Various charged thorium ions such as singly charged, doubly charged, and triply charged thorium ions trapped in the ion trap can be used to excite the Th-229 first nuclear excited state via the electronic bridge process. We present an integration of a linear ion trap with a time-of-flight mass spectrometer to investigate trapped Th-232 ions. Various charged thorium ions are produced by laser ablation and dynamically loaded into the ion trap. After sufficient collisional cooling, thorium ions are extracted along one of the radial directions for time-of-flight mass spectrometry by rapidly quenching the trapping potential and applying high-voltage extracting pulses. The charge states of thorium ions are identified and the maximum mass resolutions of thorium ions reach ∼100 with initial 300 K collisional cooling. The velocity distributions of ablated various charged thorium ions are measured, and the results agree well with Monte Carlo simulation. Lifetimes of thorium ions are determined to be a few tens of seconds in the ion trap, which are helpful for further spectroscopic studies of Th-229 nuclear transition.

The typical energies of all known nuclear isomeric states range from keV to MeV, except that the energy of the Th-229 first nuclear excited state is unique due to its lowest energy.1,2 The recently measured energy is determined to be about 8 eV,2–7  and the radiative lifetime is about 104 s.8,9 These properties make the Th-229 first nuclear excited state the only candidate to develop a nuclear optical clock,7,10–12 which can be a unique tool for tests of fundamental physics.13,14 Since the latest energy is 8.338(24) eV,7 it requires more precise energy measurements for further nuclear optical clock development. Various charged thorium ions such as singly charged, doubly charged, and triply charged thorium ions trapped in the ion trap can be used to excite the Th-229 nuclei via the electronic bridge process.15–23 Singly charged thorium ions have a high electronic level density around the Th-229 first nuclear excited state energy range, and they are also expected to find strong enhancement for nuclear excitation via an electronic bridge process.17,18 Doubly charged thorium ions are useful to determine the fundamental nuclear properties of the isomer through the laser spectroscopy of the hyperfine structure.19,20 Triply charged thorium ions can be directly laser cooled to develop the single-ion nuclear optical clock.21–24 

Compared to Th-229, the Th-232 isotope has the non-radioactive nature and shares the similar electron configuration but without a hyperfine structure. Therefore, Th-232 is often used as a convenient substitute material for the initial work of generation and trapping thorium ions.11 To produce and load various charged thorium ions into a linear ion trap, the technique of dynamic laser ablation loading has been developed in our previous work.25 With successfully loaded ions in an ion trap, molecular dynamics (MD) simulations and secular excitation are usually used to identify trapped ions.26,27 However, both methods have limited mass resolution and require the fluorescence of laser-cooled ions. Time-of-flight mass spectrometry with higher mass resolution is an alternative way to identify trapped ions without photoexcitation or fluorescence.28,29 When thorium ions are generally extracted along the trap rods for time-of-flight mass spectrometry, not only axial optical paths are limited, but also complex ion optics and timing sequences are required due to the divergence of the trapped ion clouds along the extraction axis.30,31 Meanwhile, ion extraction along one of the radial directions can take advantage of using trap rods themselves as repelling plates for time-of-flight mass spectrometry (TOF-MS),28,32 which simplifies the extraction process. Moreover, due to the reduced divergence of the trapped ion along the extraction axis, high mass resolutions have been achieved with ingeniously designed driving circuits.33–38 

In this paper, we present an integration of a linear ion trap with a time-of-flight mass spectrometer (LIT TOF-MS) to investigate trapped thorium ions. Various charged thorium ions are produced by laser ablation, and they are dynamically loaded into the ion trap. After sufficient collisional cooling, thorium ions are extracted along one of the radial directions for TOF-MS by rapidly quenching the trapping potential and applying high-voltage extracting pulses. The charge states of thorium ions are identified by TOF-MS. The numbers, velocity distributions, and lifetimes of various charged trapped thorium ions are also obtained.

The experimental setup is an integration of a linear ion trap with a time-of-flight mass spectrometer as shown in Fig. 1(a). The linear ion trap and the TOF-MS apparatus are housed in a stainless-steel vacuum chamber at a background pressure of 1 × 10−10 mbar. The linear ion trap and dynamic laser ablation loading have been described in detail in our previous work25 and are discussed only briefly here. The linear ion trap consists of four 80 mm long, 8 mm diameter cylindrical rods and two square endcaps. The radial distance from the trap center to the rods is r0 = 3.5 mm. The distance between two endcaps is 2z0 = 20 mm. The endcap near the target is also known as the entrance endcap. The ion trap is operated at RF potential with an angular frequency of Ω = 2π × 2.1 MHz and an amplitude of VRF,0p = 275 V.

FIG. 1.

Schematic of the experimental setup. (a) The integration of a linear ion trap with a time-of-flight mass spectrometer (LIT TOF-MS). (b) RF/HV switching circuit. It contains an active RF switch (in red box) and a pulsed high-voltage switch (in blue box). (c) Typical performance of the RF–HV switching circuit. The red curve and the blue curve represent the voltage of the upper repelling rod and the upper extracting rod, respectively.

FIG. 1.

Schematic of the experimental setup. (a) The integration of a linear ion trap with a time-of-flight mass spectrometer (LIT TOF-MS). (b) RF/HV switching circuit. It contains an active RF switch (in red box) and a pulsed high-voltage switch (in blue box). (c) Typical performance of the RF–HV switching circuit. The red curve and the blue curve represent the voltage of the upper repelling rod and the upper extracting rod, respectively.

Close modal

The thorium target for laser ablation is a piece of Th-232 plate. The metal powder of Th-232 is produced by the reaction of calcium and thorium oxide in an argon atmosphere at about 1000 °C and pressed into a piece of plate. It is placed ∼55 mm away from the entrance endcap along the trap axis. A diode-pumped pulsed laser at 1064 nm wavelength for ablation has 8 ns pulse duration and 450(30) μJ pulse energy. The laser is focused to an 80(10) μm spot size on the target at the incident angle of ∼30°. The ablated ions are dynamically loaded into the ion trap. A manual leak valve (Kurt Lesker, VZLVM267) is used to introduce helium buffer gas (99.9999% volume percent purity) into the vacuum chamber. The partial pressure of helium buffer gas is 5 × 10−6 mbar, and the ions are stored for at least 1 s for sufficient collisions to reduce the initial high kinetic energy.11,39 To calibrate ion numbers detected by the LIT TOF-MS system, laser-cooled trapped calcium ions (Ca+) are prepared to form an ordered structure, the so-called Coulomb crystal.40 A calcium target for laser ablation is located next to the thorium target. A 397 nm cooling laser and an 866 nm repumping laser propagate along the trap axis. Both lasers are set to the power of 1 mW and the beam waist of 1 mm. The 397 nm laser is red detuned by 20 MHz from the resonant frequency of the dipole transition 4s2S1/2 ↔ 4p2P1/2. The 866 nm laser is resonant on the transition of 4p2P1/2 ↔ 3d2D3/2. The location and number of laser-cooled Ca+ ions are determined through fluorescence images in the CMOS CCD camera (Andor iKon-M 934), which is collected by an immersion objective (Nikon, 5×) before the ions are extracted to the TOF-MS system.41,42

As also shown in Fig. 1(a), two trap rods farthest away from the CEM are used as repelling rods with higher positive potential (≈1000 V) and the other two are used as extracting rods with lower positive potential (≈800 V). The ion optics mounted in the drift tube contain a grounded plate, two Einzel lenses, and two pairs of ion deflection plates. The grounded plate with a 10 mm diameter centered circular hole is placed ∼20 mm from the trap center along the radial direction. Two Einzel lenses with 22 mm diameter and 20 mm length for focusing ion beam are placed ∼50 mm at 200 V positive potential and ∼190 mm at 450 V positive potential from the trap center. Since the TOF drift tube is kept at the ground and has a slightly larger diameter than the central cylindrical electrode of the Einzel lens, the TOF drift tube can act as the end electrodes for the Einzel lens. Two pairs of ion deflection plates are placed between two Einzel lenses. At the end of the drift tube, a channel electron multiplier (CEM, Adaptas 2120) used for ion signals detection is placed ∼340 mm from the trap center. A digital oscilloscope (Teledyne LeCroy WaveRunner 610Zi) is used to acquire and handle ion signals to produce TOF mass spectra.

Each RF/HV switching circuit contains an active RF switch and a pulsed high-voltage switch as shown in Fig. 1(b). The active RF switch is designed to rapidly quench trapping RF potential. Once the active RF switch is triggered, the half cycle of sine-wave current passes through the diode–MOSFET chains (IXYS DH20-18A and IXYS IXTH1N250) and the RF potential is effectively shorted and rapidly grounded. As shown in Fig. 1(c), the RF potential can be quenched within a quarter RF cycle (∼100 ns) without residual ringing. The pulsed high-voltage switch is designed to provide an extraction electric field for TOF-MS. The main function components are two MOSFETs (IXYS IXTH2N150) in push-pull configuration. Once the pulsed high-voltage switch is triggered, the high-voltage side MOSFET is closed and the low-voltage side MOSFET is open. High-voltage extracting pulses delivered to the trap rods rise smoothly without overshoot, and the 10%–90% rise time is measured to be ∼200 ns.

Having been described in detail in our previous work,25 once a single-pulse laser ablation takes place, the entrance endcap voltage decreases from 70 to 0 V within 1 μs. The loading time is the duration time that the voltage on the entrance endcap maintains at 0 V. By controlling the loading time of 10–50 μs, different velocity distributions of various charged thorium ions can be selectively loaded into the ion trap. The trapped thorium ions are collisional cooled by helium buffer gas within a storage time of at least 1 s before extraction for TOF-MS. The time origin of TOF-MS is triggered at a level of ≈400 V of the pulsed high voltage, which is slightly higher than the maximum amplitude of RF potential. The flight time of extracted ions is measured within the range of 0–15 μs.

In order to determine the ion species of each mass spectrum peak, a time-of-flight simulation with similar experimental parameters is used to calibrate TOF-MS by COMSOL. As shown in Fig. 2(a), the recorded experimental peaks located at 5.82, 7.87, 9.89, and 13.98 μs are determined to Ca+, Th3+, Th2+, and Th+ according to simulated flight time, respectively. The time difference between the experimental peaks and simulated flight time is less than 1% at all locations. The experimental flight time of each peak is mapped to its calculated m / q, shown in Fig. 2(b). The linear fitting indicates that the experimental flight time in the range of 5.8–14.0 μs is proportional to the m / q of ions. Therefore, the simulated flight time is precise enough to identify other ion species for subsequent investigation, such as ThO2+, ThO22+, ThO+, and ThO2+.

FIG. 2.

Calibration of TOF-MS. (a) The recorded experimental peaks (red curve) and the simulated flight time (green curve). (b) The linear fitting (red line) of the experimental flight times (black dots) against m / q, where m is relative atomic mass and q is the charge. (c) Typical TOF mass spectra of Ca+ ions. The fluorescence images and estimated numbers of Ca+ Coulomb crystals are shown on the right side of each TOF peak. The images of Ca+ Coulomb crystals with better image quality are shown in Ref. 25. (d) The peak area (black hollow blocks) and mass resolution (blue hollow blocks) of TOF-MS. The red line is a linear fit.

FIG. 2.

Calibration of TOF-MS. (a) The recorded experimental peaks (red curve) and the simulated flight time (green curve). (b) The linear fitting (red line) of the experimental flight times (black dots) against m / q, where m is relative atomic mass and q is the charge. (c) Typical TOF mass spectra of Ca+ ions. The fluorescence images and estimated numbers of Ca+ Coulomb crystals are shown on the right side of each TOF peak. The images of Ca+ Coulomb crystals with better image quality are shown in Ref. 25. (d) The peak area (black hollow blocks) and mass resolution (blue hollow blocks) of TOF-MS. The red line is a linear fit.

Close modal

Over 100 different sizes of Ca+ Coulomb crystals with high locational precision have been prepared and extracted to investigate the performance of the TOF-MS including the number of ions and mass resolution. The number of Ca+ ions is calculated by multiplying the ion density and the volume of the Coulomb crystals, which can be directly determined from fluorescence images. The uncertainty of ion number is within 5% and comes from the volume estimation of the Coulomb crystals. The Ca+ ion density is calculated as 2.5 × 1013 m−3 in our experiment by the pseudopotential approximation in the zero-temperature limit.41,42 The typical TOF mass spectra of the ion crystals containing from 5 to 14 000 Ca+ ions are shown in Fig. 2(c). The TOF peak area, which is the integration of ion signals over time, is used to represent the number of ions. As shown in Fig. 2(d), the peak area is proportional to the number of Ca+ ions in the range of 0–2000. The fitted slope is 2.67(5) × 10−3 V ns. Due to the similar CEM detection efficiency for Ca+ ions and various charged thorium ions, the number of thorium ions can be estimated with the fitted slope in this linear relationship range. When the number of Ca+ ions exceeds 2000, the peak area of the TOF signal increases slowly due to the limitation of the detection area of the CEM. The mass resolution is defined as R = t/(2Δt) = m/Δm, where Δt is the full width at half maximum (FWHM). As also shown in Fig. 2(d), the highest mass resolution Rmax ∼ 300 can be achieved when only a few ions are extracted. With the number of Ca+ ions increasing, the mass resolution constantly decreases and remains stable at ∼20 eventually. This mass resolution is still high enough to identify various charged thorium ions.

Various charged ablated thorium ions have different kinetic energies and arrive at the trap center with different flight times. The typical TOF mass spectra of thorium ions at the loading of 15 and 25 μs are shown in Fig. 3(a). With the increased loading time, the peaks of Th3+ and Th2+ ions gradually decrease, while the peaks of Th+ ions increase. The FWHM of Th3+, Th2+, and Th+ ions at the loading time of 15 μs is 64, 59, and 87 ns corresponding to the mass resolution of 61, 84, and 80, respectively. The bottom of Fig. 3(b) shows the experimental peak areas of various charged thorium ions at different loading times. The trapped Th3+, Th2+, and Th+ ions distribute at the loading time of 10–25, 10–30, and 15–55 μs. The maximum peak areas of Th3+, Th2+, and Th+ ions, which appear at the loading time of 15, 20, and 35 μs, are 0.56(6), 1.54(66), and 3.08(28) V ns corresponding to the estimated number of at least 210(23), 577(247), and 1154(107), respectively.

FIG. 3.

TOF mass spectra of various charged thorium ions. (a) Typical TOF mass spectra of various charged thorium ions at the loading time of 15 (red curve) and 25 μs (green curve). Each curve is averaged over 10 individual spectra. (b) Comparison of the peak areas of Th3+ (red bar), Th2+ (green bar), and Th+ (blue bar) ions at different loading times of the experiment (at the bottom) and simulation (at the top). (c) The velocity distributions of ablated Th3+ (red line), Th2+ (green line), and Th+ (blue line) ions corresponding to the optimal parameters of MBC distribution. (d) Mass resolutions of thorium ions mass spectrometry without laser-cooling (on the left side) and calcium and ytterbium ions mass spectrometry assisted with laser-cooling (on the right side). The solid and the hollow data points represent the mass resolutions of ions mass spectrometry without laser-cooling and assisted with laser-cooling, respectively. The numbers beside the data points represent the corresponding mass resolutions.

FIG. 3.

TOF mass spectra of various charged thorium ions. (a) Typical TOF mass spectra of various charged thorium ions at the loading time of 15 (red curve) and 25 μs (green curve). Each curve is averaged over 10 individual spectra. (b) Comparison of the peak areas of Th3+ (red bar), Th2+ (green bar), and Th+ (blue bar) ions at different loading times of the experiment (at the bottom) and simulation (at the top). (c) The velocity distributions of ablated Th3+ (red line), Th2+ (green line), and Th+ (blue line) ions corresponding to the optimal parameters of MBC distribution. (d) Mass resolutions of thorium ions mass spectrometry without laser-cooling (on the left side) and calcium and ytterbium ions mass spectrometry assisted with laser-cooling (on the right side). The solid and the hollow data points represent the mass resolutions of ions mass spectrometry without laser-cooling and assisted with laser-cooling, respectively. The numbers beside the data points represent the corresponding mass resolutions.

Close modal
In order to investigate the velocity distributions of ablated thorium ions at the late expansion stage, a 3D Monte Carlo simulation of the dynamic loading is performed using SIMION. The simulation suggests that the velocity distributions of ablated ions can be described by the shifted Maxwell–Boltzmann–Coulomb (MBC) distribution function,30 
F ( v ) = A ( m / 2 π k T ) 3 / 2 v 3 exp ( m ( v ( v k + v c ) ) 2 / 2 k T ) ,
(1)
where A is a normalization constant, kT is the ion distribution temperature, m and v are the ion mass and velocity, and vk and vc are the center-of-mass and Coulomb velocities. vk is estimated as v k = γ k T / m, where γ is 5/3 for metal monatomic samples.

As shown in Fig. 3(b), the velocity distributions of ablated various charged thorium ions from the Monte Carlo simulation also agree well with the experimental results. The corresponding optimal parameters of the MBC distribution function are presented in Table I, and the MBC velocity distributions of ablated various charged thorium ions are shown in Fig. 3(c). The singly charged Th+ ions have a wide and slow velocity distribution that is similar to the large velocity distribution of ablated Ca+ ions.25 More highly charged thorium ions are less produced and have higher velocity distribution.

TABLE I.

Summary of optimal parameters of MBC distribution function.

Th3+Th2+Th+
kT (eV) 0.44 1.21 1.21 
vk (mm/μs) 0.54 0.92 0.92 
vc (mm/μs) 4.46 2.78 0.48 
Th3+Th2+Th+
kT (eV) 0.44 1.21 1.21 
vk (mm/μs) 0.54 0.92 0.92 
vc (mm/μs) 4.46 2.78 0.48 

The mass resolutions of Th3+, Th2+, and Th+ ions in our current work are 61, 84, and 80, respectively. The left-hand side of Fig. 3(d) shows the mass resolutions of thorium ions mass spectrometry without laser-cooling including the results from Refs. 29 and 30 and our current work. Zimmermann et al. constructed a linear time-of-flight mass spectrometer to measure the ion yield and the distribution of the charge states.29 Due to the limitation of laser energy density, only mass resolutions of Th2+ and Th+ ions are obtained to be 13 and 10, respectively. Borisyuk et al. used the multi-sectional quadrupole linear Paul trap with an energy analyzer along the trap axis for the measurement of energy distributions with mass resolutions of Th3+, Th2+, and Th+ ions being 7, 21, and 34, respectively.30 Our maximum mass resolutions of thorium ions reach ∼100 with initial 300 K collisional cooling, which are improved about half orders of magnitude compared to the previous results. The right-hand side of Fig. 3(d) shows the mass resolutions of calcium and ytterbium ions mass spectrometry assisted with laser-cooling including the results from Refs. 28, 33, 36, and 37 and our current work. Our maximum mass resolution of laser-cooled Ca+ ions reaches ∼300, which is medium among the previous results assisted with laser-cooling, and would be further improved with more precise ion optics.

The total lifetime of the trapped ions consists of trapping lifetime, which is determined by the stability of the trapping and chemical lifetime, which is primarily due to reactive collisions with background gases. With an ionization energy as high as 24.6 eV, helium buffer gas has no charge exchange and chemical reactions with various charged thorium ions.43 Since the reaction rate coefficients of thorium ions with H2 and N2 are much lower than other residual gases, the dominating chemical reactants are H2O, O2, and CH4 in the background vacuum.43–47 To measure the total lifetime of thorium ions at a helium buffer gas pressure of 5 × 10−6 mbar, the TOF peak area of various charged thorium ions is measured against the storage time in the ion trap. Meanwhile, the TOF peak areas of products that consist of thorium oxide ions are measured. Thorium hydroxide or methylene ions cannot be distinguished from thorium oxide ions due to the limited mass resolution of TOF-MS. The changes in the relative proportion represent the time evolution of various charged thorium ions in the ion trap.

The fitted total lifetime of Th+ ions in the presence of helium buffer gas is 70(2) s shown in Fig. 4(a). Figure 4(b) shows the time evolution of Th+ → ThO+ (ThOH+) → ThO2+ (ThO2H+) within 100 s in the ion trap. Since the reaction rate of Th+ ions with CH4 is at least one order of magnitude lower than H2O and O2, thus this reaction is not considered.45,46 The relative proportion of Th+ ions decreases, and ThO+ (ThOH+) ions increase gradually with the extended storage time. ThO2+ (ThO2H+) ions begin to have a noticeable proportion after the storage time of 50 s. The fitted total lifetime of Th2+ ions in the presence of helium buffer gas is 38(2) s shown in Fig. 4(c). Figure 4(d) shows the time evolution of Th2+ → ThO2+ (ThOH2+ or ThCH22+) within 60 s in the ion trap. Since the reaction rate of Th2+ ions with CH4 is comparable with H2O and O2, this reaction is considered.43 The fitted total lifetime of Th3+ ions in the presence of helium buffer gas is 24(3) s shown in Fig. 4(e). Since Th3+ ions have very limited proportion and complicated chemical reactions in the ion trap, the relative proportion of Th3+ ions and product ions is not measured in the experiment. For more precise lifetime measurement and further fluorescence detection, Th3+ ions would be accumulated by multiple-pulse laser ablation11,25 and purified by adjusting the trap parameters.

FIG. 4.

The lifetime of thorium ions in the ion trap. The exponential decay curve y = A⋅exp(−t/t0) is used to fit the peak area of thorium ions, where t0 is the lifetime. Each data point is averaged at least 10 individual experiments. (a) The total lifetime of Th+ ions. (b) The time evolution of Th+ (black point) → ThO+ (ThOH+) (blue point) → ThO2+ (ThO2H+) (red point) within 100 s. (c) The total lifetime of Th2+ ions. (d) The time evolution of Th2+ (black point) → ThO2+ (ThOH2+ or ThCH22+) (blue point) within 60 s. (e) The total lifetime of Th3+ ions.

FIG. 4.

The lifetime of thorium ions in the ion trap. The exponential decay curve y = A⋅exp(−t/t0) is used to fit the peak area of thorium ions, where t0 is the lifetime. Each data point is averaged at least 10 individual experiments. (a) The total lifetime of Th+ ions. (b) The time evolution of Th+ (black point) → ThO+ (ThOH+) (blue point) → ThO2+ (ThO2H+) (red point) within 100 s. (c) The total lifetime of Th2+ ions. (d) The time evolution of Th2+ (black point) → ThO2+ (ThOH2+ or ThCH22+) (blue point) within 60 s. (e) The total lifetime of Th3+ ions.

Close modal

In conclusion, we have presented an integration of a linear ion trap with a time-of-flight mass spectrometer to investigate trapped Th-232 ions. Various charged thorium ions are produced by laser ablation and dynamically loaded into the ion trap. After sufficient collisional cooling, thorium ions are extracted along one of the radial directions for TOF-MS. To calibrate the TOF-MS, laser-cooled Ca+ ion crystals are prepared and extracted to help identify ion species, the number of ions, and mass resolution. The charge states of thorium ions are identified and the maximum mass resolutions of thorium ions reach ∼100 with initial 300 K collisional cooling, which are improved about half orders of magnitude compared to the previous results. The velocity distributions of ablated various charged thorium ions are measured, and the results agree well with Monte Carlo simulation. Based on a rough estimate of the vaporized volume of 10−11 cm3 of metal, for a single ablation laser pulse, about 1011 ions are produced and the estimated number of loaded thorium ions is 103–104, so an overall trap loading efficiency of order of magnitude 10−8–10−7 can be deduced.29 The lower efficiency of dynamic laser ablation loading is mainly due to the long distance between the target and the trap center. Tens of seconds lifetimes of Th-232 ions in the ion trap are obtained; therefore, the similar lifetimes are expected for the Th-229 ions with the similar electron configuration. Such lifetimes are expected to be sufficient to perform the electron bridge excitation on the laser-cooling Th3+ ions, which is estimated to take a few hundreds of microseconds.16 In the future, the chemical reactions between various charged thorium ions and reactive gases will be further investigated and larger trapping depths will be applied to further enhance the loading efficiency of various charged thorium ions, and on that basis, the laser spectroscopy of Th+, Th2+, and Th3+ ions will be measured to facilitate the electronic bridge excitation of Th-229 nuclei.16 

We thank Zhi Qin for the preparation of the Th-232 target and Huan-Yao Sun for expert technical support. This work was supported by the National Natural Science Foundation of China (NNSFC) (No. 12341401) and the National Key R&D Program of China (Grant No. 2021YFA1402103).

The authors have no conflicts to disclose.

Zi Li: Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Lin Li: Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Xia Hua: Resources (equal); Supervision (equal); Writing – review & editing (supporting). Xin Tong: Conceptualization (lead); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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