERISATION
To detect the radiative decay of the 229m Th isomer in the VUV spectroscopy experiment proposed in section III, it is essential to inhibit the IC decay channel. As mentioned above, this can be achieved by using large band gap crystals as a host for the 229 Th isomer. Due to the band gap being larger than the isomer energy, there are no available electronic states for internal conversion and the crystal, without dopants or colour centers, is transparent to the emitted VUV photon (or incoming VUV photons) upon decay to the 229 Th ground state. However, depending on the local atomic configuration (e.g. occupied lattice site and charge compensation mechanism) of the thorium impurities in the host crystal, states can be introduced inside the band gap energy region. If these gap states reduce the size of the band gap below the isomer energy, the IC decay channel is no longer suppressed and will dominate over the radiative channel. In addition, a hyperfine structure originating from a non-vanishing electric field gradient at the Th site causes a homogeneous shift in transition energy of the order of 10 -5 eV [45]. Since this shift also depends on the local configuration it is necessary for all thorium atoms to be in the same lattice location and configuration for a final VUV spectroscopy experiment aiming at a highest accuracy.
The concept to suppress the IC decay channel with a large band gap material is illustrated for CaF 2 , a wellstudied material and a suited host crystal with a direct band gap of 12.1 eV [46]. Theoretical calculations predict a lowest-energy configuration of Th atoms in a CaF 2 crystal, whereby the Th 4+ ions occupy Ca 2+ substitutional sites with a charge compensation mechanism of two neighboring F − interstitials [33]. Whereas this local configuration is not expected to reduce the band gap  The Light shaded areas represent electrons that are energetically not allowed to leave the bulk while the dark shaded areas represent electrons that -if not scattered -will cross the surface. The work functions for gold and niobium are 5.5 and 4.9 eV, repectively. (b) depicts the implantation depth distribution in niobium for different implantation energies, calculated via SRIM software. (c) shows the probability of an electron to reach the bulk surface as a function of its implantation depth and its energy with respect to the Fermi surface. The estimated escape probability given by eq. (2) as a function of implantation energy is given in (d) for niobium and gold hosts. For details see text.
significantly, allowing for high-resolution spectroscopy, there is no experimental insight in the occupancy fraction of this configuration, depending on the production method of the 229m Th ensemble. A low occupancy fraction could present a severe loss in signal during VUV spectroscopy. In the context of the spectroscopy approach proposed in this work, it is crucial to identify and quantify eventual non-substitutional 229 Th incorporation resulting from the implantation of a 229 Ac parent isotope (e.g. in interstitial or disordered sites). The emission channeling technique is particularly suitable for such studies [47]. After the implantation of a suitable radioactive isotope, the particles emitted upon decay (β − , β + or α) interact with the screened periodic Coulomb potential of the crystal lattice. The atomic rows and planes of the crystal determine an anisotropic scattering of the emitted particles, resulting in emission patterns that are very sensitive to the exact position of the radioactively decaying nucleus within the lattice. A sensitivity of ≈ 0.1Å can be reached for the position of the radioactive species [48]. Since the substitutional thorium configuration is the lowest-energy configuration it might be possible to increase its default occupancy fraction by annealing. A position-sensitive detector measures the 2D electron emission patterns around selected crystal axes. Fitting these experimental data with linear combinations of patterns simulated for various possible lattice sites allows to quantitatively and unambiguously determine the Besides 229 Ac, other isotopes can be used as substitute. Different isotopes of the same element are chemically identical. Hence, the local atomic configuration of thorium and actinium atoms in a crystal should not depend on the implanted isotope itself. In the future, it could be possible for the laser ion source at ISOLDE to also produce a 231 Ac (T 1/2 = 7.5 min) beam with yields of 10 6 pps. 231 Ac is an exceptionally well-suited parent isotope for emission channeling experiments because it decays (β − ) to 231 Th (T 1/2 = 25.5 h), which, unlike 229 Th, also decays via β − . The significant difference in lifetime allows the study of the lattice incorporation of the 231 Ac parent (online) and, afterwards, of the 231 Th daughter (offline) [50]. These two successive β − decays after the implantation of 231 Ac is an ideal proxy for what occurs with the 229 Ac/ 229 Th decay in the VUV spectroscopy experiment proposed here, since the positions of both 231 Ac and 231 Th can be studied in the same experiment, separately.

VIII. SUMMARY
To allow for the development of the 229m Th's potential applications, two key observables remain unknown: its radiative lifetime and excitation energy. The way the isomer is produced has a distinct influence on the results, when attempting to determine these observables through the detection of the radiative 229m Th-229 Th transition.
To this end, a concept to use 229 Ac's β decay as an alternative production method of the 229m Th isomer is presented. The photons of the 229m Th-229 Th transition will be identified and scrutinized through a high-resolution spectrometer after feeding of the isomer with the decay of implanted 229 Ac ions in a large-bandgap host. Production of 229m Th via 229 Ac reveals a number of benefits over the commonly used α decay of 233 U. These advantages include the availability of an isotopically pure, intense source of 229 Ac from the ISOLDE facility, an expected larger β branching ratio towards 229m Th, a more manageable decay half-life, a lower radioluminescence background for VUV spectrometery compared to other concepts and a controlled background characterization. Preparatory experiments, testing key ingredients of this concept, were conducted at ISOLDE. These experiments have confirmed, first, the availability of a high intensity, pure 229 Ac ion beam. Next, in an attempt to determine the β-decay branching ratio towards the isomer, no signal with its anticipated 7 µs half-life was observed and further analysis should provide more insight. Finally, emission channeling patterns were obtained for 229 Ac ions, implanted at 30 keV energy in a CaF 2 crystal, indicating a significant calcium substitutional positioning in the CaF 2 host.