Cross Sections of the ³⁶Ar(d,α)^34mCl, ⁴⁰Ar(d,α)³⁸Cl and ⁴⁰Ar(d,p)⁴¹Ar Nuclear Reactions below 8.4 MeV

Abstract

We have measured the cross section for production of the medically interesting isotope ^34mCl, along with ³⁸Cl and ⁴¹Ar, using deuteron bombardments of ³⁶Ar and ⁴⁰Ar below 8.4 MeV. ALICE/ASH analytical codes were employed to determine the shape of nuclear excitation functions, and experiments were performed using the University of Wisconsin tandem electrostatic accelerator to irradiate thin targets of argon gas.

Introduction

Production of ^34mCl (ß⁺ = 55%, t_1/2 = 32.0m) by deuteron bombardment of ³⁶Ar gas was recently reported (Engle et al., 2011a). Thick target irradiations of ³⁶Ar gas and subsequent separation techniques yield sufficient ^34mCl for use in medical imaging experiments, and irradiations of ^natAr gas provide an inexpensive chemical surrogate, ³⁸Cl (ß^- = 100%, t_1/2 = 37.2m), for developmental work. The prevalence of chlorine compounds from anthropogenic and natural sources offers varied and fertile ground for scientific explanation with their radiolabeled counterparts, and many known compounds’ biological or toxicological effects result from chlorination in functional positions (Engle et al., 2011b).

The radioisotopes of chlorine have a production history dating to the 1960’s using a variety of incident particles and energies. Though a variety of chalcogen targets have been used to produce ^34mCl, only alpha irradiations of sulfur targets with natural isotopic abundance have been used routinely or produced radioisotope in sufficient quantity and chemical utility for positron emission tomography (PET) imaging (Takei et al., 2007). While reported thick target yields for sulfur irradiations exceed those we have measured for deuteron bombardments of argon, accelerator targetry using sulphur and its compounds is problematic due to the element’s poor thermal and electrical conductivity, low melting point, and tendency to sublime (Abrams et al., 1984; Nagatsu et al., 2008). Irradiations of argon gas, by contrast, offer the prospect of clean separation chemistry and facile ³⁶Ar recovery using cryotrapping techniques, which, at Wisconsin, average >99.5% over more than 40 cycles. Williams and Irvine (1963) studied the production of ³⁸Cl by (d,α) above 10.5 MeV, but data for radiochlorine production below 10 MeV, near energies typical of modern medical cyclotrons, are absent from available literature. Knowledge of the nuclear excitation function would permit targetry optimization with implications for subsequent radiochemical syntheses. Only ⁴¹Ar (β^- = 100%, t_1/2 = 109.6m) is produced as a radiocontaminant during irradiation of natural argon gas. Previously, Fitz et al. (1968), Kashy et al. (1961), and Carvallo et al. (1975) studied the angular distribution of secondary particles and the excitation states of produced ⁴¹Ar at 11.6 MeV, 7.5 MeV, and below the Coulomb barrier, respectively, but did not characterize the (d,p) excitation function.

Methods

The ³⁶Ar(d,α)^34mCl, ⁴⁰Ar(d,α)³⁸Cl and ⁴⁰Ar(d,p)⁴¹Ar nuclear reactions were analytically computed and measured. ALICE-ASH is an advanced and modified version of the original ALICE code used for the analytical computation of excitation functions, as well as energy and angular distribution of secondary particles in nuclear reactions induced by nucleons with energies below 300 MeV (Broeders et al., 2006). Computed results of the ALICE-ASH code runs compared favorably with well-described deuteron reactions (e.g. ⁶⁰Ni(d,n)⁶¹Cu) but poorly with well-described (d,α) reactions (e.g. ²⁰Ne(d,α)¹⁸F). The latter machine’s beam profile is especially suited to cross section measurements involving small targets of enriched isotopes.

Argon gas targets were made from 0.635 cm OD, 0.159 cm ID steel tubes, cross-drilled with 0.476 cm holes sealed by two epoxied 12.5 um aluminum foil windows (Goodfellow, UK). Tubes were approximately 10 cm in length to accommodate closure valves, fittings for filling the targets, and small-volume bourdon gauges for continuous monitoring of target gas pressure. Targets were filled in an evacuated (120 mbar) container after themselves being evacuated at 20.3°C to avoid stressing the foils with negative pressure. Fill pressures were measured using an Omegadyne (Ohio) PX309 pressure transducer. The transducer was calibrated from 1 to 7 bar between -15.5 and 79.4°C with manufacturer-supplied uncertainty of ± 7 mbar at atmospheric pressure. Initial bourdon gauge and transducer pressures were recorded and, with adjustments for ambient temperature, used to monitor the quantity of target gas irradiated in each run. Pressure in all targets showed no measurable change over an irradiation period spanning 8 months. Cryotrapping recovered target gas when filling targets with ³⁶Ar gas as described previously (Engle et al., 2011a).

The targets containing either ^natAr gas or ³⁶Ar gas (99.993%, Isoflex, San Francisco) were inserted into the beamline of the University of Wisconsin Physics Department’s tandem electrostatic accelerator. Tantalum slits collimated the deuteron beam to 1 mm² at 4 cm in front of the target, as shown in Figure 1 below. After passing through the gas and both foils, the beam entered a -200 V cylindrical suppressor tube 4 cm behind the target to eliminate electrons produced by beam interactions in the target and permit accurate integration of irradiation currents hitting the molybdenum beam stop. Straightforward Stopping and Range of Ions in Matter (SRIM/TRIM) simulations confirm that fewer than 0.1% of deuterons fail to reach the suppressor at 3.0 MeV incident energy and permit estimation of uncertainty in time-integrated beam currents; these results are shown, along with a target schematic, in Figure 1 below (Ziegler et al., 2008). SRIM calculations yield an energy loss in the target chamber of 120 keV for a 4 MeV incident deuteron.

Figure 1.

Irradiation geometry, showing A) x/y slits limiting beam to 1 mm², B) target containing argon gas, C) -200 V suppressor, D) beam stop, and the radial distribution of deuterons at the beam stop for various incident energies from TRIM calculations. Dimensions are approximate.

The targets were irradiated with 200 to 600 nA of 3 to 8 MeV deuterons for 10 to 30 min. Current and dome voltage were continuously monitored and logged by an in-house Labview code at 1 kHz. Logged variation (as RMS deviation of this signal) in dome voltage was weighted by beam current for calculation of excitation functions. Deuteron energy after the first aluminum foil was computed using range tables (Ziegler et al., 2008) and used to correct logged and averaged dome energy measurements (see Figure 2 below).

Figure 2.

Deuteron Energy Loss in 12.5 um aluminum foil as a function of incident energy.

Following irradiation, targets were assayed by γ-spectroscopy using a 66 cm³ high-purity germanium (HPGe) detector (Canberra model GC1519, FWHM @ 1333 keV = 4.6 keV). For irradiations of the natural argon target, regions of interest (ROIs) were drawn over the 2.167 and 1.642 MeV peaks of ³⁸Cl and the 1.293 MeV peak of ⁴¹Ar. For the separated ³⁶Ar target, the 2.128 and 1.176 MeV γ emissions of ^34mCl were used. No contaminant γ lines other than those from ²⁷Al(d,p)²⁸Al (β^- = 100%, t_1/2 = 2.25 min, 1.78 MeV γ) were observed when counting irradiated ³⁶Ar targets. Spectra with 20 sec length were collected for 50 min using an ASPEC multichannel analyzer (MCA) and the Maestro-32 γ spectroscopy software suite (Ortec, Oak Ridge, TN).

The number of ^34m/38Cl and ⁴¹Ar nuclei at the end of irradiation was determined from known mean lifetimes and the intercept of an exponential fit of photopeak sums as a function of time (see example in Figure 3 below). Counter dead time and photopeak contribution from pileup were determined with a 10.00 Hz pulser input to the HPGe amplifier located at 2.35 MeV, whose variance over each run permitted estimation of the error in reported dead time, rejecting out of these only spectra contaminated by ²⁸Al decay emissions. Individual photopeak backgrounds were estimated and subtracted using averaged ROIs immediately above and below the photopeak area.

Figure 3.

Example fit of decay- and pulser-corrected 20 sec peak sums for a single ^34mCl run.

During irradiation, the change in the number of beam-produced nuclei, dN, in a given time dt is given by

$$\mathit{dN}=\mathit{Rdt}-\lambda \mathit{Ndt},$$

where R is the rate at which the isotope is being produced and λ is the decay constant. R can further be defined by the expression

$$R=\sigma \mathit{ITK},$$

where σ is the cross section for the isotope’s production, I is the beam current, T is the target thickness, and k is a unit-driven constant. Proceeding with the indicated numerical integration over dt, using the logged record of beam current for I(t) gives a value which can be compared to the value of N from a characteristic peak in the collected gamma spectrum with σ as a fit parameter, allowing estimation of the uncertainty in the reported σ.

Results

The following Figures (4 - 6) and Tables (1 and 2) show measured and computed cross sections from ALICE-ASH results for the three nuclides of interest along with previously reported values, when available, at nearby energies for comparison. Computed curves suggested excitation functions whose peaks were energetically below the range of previously reported values (for ³⁸Cl) and near energies achievable on modern, low-energy cyclotrons and the University of Wisconsin’s tandem electrostatic accelerator. Only statistical errors are shown in plots. Uncertainties in scale factors with anticipated uniform effects (e.g. beam current integration, bias in target pressure and thickness measurements, HPGe detector efficiency, etc…) are not shown in the plots below.

Figure 4.

Measured cross section and statistical error for ⁴⁰Ar(d,α)³⁸Cl, including previous work. Eye guide is from ALICE-ASH data.

Figure 6.

Measured cross section and statistical error for ⁴⁰Ar(d,p)⁴¹Ar. Eye guide is from ALICE-ASH data.

Table 1.

Summary of reported excitation function values for production of ^34mCl.

Energy (MeV)	± (MeV)	36Ar(d,α)34mCl (mb)	± (mb)
2.96	0.05	14.7	0.4
3.14	0.06	13.7	0.2
3.80	0.06	18.7	0.4
4.31	0.07	22.0	0.3
4.83	0.07	28.6	0.4
5.40	0.08	29.2	0.3
5.69	0.08	32.0	0.3
5.91	0.08	36.8	0.3
6.49	0.09	38.4	0.5
6.73	0.09	38.0	0.5
7.37	0.11	34.0	0.3
7.57	0.10	35.1	0.3
7.90	0.10	34.4	0.3

Table 2.

Summary of reported excitation function values for production of ³⁸Cl and ⁴¹Ar.

Energy (MeV)	± (MeV)	40Ar(d,α)38Cl (mb)	± (mb)	40Ar(d,p)41Ar (mb)	± (mb)
3.20	0.06	8.4	0.2	203.6	5.0
3.82	0.06	13.2	0.2	193.4	4.8
4.07	0.06	14.5	0.2	232.4	4.4
4.62	0.07	19.4	0.2	252.0	3.2
4.94	0.07	22.3	0.2	242.3	4.5
5.49	0.08	25.8	0.2	239.4	3.7
5.99	0.08	28.0	0.3	258.3	4.5
6.58	0.10	28.6	0.3	219.2	4.0
6.96	0.09	29.6	0.6	221.2	10.9
7.74	0.11	24.9	0.4	174.1	10.4
7.86	0.12	25.1	0.4	196.0	7.3

Discussion

Several sources of statistical error contribute to the uncertainty in these data. Random error in measured values of target pressure (± 3 mbar) causes reported results to vary by <1%. HPGe γ-spectroscopy entails the introduction of statistical error from counting, pileup, dead time, and background subtraction. Poisson-distributed error in background- and deadtime-corrected photopeaks weights the (χ² minimization, single free parameter) fit of photopeak sums in 20 sec spectra used to determine activity at the end of irradiation, allowing estimation of error in the fit from known residuals. A typical correction from pulser and deadtime data altered photopeak counts in a single 20 sec spectra by 2 ± 1% (mean ± SD) prior to fitting. Positioning reproducibility during counting of ± 1 mm produces variability of ± 0.5% in detector efficiencies, a factor of 10 less than the uncertainty in the detector efficiency for ^34mCl’s principle gamma at 2.128 MeV.

Systematic scale factor errors are more difficult to estimate. Tests of beam integration electronics’ accuracy using known sources as input yield logged currents accurate to within ± 0.01%, well inside the precision of the logged signal and in agreement with independent, parallel electrometer measurements (Keithley, Ohio). The assumption of point-source-like geometry for counting ^34mCl and ³⁸Cl is justified by previous work suggesting unity sticking probability of radiochoride’s adherence to metallic surfaces inside accelerator targets (Engle et al., 2011a). HPGe detector efficiencies were computed using calibrated sources in an identical geometric position to further account for this error. However, this same assumption is much less valid for ⁴¹Ar, which can be expectedly to diffuse throughout the target and the dead volume of the bourdon gauge over time. Collimated assays of targets conducted 4-6 hours post-irradiation show only 16 ± 3% of produced ⁴¹Ar located in the aluminum-windowed thru-hole, with the balance of the inert product distributed in the Bourdon gauge. Reported error bars reflect the less than 5% mismatch, estimated geometrically, between point source and actual counting efficiency in the case of this source distribution of ⁴¹Ar. Beam heating of the argon gas effectively thins the target even at sub-microamp irradiation currents and artificially lowers calculated cross sections. Using standard equations for conduction and convection, this effect causes systematic underestimation of results by less than 6%. We estimate total error in the measurement to be less than 9% using the effects discussed above.

Measured data for ^34mCl and ³⁸Cl differ from the excitation functions returned by ALICE-ASH computations. Notably, the measured ³⁸Cl cross section appears to peak 2-3 MeV below computational results. Predicted decline in the ⁴¹Ar cross section at decreasing energies was not observed at the lowest incident energy achievable in this experiment, perhaps because of the difficulty of describing deuteron-induced multiple nucleon-pickup reactions using computational methods. Lower energies were attempted, but these attempts resulted in unstable dome voltages and deuteron currents. Measured data do appear to agree with extrapolated literature values for the cross section of ³⁸Cl, though the energy limitations of the University of Wisconsin tandem electrostatic accelerator prevent acquisition of overlapping data points near 10.5 MeV (Williams and Irivine, 1963).

Calculated thick target yields using the measured cross section are higher than previously measured production yields trapping ^34m/38Cl on foil liners in 60 ml targets (5.2 ± 0.3 vs 1.8 ± 0.2 mCi/uA for ^34mCl and 4.6 ± 0.3 vs 1.4 ± 0.2 mCi/uA for ³⁸Cl at the end of saturated bombardment) (Engle et al., 2011a). This strongly suggests the loss of radiochloride from trapping on exposed metal surfaces in production targets; losses might be recovered by rinsing these targets post-irradiation, offering the promise of a factor of two in yield for productions of ^34mCl for preclinical imaging studies.

Conclusions

The reported cross sections for ^34mCl and ³⁸Cl establish that low energy cyclotrons are well matched to the optimum energy for these isotopes’ production by deuteron irradiation. We have measured the cross section for the production of ^34mCl, ³⁸Cl, and ⁴¹Ar using deuteron bombardments of ³⁶Ar and ⁴⁰Ar below 8.4 MeV. These data reveal the possibility of increased production yields of the medically interesting isotope ^34mCl and describe the nuclear excitation functions of three isotopes of interest in a previously uncharacterized energy window.

Figure 5.

Measured cross section and statistical error for ³⁶Ar(d,α)^34mCl. Eye guide is from ALICE-ASH data.

Highlights.

• ➢ALICE-ASH computed cross sections for ³⁶Ar(d,α)^34mCl, ⁴⁰Ar(d,α)³⁸Cl, ⁴⁰Ar(d,p,)⁴¹Ar
• ➢Measured cross sections for ³⁶Ar(d,α)^34mCl, ⁴⁰Ar(d,α)³⁸Cl, ⁴⁰Ar(d,p,)⁴¹Ar
• ➢Deuteron irradiations < 9 MeV are optimal for ^34mCl production for PET